matematik by Vitaliy Kracav4ik

BTOPEHHSI MATEPIA.nY B'"IEHHSI nMCbMOBOro >KEHHSI TA AlnEHHSI E>KAX 1000

1. CKiJibKH acboro naJIHqoK?

2. Ilpoq11Taii q11cna: 728; 340; 304; 403; 444; 19; 900. CKiJibKH coTeHb y KomnoMy qHcni; ,n;ec.HTKiB; o,n;uHMIJ.h? .f!Ke ia ~HX 'C.J:HCeJI Hali6iJihIIIe; HaifMeHrne?

3. 1) Hai<pecJIH B aornHTi Ta Ky Ta6JIH~IO. CoTHi

,D;ec.HTKH

0 JJ;HHHI.\i

2) .fl.Ke qHCJIO II03HaqaTHMe I.\Hq>pa 8, .HKIU;O 11 38IIHC8TH: y nepmy KOJIOHKY Ta6JIHu;i crrpaBa (o,n;111111u.i); y ,n;pyry KOJIOHKY cnpaBa (,n;ec.HTKH); y TPCTIO KOJIOHKY crrpaBa (coTHi)? B11KOHaii ai~rroai,n;Hi ,n;il. 3) 3arrHIIIH B Ta6JIIU.~i qncJIO, y .flKOMy: 6 co路re111~, 9 ~e颅 C.HTKiB i 7 O~HHMIJ.b; 2 COTHi i1 5 ~eCHTKin; 2 COTHi ii 5 o,n;HHHIJ.b; 8--,n;ec.HTH:ia i 2 o,n;IIHH~i. IlpoqMTali KOm:He "CJMCJIO.

CKJia~II

J.i aarrnm11 Ta6n11u;10 MnomeHH.H

~111cJia

7+ 7+ 7+ 7+ 7+ 7+ 7+ 7+ 7

5. y CHO CKJia,D;R 3a,n;aqy 3a ,n;aHMMM Ta6n11u.i. 3anHIIIM 38Ill1T8HH.R 3a,n;aqi, iI p03B' .H3811HH Ta i.n;noBi,lJ;h. ll(oAeHHa BHTpaTa

KiJibKiCTh

Ychoro

~HlB

BMTpaTHJIII

7 5

42 H'.r '!

0.o;uaKoea

6. 48: 6

30 :

6. 4

63 -

9. 3 - 18: 2

27: 3

7. CKJia.n;H i po3B'.R:>«H 3aJJ;a"CJy 3a MaJIIOHKOM. 'or-----~ ..,r

.. .

· ~ ~-

' -! -

•

8. 3a 2 ro.n; po6oTH TpaKTOp BHTpaTHB a

naJihHOro. Ha cKiJihKH ro,n;11H po6oTH BHCTa'CJHTb iioMy 56 JI naJibHoro, .RK~o BttTpaTa naJJ.hHOro 3a ro,n;MHY o,n;HaKoBa? CKJia)J;M BI1.pa3 .D;JUI p03B'.H3yBaHH.R 38)J;fft.Ii Ta 06'CJHCJJH :Horo 3HaqeHHH, .HK~O a = 14.

9°. 54: 6 56:

63 -127: 9 (63 - 27) :

42: 7 - 6 21 - 21: 3

7·5 - 3·6 81: 9 - 49:

10. 1) Ilpo1.lHTaii l.IHCJia: 286; 805; 138. HKa IJ,Hc}1pa noBTOproeThC.H B KO:>KHOMY i3 ll;MX 1.lMCeJJ? mo BOHa 03H8'CJ8€ B KO)KHOMY 3 HHX? 2) ~o 03Haqae u.11c}>pa 0 y 3anHcy 'llHCeJI 40, 407, 900? 3) Ha3Bl1 5 l.IHCeJI, noqHHalO'lIH 3 500, npHJii"llyIOtIH no 1; no 10; no 100. 4

11. l)~oBe,n;M,~o1·3 = 3;0·4 = 0. 2) Ilo.HCHH, .HK 3H8HIIIJIU peayJibT8T ,n;iJI,eHHJI. 1·5 = 5 5:1 = 5 5:5 = 1

0·4 = 0 0: 4 = 0

12. CcI1opMyJI1oi1 npaB.HJia aa p1BHOCT.HMH, aan.11caHHMH y paMKax.

a· 1 = a

a·O = O

HaBe,n;H ,n;o KO:>KHoro a npaBHJI qncJioBi npnKJia,n;H. 13. 4·7·0

8 + 1·9 40 - 0: 5

(8 - 8) · 1

27: 3 : 9

42: (7 - 0)

7: 7. 7

30 : (5

+ 0)

14. 3 O,ZJ;HOro Kyrn;a CMOpO,ZJ;IIHM ai6paJIH 18 Kr Hri,n;, a 3 ,n;pyroro - 12 Kr. Yci srro,n;M poaKJiaJI11 B .HIU;HKH, no 6 Kr y KOmHui1:. CKiJihKH HIU;HKiB noTpi6Ho ,ZJ;JI.H ~horo? (PoaB' sr.mu aa,n;a qy ,n;BoMa cnoco6aMu.) 15. Q6qn:cJI11 aHaqeHH.H KomHoro B11paay ,n;BoMa cnoco6aMH. (2 + 7). 5 (18 + 24) : 6 24 : (3. 2)

16. BuKoHaiI ,n;i1 apyt.IHHM cnoco6oM.

2. 6. 3

81 : (3. 3)

+ 9) . 5

(54 + 36):6

17°. 3na1i,n;H 3J-IaqeHH.H BHpaaiB. IIepeBip Bi,n;noBi,n;i. (12 - 7) ·8 (3 + 9) . 7

(40 + 24): 64 40 + 24 : 4

2·8·4 9. 2. 3

80: (20·2) 80 : 20. 2

18°. Ilepruoro ,n;H.H Ha c}Jap6yBaHHSI JiaBOK y napKy BHTpaTHJIH 4 6aHKH c}1apq11, no 3 Kry KomHili, a ,n;pyroro - 5 Ta-

KHX caMHX 6aHoK. CKiJihKH KiJiorpaMiB c}>ap6H BUTpaTUJIH 38 ,n;Ba ,n;Hi? (PoaB 'SI.iKH 3a,n;a~1y ,n;BOMa crroco6aMM.)

19. 30·2 3·80

60: 3 60: 30

100: 2 100: 20

(20 + 80): 4 20 + 80: 4

80 - 20: 4 (80 - 20): 4

20. 3aKp:ui1 Bi,n;noBi,n;i, poaB' .H:>KH npHKJia,n;H ii nepeBip ce6e. 528 + 275

158 +202

705 - 328

853 - 187

803

360

377

666

21. 1) 061.IHCJIH 3Ha~1eHHH BHpa31B a a = 507, b = 328.

2) 437 - 340 + 185

+ b

a - b,

.HK~O

525 - (408 - 113)

22. 3 TphOX .n;i.JIHHOK ai6pa.JIH 450 Kr KanycTH. 3 nepmol ,n;i.JISIIIKM 3i6pa.JIH 127 Kr KanycTH, a 3 ,n;pyroi - Ha 65 Kr 6iJihrne. CKiJihKH KinorpaMiB KanycTH ai6paJIH a TpeThoi .n;iJISIIIKH?

23. 3anHWH 6yKBeHe II03Ha"lleHH.H Bi,n;piaKiB, ao6pameHHX Ha Ma.JIIOHKY y BepTMKaJihHOMY rronomeaHi. BHMip.Hii i 38Illllllll ,n;oB:>KllHY HaHKOpOTIIIOro ii Haii,n;OBllIOro Bi,n;. . pl3KlB.

D p

N B

24*. CyMa '(1uce.JI,

n~o rroaaa"llaIOTh HoMepH Tphox 6y,n;HHKiB,

.HKi CTOSITb UOP.H'A Ha O,ZJ;HOMY 6onJ BYJIH~i, ,n;opiBHIOe BHaHa'lJ HOMepn ~Hx 6y,n;nHKiB.

54.

25掳. MaraaHH npo,n;aB 206 30llIHTiB y KJiiTHttKy. Y JiiHiiiKy 6yJio npo,n;aHO Ha 325 30llIHTiB 6iJihIIIe, a B KOCY JiiHiIO Ha 95 30UIHTiB MeHwe, Him y KJiiTlIHKY. CKiJihI<.n BChoro 30IIIHTiB npo,n;aB Maraa11tt?

26掳. 502 - 237 641 - 555

274'+ 186 96 + 456

9. 7 - 45: 9 16路4 + 13路3

27. PoarJISIHh aarrncH Ta no.HcH11 ycHnii i nnchMOBHii crroco6n 3H8XO,lPI{eHH.ff ,n;o6yTKY "llHCeJI 283 i 3.

283. 3 = (200 + 80 + 3) . 3 = = 200. 3 + 80 . 3 + 3 . 3 = = 600 + 240 + 9 =

=800 + 40 + 9 = 849 6

283

849

28. B11K0Haii MHo.meHH.H nHChMoBo. 207 213路 249 157 x 4 x 3 x 2 x 5 29. 1) PoarJIHHh 06q11cneHHH a1-1aqeHH.H B11pa3y (655 -478)路 3 = 531. 177 655 x 3 478 177 531 2) 3H8MAM 3HaqeHH.H BHpaaiB. (215 - 127) . 8 (140 + 283) . 2

30. Y PycaJIOHhKII 6yJio 960 nepJIIIHOK. BoHa poaKJiaJia Ix y 9 CKpHHbOK, rro 34 nep.JIHHKM B KomHy. CKiJihKH rrep.JIHHOK aa.JIMIIIMJIOCH poaKJiaCTH PycaJIOHh:a;i?

.D:Ba ~Hi ao6pa3MJIH p03B 'H3aHH.H :u;iei: aa,n;aqi 38 AOIIO. Moro10 cxeM: 3.JilBa - cxeMa rreprnoro yqH.H, cnpaBa Apyroro. IIepIIIHH yqeHh, CKJia,n;a10q11 rrJiaH poaB'.Hay. BHXO,ZI;HB 3 "CJ:HCJIOBMX ,n;aHHX, B8HHH aa,n;at.11, a APYrMii - poano'l!HHB.B Bi,n; aanHTaHH.H. Po3rJIHHh cxe. . ... Mll 1 IlO.HCHH, .HK MlpKyBaB KO.)KHHH yqeHh.

31 . 3Haii,z:v1 aa ,n;aHHMH

Maca o,n;Horo

lia3Ba

3araJihHa

Bi,n;npaBJieHHSI

KiJibKiCTb WTYK

4Kr

8 Kr 450 r

Bau,n;epoJIL IloCHJIKa

32*. l.JHCJia, JlUJJtU.

Ta6Jn-n~i Macy o,n;Hie1 6aH,n;eponi.

Ma ca

~o aaKiH"CIYIOTbC.H HyJieM, H83HBaIOTb

Kpyz-

10, 50, 100, 120, 400 - KpyrJii l.JMCJia. JJ:iuI 6y,n;h-

HKOro HeKpyrnoro TJHCJia MO:>KHa BK838TH ,n;Ba KpyrJii, Mim HKHMH BOHO aHaxo,n;HThC.H. HanpnKJia,n;, '(n1cJio 3 7 3H8XO.AHTbCH Mim 'lJMCJiaMH 30 i 40. ,D;o H:omuoro 3 lIHCeJI 17, 31, 54, 89 H83BJ1 Haii6JIH)J{"CJe KpyrJie qMCJIO.

33°. MoTOIJ;MKJiicT BHixaB a O.AHOro MicTa o 7 ro,n; paHKY i npn!xaB y iHIIIe MiCTO 0 12 rO.A ,ll;Hfl. ~orO,D;HHH BiH npo!m,n;maB 65 KM • .HKa Bi,D;CT8Hb MijK MiCT8MR?

34°. 3aBO,lJ; MaB ~O,ll;H.H BHnycKaTH .AJI.H 38MOBHMKa no

167 BepcTaTiB. 3a po6o'lJHM TMm,D;eHb (5 ,n;HiB) BiH BHnyCTHB 910 BepcTaTiB. CKiJihKH BepcTaTiB B11nycT11B aaBo,n; ,n;JI.H siJihHOro npo.n;amy?

35. 12 : 2 13: 2

16: 4 18: 4 7:2

36. 9: 4

20: 5 23: 5

28: 7 30: 7

7:3

42: 6 45: 6

8:3

37 . .D;oBm.nHa MOTY3KH 8 M 4 ,n;M. TpeTMHY MOTY3Klf Bi.n;piaaJIH . .HKa ,n;0Bm.11Ha peIII.-rn MoTyaKn?

38. 1 M

1 ,D;M 1 CM

1 ,D;M : 5 CM 1 M : 2 ,ll;M

5 .AM: 2 4 M: 8

39. 3aKiHl.JH poaB'HayBaHH.H npMKJia,n;iB. 846 : 2 = (800 + 40 + 6) : 2 =800 : 2 + 40 : 2 + 6 : 2 = .. . 975 : 3 = (900 + 70 + 5) : 3 = (900 + 60 + 15) : 3 = .. . 40. MaraanH o.n;epm.aB ,D;JI.H npo.n;amy 25 Kopo6oK a xaJIB010, no 9 Kr y Kom.Hiii. CKiJihKM BChoro KiJiorpaMiB xaJIBH o,n;epmaB MaraanH?

41. PoarJI.HHb, .HK aHaxo,n;HJIH qac·rKy ~11ce11.

972 9 7

II o .H c H e H H H.. Ilepwe HenoBHe .n;iJieHe 9 COTeHh. y qacT~i 6ytJ;e 3 ~Hc}lpH. 9 coTeHh no,n;iJIHTH Ha 3, 6y.n;e 3 COTHi. .[(pyre HenOBHe ,n;iJieHe 7 ,n;ec.HTKiB. 7 ,n;eCHTKiB no,n;iJIHTH Ha 3, 6y,n;e 2 ,n;ec.HTKH i B OCTaqi 1 .n;ec.HTOK.

12 12 0

TpeTe HenosHe ,niJieHe 12 o,n;HHH~h. 12 no,n;iJIHTH Ha 3, 6y,n;e 4. OcTaqi HeMae.

42. BnKoHaii ,n;iJieHH.H nnchMOBO ..

884 : 4

651 : 3

458 : 2

43°. BnKoHali ,n;iJieHH.H IIHChMoso. 693 : 3 926 : 2 896 : 4

245: 7

44° . ,ll;JIH npliTOTYB8HHH BHHorpa,n;HO-SI6JI~Horo COKY 8311-

•

JIH 672 JI BHHOrpa,n;Horo COKY, a .H6JiyqHoro - y k paaiB MeHrne. CKiJibKH JiiTpiB BHHorpa,n;Ho-H6ny~noro coKy o,n;epmaJIH? CKJia,n;:n s11paa ,n;JIH poaB 'H3yBaHHH aa,n;aqi Ta o6qHCJIH lioro 3HC:PieHHH, .HK~O k = 6.

45. Bi,n;piaoKAK cTaHOBHTb

Bi,n;piaKaAB. AB=

" . .3 AK • ,lJ;OB'1tHHY Bl,D;pl3Ka 3 H8H,ll;H A

10 CM 8 MM. B

46. Maca 611t1Ka 6yJia 480 Kr. 3a 'l!ac BHnacy soHa a6iJihillHJiac.H Ha

.! nonepe,n;HbOl M8CH • .HJ;(OIO CTaJia Maca 6HqKa?

3 47. 3Haii,n;H qaCTKY 324 : 6 3 IlOHCHeHH.HM.

48. BHKOHaif ,n;iJieHHH IIHChMOBO .

175 : 5

8 75 : 5

468 : 9

184: 8

49. Ilepmoro ,D;H.H xy.n;o»<.HJO BHCT8BKY Bi,n;Bi,n;aJIH 126 oci6, a ,n;pyroro y 3 paaH 6iJibllie. Yt.111i ·qeTsepTHX KJiaciB cTaHOBHJIH

Bcix

Bi)l;B~yBati:iB.

CKiJihKH 11eTBepTo-

KJiaCHHKiB Bi,n;si,n;aJIO BHCTaBKy? 9

50. TeuJioxiA illloB rro oaepy 2 ro,n; i npoliIIIoB 52 KM. IloTiM BiH 4 ro.n irnon YHH3 IIO piql.\i i npoj:rnoB 124 KM. CKiJihKH KiJioMeTpiB 3a ro,n;nHy npoxo,n;11e TerrJioxi,n; no 03epy? no pi~1~i?

51. (Yetto.) x

+ 2 = 140

X·

2 = 140

x: 4 = 140

52°. MaiicTep npau;roBaB 8 ro.n, a yt1eHh 6 ro,n;.

~oro,n;HHH

KO.»<.HHH 3 IIMX Bl1TOTOBJI.HB o.n;naKOBY KiJihKiCTb ,n;eTaJieii. MaticTep BHrOTOBl:IB 464 ,n;eTaJii, a yqeHb 132. Ha CKiJibKH ,n;eTaJieH MeHrne Bl1TOTOBJUIB yqeHb 38 1 rop..?

54.

B~piaoK

480: 6 + 80 900 - 90· 3

1000 - 210. 4 700 - 70 - 7 ·

504: 8 282: 3

53°. 684 : 9 595: 5

AB cTaHOBHTh

~ si~piaKa

AC. AB

= 22

MM.

3Han,n;n .n;oBJKHHY ni,n;piaKa AC.

Poan'HaaHHH B i ,n; n o

22·5 = 110(MM) i /J.. b: A C = 110 MM.

CMY>KKH Ta 061rn:cJIH ~OB>KHHY sciei CMy:mKM. PeayJihTaT o6qMcJieHH.H l\1epeBip BHMip10BaHH.HM. BK a a i B Ka. BHMip1oaaT11 Tpe6a B MiJiiMeTpax.

55. B11Mip.Ri1:

56. Bi'AoMo,

~o Bi,n;piaoK

OM cTaHOBHTb 5 BChoro Bi,n;piaKa. ,[(013.m.nua ei,n;piaKa OM 20 MM. HKa .n;oamHHa BChoro Bi.l(piaKa '! HaKpecJIH TaKHii BiApiaoK y 30IIIHTi :H noaHaq 11a HhOMY Bi,n;piaoK OM. u;e ~ Bciei' KiJihKOCTi yqHiB KJiacy. CKiJihKH yqHiB y qeTBepToMy KJiaci?

57. y <ieTsepTOMY KJiaci 11

si~MilllIHKiB.

58. 3Hai1,n;H qacTKY 618 : 3 3 IlO.HCHeHH.HM.

59. B11KottaH: ,n;iJieHHH 1u1chMOBo.

636 : 6

915 : 3

540 : 5

3po6H rrepeBipKy ,n;ieIO MHO:>KeHH.H.

60. 3MOJIOJIH 828 Kr nrneH1n:d. BnciBKH (Bi,n;xo,n;H) cTaHOBHJJH lllOCTY qacTHHY aepHa. O,n;epmaHe 6opornHo poac}1acyBaJIH B naKeTH, no 2 Kr y KO:>KHHii. CKiJihKH BHMllIJJO rraKeTiB 3 6opollIHOM?

61. y KO:>KHiM 3 'l!OTHpbOX

6o~OK

no 150 JI 6epeaonoro COKy. YBecL ciK poaJI11JI11 y ,n;soJiiTponi 6aHKH. CKiJihKH aHa,n;o6wJioc.H 6anoK?

62°. rocIIO,Zl;HH.H KyIIHJI8 ni,n;CT8BKY rri,n; TeJieBiaop 3a 100 rpH. BoHa BHTpaTHJia _!_ rporneii, ~o 6y.n11 B ttei. CKiJILKH rpnBeHh 6yJio y roc~o,n;1-n1i? 63°. 545: 5 520: 5

64.

(318 + 153). 2 (752 - 598). 5

921: 3 915: 3

~iB'llHHKa KYIIHJia KHHmKy 38

a:l l·b

4 rpH. 80 K. BoHa BHTpa-

THJI8 ! rpollle11, m;o 6y JIM B He!. CKiJILKH rporneii 6yJIO ,n;iB'llHHKH?

65. HaKpecJin Bi,n;piaoK AB

= 123 MM.

IToattaq Ha Bi,n;piaKy TOt.IKY M TaK, m;o6 ,n;oBmnHa Bi,n;piaKa AM cTaHOBHJia ! ,n;OB:>KHHH ai,n;piaKa AB. 3

66. 836 : 4

624 : 3

7 49 : 7

642 : 6

67. Po6iTHHKH ai6paJIH 816 Kr BHHorpa,n;y. IloJIOBHHY IJ.hOro BHHOrpa,n;y IIOKJI8JIH B .HIIJ;HKH' no 8 Kr y KO:>KHHM. IIocTaB aarr11TaHH.H i poaB '5DKH aa,n;at.1y.

68. 3 84 M TKaHHHH IIOIIIHJIH 28 oµ;HaKOBHX rraJihT. CKiJihKH TflKHX rraJihT MO.mHa IIOllIHTH 3 405 M TK8HHHl1? 69*. ,lJ;JI.H eKcrre,n;n~i1 a 15 oci6 Ha 10 TH:>KHiB HacymHJIH 450 Kr cyxapiB • .f!Ka HOpMa BHTpaTH cyxapiB Ha OAHY \

oco6y Ha OAHH TH:>It~eHb?

!. cyM11 qHceJI 630 i 210. 2) PiaHH~IO ~HceJI 705 i 245 3MeH11.1 y 5 paa.

70°. l) 3Hai1:,n;11

71°. Y KiocK rrpHBeann raaeTH. ,[(o nepepBH rrpo.n;an11 616 raaeT. 3aJIMllIMJIOCSI raaeT B 4 paaM MeHllle, Hilk npo,n;aJIH. Ilpo m;o .n;iaHaeMOCH, HKill;O 3Haii.n;eMO 3Ha'C!eHH.H no.n;aHHX BHpaaiB?

616: 4

616 + 616: 4

616 - 616: 4

72. 3ttaif,n;H ,n;o6yTKH IlHChMOBO.

231. 3

93. 4

128. 7

115. 6

73. PoarJI.HHh aarrHc IIMChMOBoro MHomeHH.H na ,n;Bo~Mcppo•

Be tIHCJIO 1 rrpotIHTan IIO.HCHeHH.H.

II 0

H c He H H .H. IlpH IIMCbMOBOMY MHOmeHHi Ha

'ABO~HcppoBe

x36

YJHCJIO crroqaTKY MHO)l<8Th na o,n;n27 HH~i, a IIOTiM Ha .n;ec.HTKH. 36 IIOMHO)KMTH Ha 7' +252 6y.n;e 252 - ~e neprn11ft ttenoBHHH .n;o6yToK. Horo 72 3aIIHCYIOTb TaK, m;o6 ~ncppa O.D;HHH~h 6yJia 972 p03Miru;eHa rri,n; 0,lJ;HHlI~.HMM. 36 IIOMHO.iKHTM Ha 2, 6y,n;e 72 (,n;eCHTKM) ~e .n;pyrHM HeIIOBHMM .n;o6yTOK. Moro aarrHcyIOTh TaK, ~06 I\M<}1pa 2 6yJia poaMim;eHa rri.n; .n;ec.HTKaMH. )J;o,n;aIOTh HeIIOBHi ,n;o6yTKH i ,n;icTaIOTh OCTaTO'C!HMH peayJihT8T 972.

74. BHKOHaii MHomeHH.H a rro.HcHeHH.HM.

45·23

51·18 32·25 19·18 75. Iloci.HJIH 15 Kr 03HMoi nrneHHI\i, a ai6panH y 23 pa3H 6inhme. CKiJihKH KiJiorpaMiB rrrnea11n;i ai6paJI11?

76. Ha 7 rpH. 84 K. MaMa KyrrHJia 8 pyqoK no 54 K. i 8 oJiiB1\iB. CKiJihKH KOIIITye oJiiBel\h?

77. ,[(o KO.iKHOl HepiBHOCTi .n;o6epu no ,n;Ba 3Ha'l!eHH.H 6yKBH b' II pH .HKHX HepiBHiCTb 6y.n;e rrpaBHJihHOIO.

25 - b > 20 b·4 < 36 b:4 > 8 78. € TPM ~IHCJia: 30, 20, 5. 3Haii.n;H BCi MO.iKJIHBi ,n;o6yTKH cyMM ,ll;BOX qMceJI Ha TpeTe qnCJIO.

79°. 33. 26

42·17

35·25

26·26

80°. Bi,n; CBoro 6y,n;HIIKY xnorrqMK npo!xaB Ha Benoc11rre.n;i B O,ll;HOMY Harrp.HMKY 300 M. IloTiM BiH IIOBepHyBC.H i B rrpoTMJiemHOMY Hanp.HMKY npo!xaB Bi,D;CT8Hh, y 3 pa3H

•

MeHIIIY. Ha HKii1 Bi,n;cTaHi Bi,n; CBOro 6y,n;HHKY aynHHMBcsr x11onq11K?

81. 3annllIM an:paaH Ta 06q11:c11111x 3HaqeHHH: a) 3MeHrnyBaHe 85, ai,u;'eMHHI< e .n;o6yTKOM q11ce11 7 i 8; 6) ,n;iJieHe 56, ,n;iJibHHK e pi3HHII;el0 l.JHCeJI 14 i 6. 82. JJ:epeBHHY HaHKpam.e CKJielOBaTH TO,n;i, KOJIH B Hiii MiCTHTbCH ,n;eB'HTa 11acTHHa BO,n;H. CKiJihKH BOAH MicTHThCH B ,n;epeBHHi M8COIO 18 Kr' roTOBiH AO CI<JielOB8HHH?

83. BHKoHaii MHomeHHH a noHcHeHH.HM.

42·21

31· 12

23·23

17-38

84*. PoarJI.HHh Ma1110noK i aanurnH ai,n;noBi,n;i Ha aanHTaHHH. .HKa Maca 0,ZJ;HOro HJI.J;HKa M8CJia? TpbOX SIIJJ;MKiB MaCJia? ,ll;BOX Hll~HKiB MaCJia?

40 Kr

85. BaThKO Mome ,n;oi:xaTH ,n;o Mic:u;H po6oTH aBTo6ycoM aa 56 XB a6o Ha MeTpO aa 28 XB. Ha CKiJihKH MeHllle 'tlacy BHTpaTHTb 6aThKO Ha .n;opory Ha po6oTy i Ha3a~ 3a 7 ,ZJ;HiB, HKIIJ;O l3,ZJ;HTHMe Ha MeTpo?

86. 06t.JHCJIH peayJihTaT i no,n;iJIH i1oro Ha ni,n;Kpec11eHe 1111c110. 3 p 8 3 0 K.

7·4+5

8 • 5 + 3 = 43 43: 8 = 5 (OCT. 3) 6·3+2 7·8+4 9·3+3

87°. y 6 MillIKax MiCTHTbCH 480 Kr aepHa, a B 9 MiIIIKaX -

450 nopiBHY . 1<r H:apTonJii, . .

KOmHoMy. Ha cKiJihKH . KlJIOrpaMlB Maca MlIIIKa KapTOITJll MeHllla aa Macy MirnKa aeptta? B

88°. Bi,n;KpHJIH I<.paH, 3 .HKoro 3a XBHJIIIHY BMJIHBaeThC.H 20 JI BO,ll;H' i 3a 8 XB HaIIOBHHJIM BaHHY. IloTi KpaH 3aKpHJIH ii smKpliJIH 3JIHBHHH OTBip, Kpi3h .HKHH YC.H BO}.l;a BHTeKJia aa 4 XB. CKiJibKH JiiTpiB BO~H BHTiKaJIO 3a 1 XB? 89.

48: 6 42: 6

6·7 8·9

7.9 63 - 51

72: 12 12·4

90. 3Haii.n;H qacTKH IU1CbMOBO. 625: 5

748: 4

726: 3

126: 2

91. Po3rJUIHh 3anMc11 i npoq11Taii no.HcHeHH.H, .HK 3Haxo.n;HJIH qacTKY qMceJI 144 i 24. 144 124 Il 0 Sf CH e H H Sf. 14 MeHIIIe, HiJK 24. Y qacT144

6y.n;e o,n;Ha IJ,HC}>pa. qacTKy myKaeMo crro0 co6oM BHnpo6oayBaHH.H. Ilepmy rrpo6Hy ~11C}>py MOmHa 3HaiiTH, .HKU\O no,n;iJIHTH qHcJIO BCix ,n;eCSITKiB ,n;iJieHoro Ha 1 -IHCJIO .n;ec.HTKiB ,n;iJihHHKa: 14 : 2 = 7. IlepeaipllMO YCHO ~Hc}lpy 7: 20. 7 = 140, 4 · 7 = 28, 140 + 28 = 168, 168 > 144. U:iu}>pa 7 He ni.n;xo,n;HTb. IlepeaipMMO a;Hc}>py 6 : 20. 6 = 120, 4. 6 = 24, 120 + 24 = 144. 0Tme, I.UU}>py 6 .n;i6paHO npaBHJibHO.

92. 3naii,n;H qacTKY 196 : 28 3 rro.HctteHH.HM. 93. 128 : 32

354 : 59

126 : 42

406 : 58

94. 3a 1c3BYK y noBiTpi npoxo.n;HTb Bi.n;cTaHb 330 M, a BaHT8)KHHH aBTOM06iJih npo!m,n;.mae 15 M. y CKiJihKlf paaiB 6iJILIIIY si,n;cTaHb rrpoxo,n;HTh 3a 1 c anyK, Him npo1m.n;mae aBTOMo6iJib '!

95. Haii6iJihIIIHii MOmJIIIBHH BiK ,n;y6a cTaHOBMTh 1000 poKiB, a Bep611 - y 10 pa3 Mettn1e. Ha cKiJihKH 6iJihIIIe poKiB Mome )KHTM ,n;y6, Hi.m Bep6a?

96*. Y ca,n;y 34 7 n6JiyHh. Pi3HHIJ;.H Mim qHcJioM .H6JiyHh i rpym .n;opiBHIOe 129. CKiJihK11 rpylll y ca,n;y? 97°. 244: 61

275: 55

472: 59

195: 65

98°. 720 eJieKTpOJiaMII p03KJI3JIM nopiBHY B 9 Kopo6oK. 4 Kopo6KM Bi,n;rrpaBIIJill .B O,ll;HH Mara3MH, a 5 - y ,n;pyrHM. CKiJihKH JiaMn o.n;epmaa KOmHRH MaraaRH?

99. 3H8HAH qacTKY ii OCTaqy.

52 : 8

25 : 4

15 : 4

9 :6

100. 3naHAH llaCTKy 294 : 49 3 noncneHHHM. 101. 219: 73

288 : 48

288 : 72

336 : 48

102. Maca cHpHx u.erJIHH CTaHOBHJia 350 Kr. IlicJI.H cywiHBH Ta BMilaJIIOBaHH.H ix Maca 3MeIIlllMJiaC.H na n 'JITY

qacTMHy . .HKOIO CTaJia Ma ca u.er JIUH niCJIH cymiHH.H Ta BHil8JIIOB3HH.H?

103*. JlHCT .)KepcTi 38B,l{OB»<.KH 490 CM IIOTpi6HO poapiaaTH Ha cMy.mKM aaB,nOB:>KKM 6 CM i 8 cM. CKiJihKH ,l\icTaHeMo

CMY:>KOK KO:>KHOro p03Mlpy, .HKIIJ.O lX KlJibKlCTb Mae 6yTM o,nHaKOBOIO?

104. Y napKy 276 6epia.

~e Ha

48 Aepen Mettrne, Him KJie-

HiB. CKiJihKH paaoM y rrapKy 6epia i KJieHiB?

105°. BiAcTaHh si.n JlLBOBa AO JKnToMnpa 360 KM, a Bi,n m11TOMMpa AO KH€Ba - y 3 pa3H Meurna. IIocTaB 3annTaHH.H, ~06 poaB'HaaTM aa,naqy ,nBOMa . ,l{l.HMH.

360KM

?, y 3

pa3H MeIIIIIC

106°. KoHeBi BaroBoaHoi nopo,nH rrp11 1uuKKi H po6oTi aa AeHh aro,noByJOTh 15 Kr ciHa, 6 Kr BiBca, a COKOBMTHX ~OpMiB (MOpKBH, 6ypSIKy, KapTOilJii) y 3 pa311 MeHme, Him ciHa ii: BiBca paaoM. CKiJihKH 1<inorpaMiB co«oBHTHX KOpM.iB )\aJOTb KOHeBi Ha AeHh? PoarJI.HHb n11paan: i 3Haii,nH, HKMii a HHX CKJiaAeHo ,nJI.H poan'.H3yBaHH.H aa,naqi. 3anMrnH 11ieli BHpaa i aHaHAH :Ho- · ro aHatieHH.H.

15 + 6: 3

(15

+ 6) - 3

(l5 j- 6):3 15

HYMEPA'-'ISI &ArATO'-'MCl>POBMX 't~CEn

qoTHPHQH~POBI

•

qHcnA

107. 1) IloJiiqH Bi,n; 95 AO 109; Bi,n; 188 ,n;o 202; Bi,n; 993 'AO

1000. 2)

Ha3BH qn:cJia, .HKi nepe,n;y10Th KOmHoMy 3 no,n;aHMX qnceJI; ii,n;yTb aa HMM: 325; 400; 699.

108. 1) IloJiiqH O)J;HI-IHI.J;.HMM ,n;o 10. HH~b? 2) IloJiiqn ,n;eCHTKaMH )J;O 10 ,n;eC.HTKiB? 3) IloJiiq11 COTHHMM ,D;O 10 COTeHb?

~o YTBOpIOIOTb

10 O,D;li-

11iec.HTKiB. ~o YTBOplOIOTb

COTeHh. JUo YTBOpIOIOTb

109. HK~O ,n;o mucatti ,n;o,n;aTH oauH' ,n;icTaHeMO 'tJ:HCJIO 1nuc.R11,a oaun. 3a qHCJIOM 1nuCJl'lll oauu i,n;e ~HCJIO ntUC.H'lll aBa, a IlOTiM - mUCJl.llll mpu, m.UC.R1lll l/.Omupu, mUCJt1lll n ' amb 1. T. ,n;. IlpoqlfT8H t.IMCJIO, HKOMY Bi,n;noai,n;ae KiJihKiCTb naJIH'l!OK Ha MElJIIOHKY.

1 l1ilf~l ~

1111[11111

~:eicTi

III

~Ba

110. 1) Ha3BH qffCJia: Bi,n; oaHiE"i muC.R1li (10CbMU ,n;o oaniEl mucal./J aeaiJqamu; Bi,n; muca11,i cma iJBaiJL,Rmu ceMu ,n;o muca'li cnia copoKa.

2) II poq11Taii 1111c11a, 16

aarr:ncaHi B Ta6JI1·n~i.

0,n;HHHl(i

THCSI'lli

COT Hi

.llec.HTKH

1 1 1 1 1

3 4

4 2

6 7

0 0

6 0 9

111. (Ycao.) 900 + 1

900 - 1 1000 + 1

499 + 1 409 + 1 1000 - 1

600 + 20 590 + 10 1000 + 5

998 + 1 999 + 1 1000 + 10

112. KopttcTyIO'llHCh rrpaBHJIOM MHO)lteHH.H cyMH Ha 1.fHcJio a6o rrepeCTRBHOIO BJiaCTMBiCTIO MHOmenHH' o6'lJHCJIH 'A06yTKH.

23 ·3

15·4

33·2

113. :IKypHaJI «,IJ;mMiJih»

2·42

3.33

4 . 24

rrepe~IIJI8TMJIH y nepIIIOMY K.rraci

18 ytIHiB, y 'APYrOMY - B 2 pa3H 6iJihllle, Him y rrepIIIoMY, a B TpeTI>OMY - Ha 26 Yl.!HiB MeHille, Him y rrepIIIoMY i 'APYrOMY KJiacax paaoM. CKiJII>KH yqHiB TpeThoro KJiacy nepe,n;nJiaTHJIM myp11aJI?

114. 3a 1 :ro'A Be11ocune,n;HCT rrpoim'Amae 12 KM. TypucT 3a

6 rO'A npORlllOB CTiJihKM KiJIOMeTpiB, CKiJihKH BeJIOCHile'AHCT rrpo!xaB aa 2 ro'A. CKiJihKH KiJioMeTpis npoXO'AMB TYPHCT 3a 1 ro,n;? 115*. ITepllle tIHCJIO 16, BOHO y 4 pa3H MeHrne 3a ,n;pyre. 3HaH'AH cyMy ~Hx 'llttce11.

116°. AsTOMo6iJieM MA3 aa O'AHH peilc rrepeBe3JIH 9 T naHTamy, aBTOMo6ineM BeJIA3 - na 54 T 6iJihIIIe. Y cKiJII>KH paaiB 6iJihIIIe BaHTamy rrepeBe3JIH aBTOM06iJieM BeJIA3, Him aBTOMo6iJieM MA3? CKiJihKH TOHH BaHTamy aa O'AHH peiic rrepeneayTh u,i anToMo6iJii paaoM?

117°. 3 asTo6yca BMHIIIJIO k nacam:upis, a aaJIHllIHJIOC.H B 3 paa:u 6iJihIIIe. CKiJibKH nacamHpiB yno B aBTo6yci? CKJiaAH BHpaa .n;.n.n poaB' 11ayBaHH.H aa,n;a~Ii Ta 06~1HcJIH :Horo 3Ha4eHHH, HK~o k 12.

118. 1) IlpoqHTaH tJHCJia: 1005; 1009; 1100; 1214; 1999.

2) HaaBH «cyci'AiB» KOmHoro 'llHCJia: 345; 1345; 1000; 1010;1100. 3) 3aTIHIIIH ll_HC}lpaMH qlicJia: lnUC.Rllll 06icmi CiMf)ecam

n amb; mucatta mpucma copoK; muca1la ULicmcom; muca'la ULicmiJec.Hm; mucatta ULicmb. 4) Ilo.HCHH, .HK MO.»<Ha o,n;epmaTM 06i mUCJllli. 1999 + 1=1000 + (999 + 1) = 1000 + 1000 = 2000. ~111c.n.a:

1000; 2000; 3000; 4000; 5000; 6000; 7000; 8000; 9000; 10 000.

119. IlpO'l!HTaH

120. (YcHO.) 3 ,ll;BOX O,ll;H8KOBHX aa po3MipaMH .n;iJISIHOK <J.>epMep ai6paB 5000 Kr nmeHHU:i i 4000 Kr .iKHTa. CKiJihKH achoro KiJiorpaMia aepHa ai6paB <l>epMep? Ha cKiJihKH 6iJihIIIe KiJiorpaMiB nmettn~i, Him .muTa, ai6paB <}JepMep?

121 . BttKoHaii ,n;iJieHHH, poaKJia,n;aroqH ye Ho ,uJJieHe Ha

apy"tJHl .n;o,n;aHKH.

38 : 2

90 : 2

90 : 5

48 : 4

122. y ca.n;y ai6paJIM 36 Kr CMOPOAHHH, MaJIHHH - y 3 p83H MeHrne, Him CMOpO,ll;HHH, ar'pycy - y 5 paa 6iJihllle, Him. MaJIHHH. Ha cKiJihKH KiJiorpaMiB 6iJibIIIe ai6paJIH arpycy' Him CMOpO,D;HHH? ~o. . KlJibKlCTb

123. 2 CTOJI.HpH BiApeMOHTYB8JIH 38 5 AHiB 80 CTOJiiB.

...

,Zl;H.H KOmHHH 3 HMX peMOHTyBaB o,n;HaKOBY cToJiiB. CKiJibKH cToJiiB peMoHTyaaa o,n;HH CTOJI.Hp aa OAHH ,n;eHb?

124 *. Poano,n;iJIH c}>iryp11 y .n;ai rpynH: rrp.HMOKYTHHKH i ae np.HMOKYTHHKH.

125°.

TypHCTH npoixaJIH BeJioc11ne.n;aM11

nponJIMBJIH

KM,

tIOBHOM

KM, a niIIIKH rrpOHIIIJilf Bi,lJ;CTaHb y

311 MeHllIY' Him IlO,lJ;OJiaJUI BeJIOC11ne,u;aIVt11

pa-

qQBHOM.

CKiJibKH BChoro KiJioMeTpia no,u;oJiaJIH Typ11cT11:?

126°. 63: 3 78: 2

127.

732: 4 432: 8

67·8 109·7

6·13 21:7

Ha3a11: 'CJMcJio, ~o 11,u;e 3a 'tJHCJIOM

1999;

iJeox muc.R'l ,u;o iJBox mucJPt iJBanaiJL{.H.mu; 'IHCJia ni,n; iJaox mucR.l£ mpunaol{.Rmu ,u;o 060X muc.R1l iJeaiJL{.Rniu.

qncJia ai,u;

128. 1) IlpO"l!HT8ll 'llJ1CJI8,

38I1HCaHi B Ta6JIHIJ;i.

CoTHi

THCSl'li

2 2 4

7 7 3

)J;ecSITKM

0 8 0 3

3 0 0 3

0AHHH~i

0 2 0 0 0 3

2) IIpo'IHTaii "l!HcJia: 2753; 4500; 4050; 3003; 4999. 129.

Po3KJia,u;11 '!HcJia Ha

po3p.H,u;Hi ,u;o.n;aHKH:

1587; 2579;

3650;5005;6800. 130.

3arrl11IIH KO:>KHY cyMy .HK 0,lJ;He 'IHCJIO.

6000 + 500 + 40 + 1

4000 + 600 + 20

8000 + 1

-qepe~i 6yJIO 57 KOpiB, a TeJI.HT y 3 pa3H MeHIIIe. Ilpo ~o ,n;i3H8CMOC.H, 06q11cJIMBllIH 3H8'LleHHSI HaBe,u;eHMX BUpaaiB?

131. y

57 : 3 + 57

57 : 3 132.

57 - 57 : 3

HaaBM c)>iryp11, ao6pameHi Ha MaJIIOHKy. B11Mip.Hii CTO-

...

pOH.ll 1 3Ha.Hti;M nepHMeTp KOJKHOro MHOrOKYTHMKa.

133*. IlpUYJ1Taii IlO.HCHeHH.H npo KyT. Kym - ue <l>irypa, yTsopeHa ,n;soMa ppoMeH.HMM (nisnp.HMMMH), ~o s11xo,n;.HTh a o,u.Hie1 T01IKH. CniJihHHH . . rroqaTOK npoMeHlB HR3HBaeTbC.H eepw.UHOIO KyTa, a CaMl npoMeHi - cmopoua.JLU KyTa. KyT noaHa-c1aeThC.H anaKOM «L » i TpboMa BeJIHKHMH 6yKBaM11. IHo,n;i KYT noaHaYiaIOTh o,n;Hie10 6yKB010. Ha MaJIIOHKY KpaiiHi KYTH Il03HaYieHO TpbOMa 6yKBaMH KYT ABC i KYT KDM, a cepe,u.Hi Ky1·11 noaHaqeHo o,n;Hie10 6yKBOlO - KyT 0 i KYT E. Ila MaJIIOHKY L ABC i L E - npR.M.i KYTH, peIIITa KyTiB ue np.R.Mi. KyT, MeHIIIMii ai,n; np.HMoro Ky·ra, H83HBaeThC.H zocmpu.!tt KYTOM, a KyT, 6iJibllIHH Bi,n; np.HMoro, Haa11saeThC.H niynu.M KYTOM. Ha MaJIIOHKY L 0 - rocTp11ii KyT, a L KDM - Tyrr11ii KyT.

/\ 3a ,lJ.OTIOMOrOIO JJiHiHKH rro6y,n;yii y 30llIHTi rOCTpHM i TYITHH KYTH.

134°. 1) KomHy cyMy aannllIH .HK o,n;He -crHcJio.

700 + 20 + 1 8000 + 300 + 7

9000 + 9 9000 + 900 2) Po3KJia,U.H -crIICJia Ha poap.H,n;Hi ,n;o,n;aHKH: 2384; 2205; 7070; 7007. 135° . .n:o IIIBe:BHOl M8HCTepHi 38Be3JIH 60 M CMTIJ.IO, 24 M cyK•

4000 + 400 + 40 + 4 8000 + 30 + 7

Ha, a IIIOBKy-y k pa3 MeHme, Him CHTIJ.IO ii CYKH8 pa30M. CKiJihKH aaaeaJin lllOBKy? CKJia,n;H Bttpaa JJ;JI.H poaB'.HayB8HH.H 38)'.J;aqi Ta o6qIICJIH :Horo 3Ha-creHH.H, SIK~O k = 12.

136. IlpO'lIHTaii qHcJia KO:>KHOI napn: 5 i 5000; 7 i 7000; 9 i 9000. IIJ.o B HHX cniJihHOro i ~o Bi,n;MiHHOro? 137. 1) 3anHIIIll qucJIO, .HKe MiCTHTb: 3 THC.Ht.Ji, 7 COTeHh,

5 ,n;eCHTKiB i 8 i 9 ):\eCHTKiB. 20

OAHHMIJ.h;

'fHC.H 11

i 9

O.ll;HHl1IJ.h;

TMC.ffq

n 'arnb muc.R1l ci.,w.com copolC mpu; 11,omupu mucatti "ipucnia; mpu muc.a1li wic1naecani oiJuu,· iJei muca 1ti eici.M. 3anHIIIH n;Hc}>paMH tIHCJia:

138. 1)

BRMipHii ,ZJ;OBJKHHY CMYJKKH Ta 06 1rHCJIH, qoMy

AOpiBHIOe

!_ iI. 4

B11Mip.Hi1

cMy.iKKH

-- -

-- .

Ta o6'IHCJIH ,ZJ;OB:>KHHY Bcie!

...

CMY.iKKH •

.___~---~~--~---~___.

139. 1) 3H8HAH !_ Bi,n;: 2 rpH.; 3 rpH. 20 K.; 10 rpH. 4 2) 3anHIIIH y rpHBHHX i KOilittKax: 520 K.; 7050 40009 K.; 80080 K. 140. Ha

CI<:Jia,ZJ;i 6yJio

6epe30BHX i

K.;

COCHOBRX KOJIO,ZI;.

'lleTBepTy t.IaCTHHY COCHOBHX KOJIO,ZI; p03IlHJIHJIH Ha ,n;olliKH. CKiJihKH KOJIOA aaJIMlliHJIOC.H Ha CKJia'Ai?

141 .

Poas'.HmH aaAat1y ,ZJ;BOMa cnoco6aMJ.C Ha ,n;ai

AJIH peMOHTY O,ZJ;Horo KJiacy BRTpaTHJIH 611

i 3

Kr Kop11:qtteBoi.

Il0Tpi6Ho ,ZJ;JIH peMOHTY

142.

3anHIIIH: Hai1:6iJibIIIe

TPH Ail.

Kr 6iJioi <pap-

CKiJihKH KiJiorpaMiB q1ap611

12 T8KI1X

KJiacia?

HaliMeHme qQTHPHUHcppoei q11c-

Jia; n' .HTh IlOCJii)::(OBHHX qHceJI, l1011HH810qH 3 q11:cJia

143°.

3an11mH q11cJIO, .HKe MiCTHTb:

C.HTKiB i

O,ZJ;MHHIJ;h;

1 THCSiqy' 3

+ 45

COTHi i

THcnq,

AeC.HTKiB;

TMC.H 1 Ii,

,ZJ;eCHTKH i

THCHq

i 9

6997.

COTHi,

'Ae-

OAHHHl..{h;

COTeHh.

64: 16 17· 5 28 + 2· 3 90: 10. 3 84-56 65: 5 51: 17 145. 1) IlpoqHTaii qHcJia: 7289; 2090; 4444; 4440; 4004. 2) HaaBH «cyci,n;iB» q11cJia 8000. 3) IloJii Ill Bi,ZJ; 4997 ,ZJ;O 5010. 146.1) 3anMmH IJ,Mc}>paMH q11cJia: mucR 1.a n'Jlnib; BlCl.M 144°. 37

54: 9 7·8

1nuc.R'l nipucma: ci.M. mucRll mpuou,Rmb; iJBi niuc.H.tti cmo.

2) KomHy cyMy

aarr11Ill11 HK OAHe qHcJio.

300 + 2 4000 + 50 8000 +,. 800 + 8 40 + 500 3000 + 200 8000 + 800 + 80 3) PoaKJiaAM Ha poap.HAHi AOA8IIKM 1:IMCJia: 1105; 7007. 4) B11K0Haf1 ,n;i!: 99 + 1, 999 + 1, 9999 + 1. 147. 1) CKiJihKH

B KO:>KHOMY ia aarrHcatt11x y Ta6J111uJ q11ceJI

T HC.Hq; COTeHh; .n;ec.HTKiB; O)l;MHMI~b? 1.JHCJIO

TucS11:1

8456 6303 8456

2) CKiJihKH

CoTenh

JJ.ecHTKiB

s KO:>KHOMY qncJii B c h o r o THC.Hq; y c ho-

r 0 COTettb; y c b 0 r 0 AeC.HTKiB; y c b 0 1

0 OAHHHI.l;b?

Ychoro

1HCJIO THC1P:I

COTeHb

,z:teCHTKiB

0,ltHHHD;b

845

8456

8456 6303 9010

148. 3 + 4

3 THC.

+ 4 THC.

8- 5 2·3

8 THC.

5 THC.

2 TMC. • 3

9000 - 6000 5000 + 2000 5000 + 5000

149.

3HaHAM 3HatieHH.H BHpaay

150.

IleTpMK ai6paB

0,z:tHHHUb

HaTaJIKa

48 Ha

8000 - k. 3,

rpM6iB

.HKI.QO

k = 2000.

12 paa MeHille,

MeHllle,

nim IleTpHK.

rp116iB, MHlllKO -

2000. 4 6000: 3 5000: 5

CKiJibKH BCboro rpH6iB ai6paJIH ,n;iT11?

151 .

Ha IIOlllMTTH

O)l;H8KOBHX KOCTIOMiB BMTpaTHJIH

15 M

TK8HMHM. CKiJihKH TRKHX KOCTIOMiB MO>KHa IIOIIIHTM 3

M TK8HHHH?

CKJia.n;H BMpaa ,n;JIH poas'.HayBaHH.H aaAa'tli Ta :Horo 3HalfeHH.H, HKI.IJ;O

152. 1)

PoarJIHHh MaJIIOHOK. B11Mipnti

,n;opiBHIOe paAiyc Kpyra T oqoK HaJiemaTh Kpyry.

= 45.

OA.

o6'tJHCJIH

aanHlllM,

qoMy

3anMUIM, .HKi a rroaHa'tleHHX

2) HaKpecJIH KOJIO, pa,zdyc .HKoro ,n;opiBHIOe 1 cM 8 MM. IlpoBe,n;H B ~hOMY KOJii ,n;Ba pa,n;iycH.

153. y 3MaraHH.HX ia CTpH6KiB 6paJIH y~1acTb 18 ,n;iB'l8TOK, ix 6yno y 3 paaH MeHllie, Him xnonq11Kis. CKiJihKJI BChOro .n;iTeii 6pano yqacTb y aMaraHH.HX? ,ll;iBqaToK_- 18, y 3 paaH MeHIIle XJIOil'lHKlB - ? ~

I }? •

154°. Ilonen101I1Ka aa 3 ro.n; noca,n;HJia 15 KYl.I.\iB TpO.HH.ZJ;. CKiJihKM Kym;iB BoHa noca,n;HTb aa 5 ro.n;, KOJIM aa 1 ro,n; ca,a;maTHMe Ha o,a;11H Ky~ 6iJILI.IIe, Him paHiI.IIe? CKna,n;aIO'tlH n11aH poaB' HaysaHH.H aa,n;a11i, BHKOpHcTali rro,n;aHy cxeMy.

•

155°. 1) 3an11m11 ~11c}>paMH lIHCJia: mucalla o6aHaiJqJtmb; mucJtita iJBaiJqRmb: mucJtlla oBicmi; mucJt1la iJBa; ciM mucR"l cmo oouuaiJqJimb; wicmb mucJt1l wicmcom.

2) Komtty ia cyM 3RITHllIH .HK 011.He tIHCJio.

7000 + 600 + 60 + 5 8000 + 300 8000 + 30 8000 + 3 Il'.HTlfl~HcllPOBI

156. 10 000

l.JHCJIA

+ 1 = 10 001. HK~o 11.0 10 THCHtI 11.011.aT11 oiJun,

AiCTaHeMo tIHCJIO iJecamb mucsPt oiJun. 3a IJ.HM tIHCJIOM i11.e 1IHCJIO iJecamb· muca11 06a, noTiM - iJecamb muc.Rtt mpu IT. Jl.. Haasn ~111cJia Bill. iJecamu muca11 11.0 iJecamu muca1l iJBaHaiJqamu.

157. IIpotIIITaft 'lIIICJifl, aarr11catti B Ta6JI11.uJ • .nc cSITKH

0,n;HHHI..d

THCSl'll

1 1 1 1 1

0 0 1

CoTHi

AecSITKH

3 0 0 4

2 3

0,zvnunI.i

0 1

1 0

0 0

0 5

158. PoaKJI8/l.H Ha poapHJl.Hi Jl.O'ABHKH: 12483; 16500.

159. 3arrl1lllH ~Htl>paMM lIHCJia: 12 TllCH~l 755; 15 TMCHlI 80; 18 THCHtI 800; 18 THCHtI 8. 160. 1) HKi npIIKJI8/J.II poaB' .H3aHo HenpaBHJihHo? IIoHCHII, l!OMy BMHIIKJIII IlOMIIJIKH i p03B, HiKM II.i npHKJI8,AII npaBMJibHO.

+ 475 206 681

+443 268 611

+ 556 184 730

+785 27 802

2) B11K0Hai1 11.011.aaattHH nuchMoao.

128 + 666

37 + 847

236 + 123

57 + 284

161. Bi,AcTaHh Mim ABOMa MicTaMM 250 KM. Ia D;IIX MicT HaaycTpi~1 o,AIIH O/l.HOMY OAHO"CJacno a11ixaJIM 11.sa aBTo6ycII.

HKa ai,ncTaHb 6yJia Mim aBTo6ycaMH, KOJIH nepllIIIii 3 HIIX npo!xaa 127 KM, a ,ApyrHH 93 KM?

--~~-12_7_K_M~~---L

162.

250 KM

.1~~~--:_3_KM~~~J

CKJia,n;n aa.n;a1.1y aa KopoTKHM aarn,rcoM

155 Kr

poaa'Hmtt

i.I.

I - 52 Kr.II - Ha 4 Kr MeHlllel III-?

{

163. B1111llIH TaKi q11cJia, II.\06 HepiaHocTi 6yJIH npas11JihHi. 12 - 4 < 0- 4 20 + 5 < 20 + D 9- 5>9- D 164*. Y

.n;aox KJiacax

6iJihllle, Him s

yqHin. B o.n;HoMy KJiaci Ha

iHilloMy. CKiJihKH yt-rHiB y

y"tJ:Hi

KomHoMy

KJiaci?

165°. Y

KHI-IiKIJJ

cTopiHKH. XJiorrtiMK npO'IHTaB TpeTIO

qacTHHY KH11mK11. CKiJihKH CTopiHOK i1oMy aaJin111ttJioc.H rrpoq11TaT11?

166°. 1)

3arr.HlllH 1-(H<l>PRMH 'llHCJia:

10 THC.H'll 500; 10 THC.H'll; 10 TMC.H'I 50; 12 THC.Ht:I 85; 12 THC.Hq 80; 12 THC.H'll 5. 2) PoaKJia~H Ha po3p.H~Hi ~o~aHKII: 17487; 16 300.

167. 1)

Ilpo~Il1T8ll l:{:HCJia:

13489; 15080; 5800; 7003.

CKiJihKH B KomttoMy 'llHCJii BChoro .n;ec.HTKiB; coTenh; THC.H'll?

•

2) 3arrHlllH l!HCJIO, y .HKOMY 12 THCSJq i 750 O,ZJ;HHHD;h; 9 Tl1CHq i 95 O,ZJ;HHH~h; 1 7 .THC.Hl! i 7 O,D;HHH~h. 168. 1) HaaBH

«cyci~iB» qncJia

19 999.

20 THC.H'll. 19 999 + 1=10 000+9999+1=10 000 + 10 000 = 20 000.

IloHCHH, .HK MOmHa YTBOpl1TJ1 l.Jl1CJIO

169. IlpotIMTaii tIHCJia: 10000; 20000; 30000; 40000; 50 000; 60 000; 70 000; 80 000; 90 000; 100 000. 170. 1)

3Haii,n;H .n;Ba rrpHKJI8,ZJ;H' p03B, .H3aHi HerrpaBHJihHO.

Ilo.HCHH, ~OMY Bl1HHKJil1 ITOMMJIKl1,

poaB'.HmH ~i rrpHK-

Jia,n;H npaBHJihHO.

8'74 ;5 93 381

501 - 2·52

249

381

280

101

'T57

709

2) BHKOHali Bi)ll;HiMaHH.H IIHCbMOBO. 480 - 283 '544 - 155 831 - 214

1-~.-?-,

505 - 125

_ ua _ 6_ 8 _M_M _e _H _ . [_u· _ e ____ ? _ _ _ _ _ _ _4_o_9_M ___

172. 3 ,m;iJllJIHKH ai6paJIR 600 Kr 3epna. ~ 3epHa CT8HOBHJIO 1 3 c . .>KHTO~ .5 -· IIIlleHMIJ;.H, pelllTY I<yKypy.n;3a. KlJlbKII BChoro KiJiorpaMiB mnTa i nrneHHU.i 3i6paJitt?

173. 3arrnmH, .HKi cTopoH11 TpHKYTHHKa ABC nepeTHHa€ si.n;pi30K KM. B11MipHi1 cTopoHM TPHKyT1u11<a ABC •

3Ha.11,n;11 11oro nepnMeTp. B

174°. y 1.n;aJibHi 6yJIO 800 Kr KapTOilJli. Ilepworo ,l.J;H.H BHTpaTHJill

.!. ncie1 4

KapTorrJii, .n;pyroro .n;HSI -

Ha 120 Kr

6iJih111e, Him nep111oro, a TpeThoro .D;HH -

peIIITY Kap-

TOnJii. CKiJILKH KiJiorpaMiB KapTOilJii BHJ'P8TMJIH TpeTbOro

175掳.

,n;Hs"!

4 ,n;i1.)

(3a.n;a'l!a Ha

3arrHIIIH TPH 6y,n;L-.HKHX Tp1-n..vul>pos11x 路q11cJia, TPM qo-

TMpMI(MC}>ponwx 'llHCJia

176. 1) IlpO"llHTaH qHcJia,

TPM n 'HTMI(HC}>POBHX 'l!HCJia.

3aITHCaHi B Ta6JIHI(i.

L{eC.HTKH THC.Hll

0,ZJ;IIHHUi THC.fill

CoTHi

.l(ecHTKH

0~11H11U,i

0 7 7 7 7

0 0 3 3 0

0 0 0 5 5

0 0 0 0 1

2 2 2

2) IlpotIMT8M 'llJllCJia: 50 000; 50 500; 73 273; 80 005. 177.

3anHIIIH "lIHCJIO,

HKOMY

THCH'l! i

800

OJ];llHln:i;L;

70 THC.H'l! i 35 0.D;HHHnL; 90 THC5Jq i 999 O.D;HHMIJ;b. 178. 1)

PoaKJia,n;M Ha poap.H,n;ni .n;o,n;aHKM llMCJia:

25 756;

83 400; 83 004; 83 040; 10 510. 2)

3arrnll.IH KomHy cyMy .HK o,n;He 1:.IMCJIO.

50 000 + 6000 + 700 90 000 + 5 179.

(YCHO.)

180. 936: 72 181 .

28 000- 20 000

80 000 + 300 + 3 40 000 + 40 8000路4

876 - 338 - 292

36 000: 3

876 - (338 - 292)

,lJ;JI.R MOJIO.D;IIIHX lllKOJIHpiB npll.n;6aJIH BCbOrO

KiB:

KBHTKH -

peIIITH -

y l(MpK,

np11.n;6a.n11 KB11TKiB

182.

+ 20 + 5

KBHT-

B JI.ffJibKOBHM TeaTp, llIOCTY 'lJ8CTMHY

sci iH111i -

KiHoTeaTp. CKiJILKH

KiHOTeaTp?

3a M8JIIOHKOM i 38TIHC8MM CKJia,n;H i po3-

B '.H

200

mu aa,n;a qy. OA=AE OE= 18cM IIepHMeTp -

OA-?

183°. 1) PoaKJia.n;H Ha po3p.H.n;Hi .n;o.n;aHKl:f q1:1cJia: 64 54 5;

3451; 60 070; 67 000; 60 007; 60 700. 2) K omHy cyMy 3anHmH .HK o.n;He qHcJio.

50 000 + 6 50 000 + 60 50 000 + 600 + 60 + 6 80 000 + 60 80 000 + 8000 70 000 + 7000 + 7 184°. CyMa Tphox ,n;o,n;aHKiB 853. IlepmHi1: .n;o,n;anoK 275, .n;pyr11i1: 198. ,n;py r oro?

Ha cKiJihKM TpeTii1 .n;o.n;aHOK 6iJibll1MH Bi.n;

185. 1) 25 100> 25 010

10 000 0 9000 59 000 0 95 000 37 000 0 37 700 40 009 D 40 090 7070 0 70 007 2) 3anMlllH «cyci.n;iB» qnceJI: 300, 3000, 30 000.

186. 1) 3annllIM qncJIO, y HKOMy: 33

THCsr~Ii

i 542 O,ZJ;MHMll;i;

28 T:Hcsrq i 5 7 O,ZJ;MHHll;h; 90 TMCHq i 9 O,ll;MHMll;h. 2 ) 3anMll1M u;uqJpaM1:1 qncJia: copoK muc.R 1t iJBicmi; copoK mucsl1t iJBaiJq.Rmb; cii'4iJec.Rm iJee' amb mucatt iJeicmi.

187. CKiJi bKH B £JlfCJii 28 345 ychoro TMCHq; ychoro COTeHh; ychoro .n;ecsrTKiB?

188. 3aIIHllIH y MeTpax i caHTHMeTpax: 480 CM; 28 004 CM;

6020 CM; 148 CM; 3544 CM; 38IIHIIIH y KinorpaMax i rpaMax:

137 Kr; 8060 r;

40 009 r; 7050 r, 80 080 r. 189. B nKOHai1 .n;ineHHH i 3po6M rrepeHipKy .n;iero MHomeHH.H.

618 : 3

918 : 54

432 : 54

190. CyMa Tphox qncen 87 4. I1epme q11cJio .n;opiBHIOe 355, ,n;pyre -

89 MeHme. 3HaM,n;H TpeTe "CJHCJIO.

191. 3a 1 XB yqeHb ql:fTae BrOJIOC 80 CJiiB, a MOB£IKM-

200 cnis. Ha CKiJibKH 6iJibIIIe cJiiB npoq11Tae

~eHh 3a

5 XB MOB'lJKH, Him yroJioc? (P03B 'H:>RH 3a.n;aqy ,ZJ;BOMa c11oco6aM11.)

192°. Ila 6y ,n;iBHHll;TBO np11seaJI11 126 T ~eMeHTY, a nicKy B 4 paa:n 6iJihrne. 3a .n;eHh BH'rpaTHJIH a T nicKy. CH:iJibRH 'l'OHH rricKy aaJIMillMJioc.H'? CKna,u,11: B11paa ,ZJ;JIH poaB '.H3YBaHH.H 3a,ZJ;alJi Ta o6~u.fCJIM 3Ha£IeHH.H, .HKI11;0 a = 450. 28

193째.

3anMIIIH, CKiJihKH BChoro Tl1C.HYI B KO.iKHOMY 3 ~1ucen:

48 355; 5080; 60 780; 12 310; 1850. IlIECTH~Hcf>POBI

194.

fy,n;3HKH

npnKpiIIHJIH

10 lliTYK Ha 10 cMy.moK KeTiB -

qifCJIA

K8pTOHHi

CMY:IB:KM,

110

KO.iKHy. IloTiM n.i CMY.iKKH CKJiaJIH TaK: y 3B'.H3Ky,

10 3B'.H30K

y rraKeT,

10 na-

y Kopo6Ky. Bchoro BHMIIIJIO IIIiCTh Kopo6oK,

siciM rraKeTiB, rr'.HTb 3B'.H30K, 'CJOTHPH cMy:m:KH I I.Qe BiciM r'y,n;aHKiB OKpeMo.

Kopo6KH

IlaKeTH

3R'.H31\ll

CMymKn

fy,D,3UKH (OKpeMO)

3anttIIIH, CKiJJbK11 BCbOro 6yJio r'y,n;a111<.iB. IlpO'tJHTaM u;e "l!HCJIO.

85 4 72; 40 210; 35 020; 90 009. 3a. IlMlllll U.l 'tlHCJia, KOpHCTYlO"lJHCb CJIOBOM muca1la.

195.

flpO'tJHTRM "lJHCJia:

3 pa 3 0 K.

23 014 -

u;e

THCH'tJi

14.

196. 100 000 + 1 = 100 001. HKw;o ,n;o 100 THCH'tl ,n;o,n;aTH oiJun, ,n;icTaHeMo 'tJHCJio cmo mucall oiJu.n. 3a IJ.HM 'tlHCJioM i,n;e t.111cJ10 cmo muca1l iJ6a, rroTiM - cmo muca1l mpu

1 T. ,n;.

197.

PoaKJia.n;11 Ha poap.H.n;Hi ,n;o,n;aHKH qncna:

128 345;

144 500; 105 307; 100 008. 198.

IIpo'tlHTaii qncJia, aanncaHi B Ta6Jin~i. CoTHi

,l(ec.HTKH

0,nunnu.i

THC.H~I

1 1 1 1 2

199.

0 0

0 9 0

3anHIIIH qucna

0 0 0 9 0

CoTHi

.D;ec.HTKH

0A11HMIJ.i

0 0

1 0 3 0

u;11c}>paMM: 125 TllC.flq 753; 130 TMC.flq

72; 13 THC.HY! 72; 100 THC.H'tl 20; 199 THC.Hq 990. 29

200. 1)

IIepeBip, 'lIH

rrpaBHJihHO BHKOHaHo

IlHCbMOBe ,D;lJieHH.H.

SIKi 3pyqHi ,n;o,n;aHKH (HerroBHi ,n;iJiefli)

9 72?

p03KJI3,D;8JIM "CJHCJIO

2) BnKoHatt ,n;iJieHH.H

684 : 2 201. y

ca,n;y

cl1pyKTOBHX ,n;epeBa. -

CJIHB y ca,n;y "! B

516 : 3 1

864

. a

.H JIYHl'

7 6

nHChMOBO.

5 75 : 5

JI.HTb rpyrn1, -

202°.

_ 972 LQ._ 9 1324

0 IJ;HX ,n;epeB CT8HOB-

pelllTY -

CJIHBl1.

c· KlJlbK11

aBTorrpo6iry 6paJio yqacTh

216

MamHH. EKirram

KO:>K.Hoi' M3IllHHH CKJia,n;aBCH 3 TpbOX cnopTCMeHiB. JJ:o c}1ittirny np116yJI11

384

cnopTcMeHH.

CKiJihKl'.I MaIIIHH

3iHlllJIO 3 ,ZJ;HCTaHuii:?

203°. 1) 3anHIIIH

cmo iJec.Rmb muc.Rll mpuc1na iJBa; cmo copolC iJBi muc.Jtlli 8ici.Mcom mpu1-tao4amb," wicmiJecam ci.M. muc.Jt'l 1npucma.

2) KomHy

:a;H<}1paMH qncJia:

cyMy 38IIHlllH .HK o,n;He qHcJio.

100 000 + 50 000 + 4000+200+10 + 8 100 000 + 5000 + 500 + 5 100 000 + 800 204. 1) IloSICHH, .HK MO:>KHa ,uiCT8TH "t!HCJIO 200 THCH"CJ. 199 999 + 1=200 000 199 999 + 1 = 100 000 + (99 999 + 1) = = 100 000 + 100 000 = 200 000 2) Ilpo,.n1Tai1: "lJl1CJia i'1 3an1111111 Ha:i16iJihllle i nai1:MeHIIIe 3 HHX: 140 350; 59 605; 199 000; 99 999; 200 000. 3) CKiJihKH BChOro THCJiq y KO:>KHOMY 3 qJ'.ICeJI: 19 540; 58 400; 160 000; 133 333; 200 000? 205. Ilpo'llHTaH 'llHCJia: 100 000; 200 000; 300 000; 400 000; 500 000; 600 000; 700 000; 800 000; 900 000; 1000000. Tucn•1a THCH'I - u;e MiJILiiou. 206.

3anHlllH

,n;o,n;aHKlB.

qHCJIO

184 532 y

BHl'JIJI,n;i cyMH po3pJI,D;HHX

207. BcTaB

rrporry~eHi

3 M 7 CM = 0 CM 4 ,ll;M 5 CM = 0 CM 1 CM 9 MM = D MM 208. 240: 3 500: 10 70 . 7 500 : 2

qncJia. 80 MM = 0 CM 540 CM = 0 M 0 Cl\l 540 CM = 0 M D ,llM

720: 9. 2 60 . 3 + 7

280: 4·10 620 + 80 : 8

972: 36 288: 36

209. y Mara3IIHi 6yno 354 Kr KpyrriB. PRC CTaHOBHB . Kpyn1B, a IIIIIOHO 6yJIO B Mara3HHi?

1 . - pewTu Kpyrr1n. 4 Ychoro

~ ~ _,,,,,,.

,,,,, ..,.,,,.

Bcix

354

BCiX

3 IIIIIOHa

PemTa

Kpynie

----------......... --......_,._

c KlJibKII .

........

------

-!-- --..- .-- .--

~--------------

---- --

......... ..__

---

peUITH

210. 1000 Kr nllloHa poac11nan11 y rraKeT11 no 2 Kr i 3 Kr. IlaKeTiB no 3 Kr?

2 Kr 6yJio 245. CKiJihKII 6yJio rraReTiB no ·

211°. 3annmH u.11q>paMM q11cJia: n 'amb muca 1t; copoK mucall; a6icmi muc.R.tt; Cl1l0 Ci.MHaaq.H.nlb mUC.Rll mpucma. 212°. IIepllIHH onepaTop Ha6paB Ha KOMil'IOTepi 900 CTopi-

•

HOK TeKCTY 38 6 TIImHiB, .n;pyrHH Ha6paB TaKy caMy KiJihKiCTb cTopiHoK aa 5 THmHiB. Ha cKiJihKl1 6iJibme CTOpiHOK 38 THm,n;eHb Ha611paB .n;pyr11ii onepaTop, Him nepllIHH, HKIJJ;O ~OTII)KHH KO)KHIIH 3 HHX Ha6Hpaa o,n;HaKOBY KiJibKiCTb CTopiHoK?

213. 1) IlpoqHTRH 'IHCJia, aarr11caHi B Ta6JIJU~i.

CoTHi

)l;ec.HTKH

0,AHHHIJ,i

TIIC.Sl'CJ

TRCSitI

THC.ff'll

1 2

3 2 9

7 8 0

0 0

CoTHi

,Uec.HTKH

O~HHHI.J;i

1 8

2 4

0 0 0

5 0 0 0 1

2) Ha .HKOMY Micu.i crrpaaa B -c1HcJii nHI.IIYTbC.H o,nHHHIJ.i; AeC.HTKH; COTHi; OAMHHIJ.i THC.Hl.l; ,u;ec.HTKM TIIC.Hll; COTHi THC.Hll? 3) IlpolIHTaH lIIICJia i BH3Ha1I, CKiJibKH B KOlliHOMY 3 HHX BChOro THC.Hll: 23 400; 210 175; 5253; 945 000;

735 428; 17 405. 214. 3anHlllH

~uc}1paMH l.IHCJia: n 'JI ntb mu.calf. ci.JJtcom copoK

wicn1b; Bici.MiJecam 1nucJzr.1 cn10 iJ<1aiJqRtnb; m.pucma iJeC.Rnlb mUCJl'l

Oe6' JlHOCmO;

cmo mpu mUCJztti BiCiM COm

oaunaiJ~Jtnlb.

215. 945 145 > 888 888 90 000 D 890 000 111111 D 90 000

435 784 D 345 784 494 700 D 449 700 260 000 D 206 000

216. PoaKJia,u;11 Ha poap.H,n;Hi ,u;o,u;a.HKH t111cna: 234 725; 777 777; 500 400; 540 000; 225 225. 217. fHOMH ttaa6HpaJin 300 rpn6is. 3 28 rpH6in BiJioCHi>ItKa 3B8PHJia cyn, a pewTy HaHH38Jia nopiBHY Ha 8 HHTOK. CKiJibKH rp116ia 6yJio Ha KomHiii HHTuj?

218. 8 u; nepcHKiB poaKJiaJIH B .H~HKH no 10 Kr i 15 Kr. H~H足 KiB no 10 Kr 6yJio 50. CKiJibKH 6yJio .HI.QHKiB no 15 Kr? 32

219°. 100 6aHKH.

JI COKY p03JIHJIH y Tp11JiiTpOBi Ta rr' HTHJiiTpOBi 1

1 puniTpoB11x

6aHOK 6yno

10.

CKiJihKH 6yno

n '.HTl1JiiTpOBHX 6aHOK?

220°. 1)

n'JZmcom muc.R'l cnio,· cmo niuCR.'l n 'Jtmconi; iJeauaol{R.mb muc.R'l iJBaOq.Rnib n'.Rmb; ciJuconi copoK mpu muc.R'li mpuOl{.Rmb mpu. 3arrHllIH II;Hc}>paMn qncJia:

2) Komny cyMy

aann11I11 HK o,n;He qHcJio.

200 000 + 30 000 + 4000 + 600 + 70 + 8 600 000 + 50 900 000 + 90 000 + 9000 + 900 + 10 + 9 60 000 + 500 3) 3arrMIIIH Haii6iJibme i 221.

y y

H8MMeH11Ie rr' .HTl1~11Cl>POBi 'lll1CJia.

Ilp0'£1HT8ll IIO.HCHeHII.H rrpo po3p.HJJ;H

i1:

KJI8CH B qHCJiax.

6araTOII;HC}lpOBOMY qJicJii poap.HJJ;H rpynyIOTb y KO.>KHOMY KJIHCi TPH

po3paiJu.

ICJlacu.

Memax IIIeCTHl1-Hc\>po-

BHX l.IHCeJI Ma€MO JJ;Ba KJI8CH: nep11n1.i1 i ,n_pyrHii. 0,n;HHMII;i, JJ;eCHTKH ii coTui cTaHoBJI.HTh KJLac

oOuHUL{b (rrep-

1I111ii KJiac). 0,L\HHnu_i THC.Ht.I, JJ;eCHTKH THC.Hq i THC.Hq CTaHOBJI.HTb

COTHi

1i.llaC mucatt (JJ;pyrHH KJiac).

Knac Tncs111

KJiac OJ.\HHHI.\h

CoTHi

,l(ec.HTKH

0 ,D;lllllU.d

THCSll.I

Tl1CSl1.I

THCSJ\1

0,lJ;HHlfn_i' JJ;eCHTKH i COTHi -

CoTHi

Aec.HTKH

0 ,D;HHHUi

H83BH rreprnoro, JJ;pyroro i

TpeThOro poapH,n;iB neprnoro KJiacy. 0,n;HHHn_i THC.Hq, JJ;eC.HTKH THC.Hq i COTHi THC.Hq -

H83BH

nep11Ioro, JJ;pyroro i TpeThoro poap.HJJ;iB JJ;pyroro KJiacy. HaaBM niqMJihHHX (poap.HJI;HHX) OJJ;HHHI1-h nep11I11x JJ;BOX

KJIUClB TaKl: JJ;JI.H KJiacy O,D;HHMIJ,b COTH.H; JJ;JI.H KJiacy THC.Hq -

O,ll;HHHIJ,.H, JJ;eC.HTOK,

0,D;HHHII;.H THC.Hq, JJ;eC.HTOK

THCHq, COTHH THC.Ht.I. HKI.QO OJJ;HHH~i .HKHXOCb poap.HJJ;iB nii:i;cyTHi, TO B ycHiii HyMepa~iI Ix He Ha3HBaIOTh, a B nnchMOBii1 -

rroaHaqaroTh HyJieM. BH.D;iJI.HIOTb TaKom.

OJJ;HHHUi KJiacin. 0JJ;HIIH11-el0 KJiacy THCWI € THC.Ht.Ia. II(o6 npoqHT8TH 'lJQTHPHII;HC}lpOBe, n, .HTH~HC}>poBe a6o llieCTH1.l;HC}lpOBe l.JHCJIO, B HbOMY

0/~11Hl11J;b

CI10'll8TKY Tpe6a H83B8TH, CKiJibKII

HHI.\b KJiacy o,z:i;:HHHU.b (cnoBo 2. MaT~~nT11Kn, 4 K.11.

KJiacy TMC.H'll, a IlOTlM, CKlJibKH O)l;H-

oOUHUU,b He Bl1MOBJIH10Th)..

222. 1) PoarJUIHh Ta6J1nu.10 poapH,nia i KJiaciB. Knac THC1tt1

I\nac

CoTHi

,[(eC.HTKH

0,D,HHHI{i

THCHl.l

THC fl~

THCHl.I

6 8 6

7 8 2

5· 0

WJ;HHHU.h

CoTni

Aec.HT1<11

0,D,HHHI{i

3 6 0 2 0

9 3 0 3 3

2 7 0 8 4

2) Ilpu1n-1Tai1: neprue 1.JMCJIO Ta6JIHUi. CKiJihKH n HbOMY 0,l(HHMUb KJiacy THCSPI; KJiacy 0,ZJ;HHHUh? 3) Ilpoq11'raii ,n;pyre i 'rpeTe q11cJia Ta6JIRUi. ~o B HHX cniJibHOro i I~O Bi.n;MiHHOro? 4) IIpoqnTa:H tieTBepTe -.:1ncJio Ta6Jinu.i. Il~o aoaHa"tlae KOJKHa ia u:ncl>P y iioro aau11cy'! 5) mo Il03H31.18IOTL HyJii B 3flilUCY n'.HTOrO 1.lHCJia~/

223. Ilpo1.JJ1T8H qHCJia B TaKOMY nop.H,n;Ky: 'tlOTHPHUIH}lpOBe, n' .HTHU.1-H}lpOBe, mecTHU.Mc}>poBe.

30 281

990 105

6&40

224. Cn111.1IH quc;1a :H ni.n;KpecJIH B KomHoMy KJiac THC.Hq.

318 451 225. 228·3

23 500 48·23

7480

60 006

782 : 23

600 133

133 600

161 : 23

226*. B o.zi;HoMy pa1'10Hi MicTa MHHyJioro poKy no6y,n;yaaJIM

6 O,lI_HaKOBHX 6y.zi;HHKiB, no 126 KBapTMp y KOJKHOMy. ~boro poKy no6y,n;yBaJIH Ha 240 KBapTnp 6iJihllle. CKiJihKH ciMeii o,n;epmaJIH KBapTnp:n B HOBHX 6y,n;MHKax UhOro poKy?

227°. 1) 3anHlllH

~H(}1paM11 -.:111cJia, B nKux:

nipucni.a copoH: n '.Rnib o.n;MHHIJ.h KJiacy THC.Hl.J i iJBicmi Bici.11·iiJecani ttomu-

pu o,zi;MHHU.i I(Jiacy o,n;nHttU.h; n 'R mco1n mpuiJu,JLmb ciJrt. O)J;MHHU.b KJiacy THC.Hl.J; copo1c O,ll;HHHU.b KJiacy THC.Hq i cnio <)aaiJq.Rmb O)J;HHHU.b KJiacy O,l(HHHIJ.b. 2) 3anHllll1 l.lllCJia y BHrJI.H,n;i CYMH poap.H,lJ_HHX ,n;o,n;aHKiB:

57 454; 570 454; 456 702; 4037. 34

228°. 3a 3 JJ:Hi aBTOM06iJib rrpoYxaB a KM. 11eprnoro JJ:IUI BiH npoixaB 300 KM, a J\pyroro - Ha 20 KM MeHIIIe. CKiJibKH KiJioMeTpiB npoixan aBTOMo6iJih TpeThOro ,ZJ;H.H? CKJI8~H BHpa3 JJ:JI.H poaB' HayBaHH.H aa.u;a-qi Ta o6"CJHCJIH iioro aHaqeHH.H, .HK~O a = 960. 229. HK npoquTaTH q11cJio 63 439? Y u;hoMy qHcJii 63 OJJ:HHHU.i KJiacy THC.Ht{ (~pyroro KJiacy) i 439 O,ZJ;HHHll,b KJI8cy 0,D;MHHIJ.b (neprnoro KJiacy). 'llHT8eMO T8IC 63 THCH'CJi 439. (CJIOBO oouuuu,i He BMMOBJI.HeMo.) IlpoqHTaif q11cJia: 962 548; 30 655; 100 125; 25 200; 37 007; 900 009; 30 009; 9000.

230. 3anHIIIM ll,H<}.lpaMH l.IMCJia, HKi MiCT.HTb: 24 7 0,ZJ;HHHIJ.h 11:pyroro KJiacy i 572 o,u;HHHU.i nepmoro KJiacy; 4 7 o.u;nHHU.h 11:pyroro KJiacy i 50 o,u;HHHIJ;h nep1uoro RJiacy; 8 OJJ:HHH~h 'APYroro KJiacy i 7 o,n;nHHIJ.h neprnoro KJiacy.

231. 3an11rn11 u;Mc}lpaMH l.IHCJia: mpucma. copoK; mpu.cma iuicmcom CiM; UJ.icnuta.fh~.Rlllb tnuC.R'l uticmoecam: oBicnii mpu niuca 11.i <7Bicmi iJaaiJqamb; aea'anocmu

mUC.R'l

11.omupucma n1uca 1t tJici.M.iJecRni.

232. 9999 + 1 1000 - 1

124 000 124 000

+ 200 + 20

43 690 - 90 43 690 - 600

233. Po3rJISIHh 38IIHCH. 10. 2 = 20 100· 2 = 200 2·100 = 200 2·10 = 20 2 • 10. 10 = 200

20 000: 4 30 000. 2

1000. 2 = 2000 2 • 1000 = 2000 2·100·10 = 2000

CKiJibKH nyJiiB Tpe6a .u;on11:caTH .u;o "CJHCJia cnpaBa, ~06 IlOMHO}KHTH u.e qncJIO H8 10; Ha 100; H8 1000?

234. PoarJI.HHb aarrMCH. 4000 : 10 = 400 400 ,n;ec. : 1 .u;ec. = 400

4000: 100 = 40 40 COT. : 1 COT. = 40 4000 : 10 : 10 = 40

4000: 1000 = 4 4 THC. : 1 THC. = 4 4000 : 100 : 10 = 4

'Jlr

CKiJihKM HyJiiB Tpe6a Bi,n;KHHyT11 s 3arrucy qttcJia, ~06 no,n;iJIHTH u;e t.IHCJIO Ha 10; Ha 100; Ha 1000? •

235. 3MeHlll y 100 pa3 1U1CJia: 500; 6000; 3800. 36iJihllI y 10 pa3 q11cJia: 500; 10; 9000.

236. 36 000 : 100. 10 800. 10 : 100

237°. 260 000: 100 80000. 10

600. 10 • 10 180. 100 : 10

(260 + 140): 100 (860 - 50) • 10

(100 + 300). 4 36 000 • 10: 1000 8400 - 80 000: 10 8100. 100 : 1000

238°.Sa ,n;eHb y ca,n;y 3i6paJIH 7 40 Kr .H6JiyK. qaCTMHY SI6JiyK p03KJiaJil1 B 26 5!11VIKiB, 110 10 Kr y RO)KHHM, a pemTy p03KJiaJIH B 6iJibllli H~HKH' no 12 Kr y KO)KHHM. CKiJihKn achoro BHKOpHCTaJIH .HI.I.1-MKiB?

239. 1) CKiJihKH o,n;MHHll;h nep1noro KJiacy

KomnoMy 57 009; 300 001; B

qncJii: 217 533; 20 705; 7037; 680 000? 2) CKiJihKM BChoro o,n;MHMIJ;b no3Ha"Ciae u;11q1pa 2 B 3anncy l{Q)KHOrO 3 '-IIICeJI: 245; 320; 127 300; 844 002?

240. 36iJihlll y 1000 pa3 qncJia: 7; 75; 700; 705. 3MeHm y 100 pa3 qncJia: 1000000; 8000; 380 000.

241. y '-IHCJii 230 758 ychoro 23 075 ,n;eCHTKiB . .HK ,n;i3HaTHC.H, CKiJihKH BCbOro ,n;eC.HTKiB y qlfcJii? UJ,06 iJi3namuca, cKiJtbKU 6Cbozo iJecanuciB y ttucni, 1npe6a BiiJKunymu ocmannro ~urppy cnpaBa. l/ucno, fl!O 3anumunoca, noKa31ce, cKinbKU ecbozo iJecamKiB y ttucni.

242 . CKiJibKM BChoro coTeHh y q11cJii 578 445? CKiJibKM BCboro TMc.flq? CKiJihKH BChoro ,n;ecHTKiB THCJITI? IloHCHH, .HK ,n;i3HaTIIC.H, CKiJibKH BChoro COT€Hh, ychoro THCHt.I, ycboro ,n;eCHTKlB THCHq, ychoro COTeHb THCHq . . MlCTHTbC.H B lJHCJll. •

243. 702 - 384 + 75

78: 13

(140

+ 350):

7 ·O

244. BypaTiHo o,n;epmaB Bi,n; MaJibBiHH 3aB,n;aHH.H po3B '.H3aTH 240 npnKJia,n;iB 3a 10 ,n;HiB. IlpoTe BiH p03B'SI3yBaB n~O,IJ,H.H Ha 2 npHKJiaAH Mettme, uim 3arrJiaHyBaJia 36

MaJibBiHa. CKiJihKH npHKJI~iB poaB'SiaaB BypaTiHo aa

10 ~HiB?

245. 3 Kr .H'CJMeHIO 38 IlO.iKllBHiC1'IO 3aMiHIOIOTb 4 Kr BiBca. CKiJihKII noTpi6Ho KiJiorpaMiB aqMeHro, ~06 aaMiHHTH 120 Kr ninca? 4 Kr- 3 Kr 120 Kr - ?

3 p a a o K M i p K y B a H H H. KomHi 4 Kr eiaca MO.iKHa aaMiHIITH, yaHBIIIH 3 Kr HtIMeHro. 0Tme, Tpe6a 'Ai3ttaTHc.H, CKiJibKH pa3iB no 4 Kr MiCTHTbC.H B 120 Kr. IloTiM cTiJihKH paaia Tpe6a 6yAe a351·r11 no 3 Kr. Ilepme aan11TaHH.H MOmHa cc}lopMyJIIOBaTH ii TaK: «Y cKiJihKH paaia 120 Kr 6iJihllle, Him 4 Kr?» CKJia~H IIOBHHii nJiaH p03B'H3yBaHH.H, 38IlHillll p03B'.H38HHfl 3a~a11i.

246 . PoarJI.HHb MaJIIOHOK. CKiJihitH Ha MaJIIOHKY qoT11p11KYTHHKiB; rrp.HMOKYTH11Ria; TPHKYTHHKie? Haaa11 eci KYTH 3 aepm11Ho10 y Toqu;i A.

247*. 5

Kr JiytIHOrO ciua 3a TIO>KHBHiCTIO 38MiHIOIOTb

BiBC.HHOl COJIOMH. CKiJibKH IIOTpi6HO Ki~rpaMiB BiBCSIHOl COJIOMH' l~06 aaMiHHTH

248°.

15 000

Kr JlytIHOro ciHa '!

BpMra.n;a caHTex11iKiB MaJia BCTaHOBHTM

160

JiiqnJih-

8 Jii 1 IHJlhHHKiB 3a )J,CHh, a;1e BCTaHOBJIIO10. Ha cKiJihKH ,QHiB paHirne cTpoKy 6p11ra,n;a

HHKiB BOl(H, no BaJia no

BlIKOHaJia po6oTy? Ilo.HCHH, HK CKJiaJIH Bllpa3 ,D;JI.H poas' H3YB8HHH aa,D,aqi, Ta 06q11CJIH :f1oro 3HffCJeHHH.

160 : 8 - 160 : 10 249°. Ha

M TKaHHHM, a Ha copo1IKY 2 M. M TKaHHHM norn11JI11 cy1<ui i copo 11K11. CyKOHb

cyKHIO

Ia 114

noIIIIIJIH

250.

18.

iiAe 5

CKiJihKM non111JIH copot.101<?

Ilpol.n-1Ta11 't.JHCJia, aannlllH Ix.

340 505

6006

502 620

345 500

4025

Ili,n;KpecJIM TpeTe qncJio. HK11ii BHI.l\HM poap.H.n; y I.J.hOMY qncJii '! O.n;nHHl.J.h HKHX po3p.Hp;iB HeMae B 1.JHCJii? CKiJihKH B q11cJii nchoro o.n;MHHI.J,h neprnoro KJiacy; .n;pyroro KJiacy'! CKiJihKH y YJHCJii coTenh; ,n;ec.HTKiB; THC.H 11? HaaB11.n;ec.HTKon11ii CKJia.n; :a;horo 1111cJia. 3arrnmH O,D,IIHHUIO .n;pyroro poapn,D,y ,n;pyroro KJiacy.

251 . Ilpo1111TaH

ITO.HCHCHH.H npo ,n;ec.HTKOBY ClIC'feMy 'lJHC-

JieHH.H.. IIepeJiitiyro11H 6y,n;h-.HKi npeJJ,MeTH, aaa11BaIOTh qncJia:

oau1t, aaa., mpu., IJ,01nu.pll, n '.Rmb, UJ.ic mh,

Ci~t i T. ,n;. ~e

qucJia. .HK~o aarrncaTH !x TaK, LQO aa KomHHM 1u1TypaJihHHM l.JHCJIOM 6y.n;e HTH 1n1cJio, Ha

namypaJtbHi

OJJ;HHUI.J,IO 6iJihll1e Bi,ZJ; rronepe.n;HbOro,

TO ,n;icTaHeMO

HamypaJLbllUit pRiJ '-IHCeJI. y HbOMY H8MMeHUie "CJHCJIO O,ZJ;l1HHI.J..H, a Haii6iJihllIOro 1.JHCJia He icHye. CnotiaTKY KomttoMy HOBOMY ttMCJIY .zi;aBaJiu oKpeMy HaaBy • .Arre TIOCTYTIOBO IlOlJ8JIH 3aCTOCOBYB8TH cne:u;iaJibHi cnoco6M JJ;JI.H HaansaHH.H ii noaHal.JeHH.H 1n1ceJI • .HKnM 611 BeJIHKHM He 6yJio qlfCJIO, iioro MOmHa 38ITHC8TH 3a .n;ono-

1, 2, 3, 4, 5, 6, 7, 8, 9, 0. 3anncyroqH i1 '-U1Tarot.n1 qncJia, BM.-

MOrOIO TiJILKH .n;ec.HTH 'IHCJIOBHX 3HaKiB -

UH<}1p:

KOpHCTOByeMO rpynyBaHHSI no 10: AeCSITh OAHHHIJ;h . ,n;ec.HTOK; lJ.eC.HTh lJ.eC.fl'rKlB - COTH.H; ,n;eG/ITh COTCHh THC.frqa; AeC.HTb THC.H'll - _n:ec.HTOK TMC.Hlf i T. /J.. TaKHH crroci6 Jii'l16H rpynaMH no 10 xapaKTepttuii /J.JI.H iJecamKOBoi" cucme.Mu 1tuc.ne1t1t.R, a6o iJec.RmK060t nyMepau)i". AecHTKOBe rpynyBaHH.H '(n1ceJI ayMOBHJio IIO.HBY noH.HTT.H npo poap.H/.1., poap.H,n;ui qac.Tia, poap.HlJ.Hi o_n;11H1,u~i. B ycHii1 uyMepau;i1, KpiM po3pH_n;1101 Jii'l1611, aacToconyIOTh ~e cnoci6 rpynyBaHHH poap.H,n;iB y KJiacH. ~06 rrpotIMTaTH 6araTOIJ;HCl>pose l.JHCJIO, .Moro 38IIHC po36HBaIOTh Ha rpyrr11, no TPH n;HcppH y Komaii1. Tptt nepmi n;nq>pM crrpaBa yTBOpIOIOTh KJiac O/J.MHHIJ;h, TPH HacTyn. HI - KJI8C Tl1C.fl'll. , , / , / / / , / / / / / / / / / /

/ / , / / / ./ / / / , l/ / / / / , , , , / / , v / , , / / / ./ ./ ./ / / v v v v v v / ./ / / , / / / / / / ./ / ./ , / / / , ,/ / / v v v I-" l/ v I / / / / / l/v vvv / v / / I// v / / / // /"'/v vvv"' // ..,.vvv // /// vv vvv // /..,.v vv vvv /"' ,,,v_,,v //_,,"' / / I/ / / l// v / v l/ /v l/1....Y ,

:. . Y

1000

TaK caMo yTBOPIOIOTh KJiac11 /J.JIH q11ceJI, .HKi 6iJihllli aa MiJILMOH. Y KomHOMy KJiaci CBO.fl JlittuJtbua oou1tuij.R. 0'AHHHn;ero neprnoro KJiacy e OJJ;HHHIJ;.H. Y lJ.pyroMy KJiaci Jii'lfHJlhHOIO OJJ;HHH.UelO e TllC.ffl{fl. qHT8IO'lJH q11cJia, Ha3HBaIOTh 'l!HCJIO O,ZJ;HHHU.b Komuoro KJiacy' caM KJiac. IlHChMOBa HyMepan;i.H rpyHTyeThCR Ha IIOMiCIJ;eBOMy 3HalJeHHi IJ.HC)>p (llO:JUijiUHUU npU.lll{Un), T06TO 3H3'-leHH.H .uuc}>pH B 38IlHCY lJHCJia 3aJiemHTb Bill. 'l'Oro, HKe Micn;e (rroau1.1,i10) BOHa aaiiMae. HKIQO 1.1,11c}>py rrepecTaBHTH Ha O,ZJ;He Micn;e BJiiBO, ii 3HaqeHH51 a6iJihllIY€TbC.H B 10 paa~

a HKI.l\O Ha 0,D;He MiCI..\e BIIpaBO, TO eThC.H B

3HatJeHH.H 3MeHIIIY-

10 pa3.

MomHa CKa3aTH, IQO HyMepa~i.H rpyHTyt ThCSI IQe Ha

npuuu,uni iJoiJa<-Jall HR,

ocKiJlhKH 1 1MCJIO

He ~o iurne,

.HK aarr11c cyMu iioro poapH~H11x ,n;o,n;aHKiB. 1-IanpttKJia,n;:

34 415 = 30 000 + 4000 + 400 + 10 + 5 252.

Ilpoti11Taii qHcJ10

723 57 4.

CKiJihKH

I..\hOMY

111cJii

0,ll;HHHI..\h y KJiaci THC.Ht.I; y KJiaci O,ZJ;HHHI..\h?

253. 1) IIopiBHHM tJHCJia B KomnoMy CTOBfl 1HKY. 1 5 30 35 10 50 300 350 100 500 3000 3500 1000 5000 30 000 35 000 y CKiJihKH paaiB a6i.nhlllyeThCSI lJHCJIO, KOJIH 1

,[(O HbOro

crrpana ,ZJ;OilHCYIOTb O,ZJ;llH HYJih; ,n;Ba HyJii; Tpl1 HyJii?

HK aMiHHThC.H qllCJIO

9000,

HKI.l\O ni,n;KHHYTH B iioro

3anucy OAHH HYJih; ,n;Ba HyJii; Tpl1 HyJii?

254.

(YcHo.) Po3a'am11 piBH.HHH.H a Heei,n.oMHM ,n;iJieHHM.

x - 4 = 24

x : 4 = 24

255. Y ca,n;y ai6paJIH 428 Kr y 20 BeJIHKHX i 12 M8JIHX K.naJIII no

256.

16 Kr CJIHB.

x. 4 = 24

x : 7 = 14

CJIMB. Yci CJIHBU poaKJiaJIH SII.D;HKiB.

BeJUiKllM Slll\HK

CKiJihKH KiJiorpaMiB CJIHB KJiaJin

MaJIHH .H~HK? Y 1 reHh aanttcaB yci 'llOTHpH~H<}>poBi 'llHCJia, y KO:>KHOMY

3 .HKHX cyrv1a u;u:c}>p ,n;opiBHIOe TpbOM:

3000 1110

2100 1200

2010 1020

2001 1002

1101 1011

3arrHIIIH sci l.JOTHp11u;11c_l)poBi lIHCJia, y KOmHOMy 3 SIKHX cyMa ~nq>p ,n;opiBHIOe JJ;BOM.

257°. 1 ~ 80

Kr oripKiB p03KJI8JIH B

OJJ;H8KOBHX .Hll\HKiB.

CKiJihKH IIOTpi6Ho TaKHX .H~IIKiB, ~06 p03KJI8CTH oripKiB?

258°. 43. 23

753 - 187. 3 40

984: 24

216: 24

(442 - 294) . 4

8· 109 - 618

O,l1J1HMI.JJ BllMIPIOBAHHH BEJI11q111-I 0.zi;HHH~i BHMipIOBaHHJI )l;OB~HHH

259. 1) Ha3BH ei.l(oMi To6i O.l(HHH~i .l(OBmHHH, noq11Ha1oqn a H8IlMeHlllOl (MiJli..litemp) i 3aKiH"(1y10q11 Hai16iJihlllOIO (KiJtoM.emp). 2) Ilpo1 n1Taii i aanaM'HTa:i1. 1M=10 .l(M 1M=100 CM 1M=1000 MM

1KM=1000 M 1.l(M==10 CM 1CM=10 MM

3) Y CKiJihKH pa3iB 1 M 6iJihllIUH Bit( 1 CM; 1 .l(M; 1 MM?

260. B11paa:u B KiJIOMeTpax i MeTpax: 67 250 M; 5080 M; 3008 M; 157 888 M. 3 pa 3 0 K Mi pl{ y Ba 1-1 H H. 1 KM CT8HOBMTb 1000 M. 0Tme, Bi,D;CT8Hb 67 250 M MiCTMTb CTiJihKH KiJIOMeTpiB, CKiJihKH THC.H 1 1 y 11HCJii 67 250, T06TO 67; 67 250 M = == 67 KM 250 M.

261 . 1) CKiJihKH nchoro coTeHh y qncJii 2800? CKiJihKH MeTpiB y 2800 CM? 2) B11pa3u 6785 CM y MeTpax i caHTHMeTpax.

262 . 3arrOBHH nponycKH T8K,

~06

piBHOCTi 6yJIH npaBHJib-

, "- HHMH. 64 KM== D M 10 KM= DM 10 M =DCM

25 M ==DCM 25 M = D .l(M 25 M= D MM

20 M8CM= DcM 20 M 8 AM = D .l(M 20 M 8 MM= D MM

63 . 3 3 Kr cnpo1 K8BH BHXO.l(HTh 2 Kr CMameHol. CKiJihKI1 KiJiorpaMiB CMameHOl KaBH BHH,D;e

264. 36 - 16. 2 978 - 984: 3

50: 7 810: 54

12 Kr cnpoi?

238 + 475 540: 6

265 . Ha MaJIIOHKY (c.42) -

KapTa rJiyxiBChKOro palioHy CyMChKOi o6JiacTi. Bi,n;cTaHh n 1 MM Ha KapTi BiAnoei.n;ae 750 M Ha Mfc~eeocTi. KopHCTy10q11ch KapToro, attaii,n;n TaKi Bi.D;CTaHi (no IIp.HMiH): rJiyXiB - llieBqeHKOBe,

rnyxiB - qepBOHe, IllaJIHrHHe - BaHHlfi, IlycToroPOA - "C.J:epBOHe - rnyxiB, YJiaHoBe - qepBOHe rnyxiB.

o flycmozopoiJ

266°. 3 KO)KHHX 100 Kr CBi»<HX c}lpyKTiB BHXO,ZJ;HTb 18 Kr cyIIIeHHX. CKiJibKH KinorpaMiB cymeHHX c}>pyKTiB o,n;epmHMO 3 900 Kr CBim11x? 267°. 3anHIIIH y MeTpax: 10 KM 80 M; 6 KM 55 M; y caHTHMeTpax: 4 M 36 CM; 8 M 2 CM; y MiJiiMeTpax: 3 AM 7 CM; 3 CM 7 MM. 268° . .no OBO"lleBoro Mara3MHY np11Be3JIH 10 MiIIIKiB 6yp.HKiB i 5 .H~HKiB IJ:H6yni. 3araJILHa Maca OBO'lJin 780 Kr. Maca OJJ.HOro MiIIIKa 6yp.HKiB 68 Kr. HKa Maca n;n6yni B OJJ.HOMY Sl~HKy? 0.n;HHH~i BHMiproBaHHn M3CH

269. flpO'lfHTaii i 38IlHll111. 1T = 1000 Kr 1Kr = 1000 r

1[( = 100 Kr 1T=10 IJ;

270. IlpoJJ;aBe~h nocTaBHB Ha Tepe311 6aHKY 3 Me,n;oM. Tepe3H rroKa3aJIH Macy 1 Kr. HKa Maca Me,n;y, .HK~o Maca

6a1-1Ku 300 r? 42

271. Maca o.n;aoro MiIIIKa n;yKpy-nicKy 1 u;. CKiJibKH MiIIIKiB u;yKpy-nicKy MO.iKHa nepeBe3TM 8BTOMo6iJieM, B8HTamHiCTb HKOro 3 T 500 Kr?

272. 3anHIIIM y KiJiorpaMax: 3 T 80 Kr; 20 000 r; y rpaMax: 7 Kr; 12 Kr y ueHTHepax: 3 T 6 u;;

273. 3H8H,l\H .!_ Bi,ZJ; 1 !.\; 2

. -1 Bl)l. 5

60 r; 3800 Kr.

1 T; -1 Bl)l. . 1 Kr. 10

274. 2 u; HaCpTM ,ZJ;810Th CTiJihKH TenJia, CKiJibKM 3 ~ KaM'SIHOro nyriJIJISI. CKiJihKH TOHH Hac}>TH noTpi6tto, ~06 aaMiHHTH 60 T KaM' HHOro ByriJIJISI?

275. Y ,n;sox . ~MCTepHax 6yJio 5000 JJ. BOJJ;H. KoJIH a O'AHiei ll;MCTepHH B3HJIH 1000 JI BO,ZJ;H' TO B o6ox I.J;HCTepHax BOAR CTaJio nopiBHY. CKiJibKH Jii TpiB BO,ZJ;M 6yJIO B KO.iKHiii ~HcTepnicnoqaTKy?

276. 32000·10: 100

(340 + 600) : 10

4·13 57: 3

43·14 - 549 : 9 42·13 + 78 : 13

277*. Maca 15 JI racy 12 Kr 300 r . .HKa Maca 60 JI racy? 278°. 3anHIIIH, CKiJibKH KiJiorpaMiB y 4 T; y 6 u.; y g u; 15 Kr; y 12 T; y 130 T 300 Kr; TOH H y 5000 Kr; y 20 000 Kr; y 300 000 Kr; y 420 000 Kr; rpaMiB y 2 Kr; y 20 Kr; y 2 Kr 500 r; y 12 Kr 30 r.

279°. Ha o.n.Hii1 ,n;iJIHHa;i rocno.n;apKa BHpocTHJia 124 Kr noMi.zi;opiB, a Ha .zi;pyriil - y 2 paaH 6iJJ.bIIIe. 't.JeTBepTy qacTHHY scix noMi,n;opiB Botta aacoJIHJia. CKiJibKM KiJiorpaMiB noMi,n;opis 3acoJIMJia rocno.zi;apKa?

280. IIpoq:HTai1, BCTaBJIHI011H

6 M = D MM 6 M = D CM 6 M = D ,ZJ;M

npony~eHi qHcna.

5 M 2 ,ZJ;M = D ,n;M 5 M 2 CM = D CM 5 M 20 MM = D MM

26 000 M = D KM 3030 M = D RM D M 9000 CM = D M

281. 3anHIIIH B KLTiorpaMax: 48 000 r; 20 T 20 Kr; 3 u; 25 Kr; 500 000 r; 15 T 630 Kr; 3 n. 5 Kr.

)

282. 3 q11ceJI 20, 25, 30, 35 BM6ep11TaKi3HfflJeHH.H 6yKBli x, ,ZVIH HKMX rrpaBHJibHa HepiBHiCTb 120 - x .< 95. 283. 420: 7 50路8

200: 4 300路5

48 000: 8: 3 30路 7 + 3

180 + 20. 5 300 + 300: 2

284. 3 o,n;Hie1 BHllIHi ai6paJIH 16 Kr .Hri,n;, a 3 .n;pyrol 19 Kr. Yci .Hro,n;11 po3KJiaJIM B .H~HKH, no 7 Kr y KO)IOIHH. CKiJibKH noTpi6Ho ,n;JIH IJ;boro 51~HKiB? PoaB '.HmH aa,n;at.Jy, a rroTiM cK11a,n;u o6epHeHy aa,n;aqy i p03B' .H)Klf 11.

285. Jl:JI.H np11:roTyBaHH.H 6eTOHY Tpe6a B3.HTM 1 'l{3CTHHY u;eMeHTY, 2 t:1acT11u11 rricKy i 4 qacTllHM m;e6eH10. CKiJibKH rroTpi6Ho B351TH oKpeMo rricKy li ~e6eH10, .HK~o e 8000 Kr n;eMCHTy? 286. Ha Ma1110HKY KapTa YKpa!nn. Mac1IITa6: B 1 CM 100 KM. Kop11cTy10't11Icb KapT010 i MaCIIITa6oM, 3Hai1,n;11 npoT.HmHiCTb TepnTopii Y Kpai'.HH ia 3axo,n;y Ha Cxi,n; i a IliBHO"lli Ha IliB,n;eHb.

287*. KopoBa AaJia aa ,n;Ba y.n;o! 25 JI MOJioKa. BpaH~i BoHa ,n;aJia Ha 3 JI 6iJILIIIe, Him yBe"l1epi. CKiJihKH niTpiB MonoKa ,n;aJia KO PO Ba BpaHu.i i CKiJihKl1 yseqepi '?

3 JI

YpaH1~i----------------- } YBeqepi-----------~--

288°. 3anMIIIH B KOniliKax: 3 rpH.; 25 rpH. 5 K.; 10 rpH. 5 K • •

IlopiBH.flH BeJIU"lIHHH:

1510 K. i 15 rpH. 10 K.

289°. ABTOM06iJih Ha KOmHi 4 KM UIJI5IXY Bl1Tpa'(1ae 360 r 6eH3HHY' a MOTOI..J.HKJI Ha 3 KM IIIJI.HXY BHTpaqae 120 r. Ha cKiJihKH rpaMiB 6eH3MHY 6iJihlIIC BMTpaqae Ha Bi,n;cTaHi 1 KM aBTOMo6iJib, Him MOTO~HKJI? 0AHHH~i BHMipJOBaHHB

'lacy

290. 1) Ilp0"4HT8H i CilHIIIH. B o,n;Hili .n;o6i 24 ro,n;MHH.

60 XBHJIHH. B o,n;Hitt XBMJIMHi 60 ceKyH,n;. B o,nHiif ro,n;HHi

2) CJIOBa zoouua,

ce1CyttiJa 6iJI.H "llHCeJI IlHllIYTbC.fl CKOpo"lleHO, 6ea KpaIIOK (HanpttKJiaA: 9 rOA 25 XB 30 c). 3anHIIIH I..J.IHl>paMH: OeC.Rmb ZOiJUlt CiMHllOij.Rmb X6UJlUH copoK oei ce1<ynou. 3) IOHaK npo6ir 1 KM aa 3 XB 7 c. 3arrHIIIH u;e 'lJHCJIO B ceKyHA8X. X6UJlU1lll,

291. 3anHIIIH y CCKYHAaX: 2 XB; 3 XB 12 c; y XBMJIMHax: 4 ro.n;; 300 c; y ro,n;uHax:

3 'A06H; 180 xn.

292. 1) 3a 1 rOA TYPHCT npoiiIIIOB 4 KM. 3a CKiJihKH XBHJIHH BiH rrpoxo,n;MB 1 KM? 2) XJIOII'lIHK rrpo6ir npo6iraB 38 1 c?

30 M 38 6 c. CKiJihKH MeTpiB BiH

293. 3i JlhBOBa .n;o KHeBa KYPCOM "lie pea m11TOMMp o.n;HoqacHO BMJieTiJUI .n;Ba JiiTaKII. qepe3 ro.n;HHY QJJ;HOMY JiiTaKy 11\e 3aJIHlll11JIOCh JieTiTM ,ZJ;O jKHTOMHpa 50 KM, a .n;pyrHH yme 6yB Ha Bi.n;cTaHi 65 KM 38 m:ttTOMHpOM. Ha CKiJibKH 6i11hrne J{iJioMeTpiB nponeTiB .n;pyrIIii JiiTaK?

294. KoTpy ro.n;HHY noKaaye KOmHHH ro.n;HHHHK? KoTpy ro.n;11tty noKame KO:>KHHH ro.n;HHHHK qepea 42 xB?

295. 3 4 Kr npoca BHpo6JIHIOTb 3 I{r nllloHa. CKiJihKH KiJiorpaMiB rrllloHa s11ii,n;e a 1 u; 20 Kr rrpoca·! 296. 1) 3anHIIIH y ro.n;HHax: 240 xB; 2 .n;o6:tt; y XBHJIHHax: 120 c; 3 ro.n;; y ceKyH,n;ax: 4 XB; 5 XB 30 c. 2) (YcHo.) YqHi 6yJIH Ha eKcKypcii 1 ro.n; 20 XB. CKiJihKH BChoro XBHJIHH TPHBaJia eKCKypciSI?

3) ro,n;HHHHK noKaaye niB Ha .n;ecSITY neqopa. CKiJihKH ro,n;HH i XBMJIHH MHHYJIO Bi.n; noqaTKY .n;o6H?

297. 2408 - x = 957

x - 5450 = 9758

10 - x > 5

298*. ~eC.HTHMeTpOBY KOJIO.ZJ;Y poapiaaJIH Ha 8 piBHHX qaCTHH, a ceMMMeTpoBy KOJIO,ZJ;H ,ZJ;OBIIIi •!

299°. 218 + 385

800 -

+ 47 (213 + 478)

5. IIIMaTKH (ni,n;piaKn) HKoi

925: 37 536: 67

360 000: 10 440 - 40· 2

300°. ,[(JISI 4 KOHe:ti i 24 Kopin BH'AaJilf 2 a; ciHa. KomHOMY KOHeBi .n;aBaJIH 8 Kr citta. CKiJihKM KiJiorpaMiB ciHa .n;aBaJIH o.n;Hiii KopoBi?

.,,

AHHR I BIAHIMAHHR

. •

Cl>POBMX 'IMCE.n

,D;O,D;ABAHH.H I Bl,[(HIMAHHH HA'fYP AJibHllX q11CEJI 301.

IlpotIHTaii IlOHCHeHHH npo ,n;iro ,n;o,n;aBaHHR Tall 33KOHM.

By,n;L-SIKi ,n;Ba HaTypaJihH11x '-IMCJia Mom.Ha ,n;o,n;aT11. qncna, HKi ,n;o,n;aIOTh, Ha3HBaIOTh ,n;o,n;aBaHH.H -

7 i 5 -

iJoiJau.1ca.Aut,

cyM010. HanpllKJia,n;:

12 -

,ZJ;O,ZJ;8HK:H, a

a pe3yJihTaT

7 + 5

= 12.

TyT

cyMa. 3HaK ,n;o,n;aBaHHH

(IIJIIOC). ,ll;iro ,n;o,n;aBaHH.H MOm.Ha BM3HRlJHT11 33 ,ll;OIIOMO-

roIO IlOCJil,lJ;OBHOCTl HaTypaJibH11X '-BfCeJI.

1 2 3 4 5 6 Ilo3HatIHMO B IJ.hOMY p.H,n;i 411CJio

Bi,n;Jii'-IMMO Bi,n; Hboro

BIIpaBO II'.HTb tIHCeJI. ,ll;icTaHeMO qncJIO BaeTbC.H CYMOIO tIHCeJI

12,

HKe Ha3H-

7 i 5.

IlepecTaBHHH aaKOH )J;O)J;aBaHHH. Ilo3HatJHMO B HaTypaJibHOMY pH,n;i Cil0'-18TKY 'lJJ1CJIO

. . . Bl,ll_JIIqHMO ClM qHceJI. 1 2 3 4

®6

a IIOTiM Ri,n; Hboro

7 8 9 10 11

12. OTme' 7 + 5 = 5 + 7.

,ll;icTaHeMo 3HOBY "CJHCJIO

. . KOHyeTbCH plBHICTb

TaK caMo ,ZJ;JIH 6y,n;h- .HKHX HaTypaJILHHX 'lIHceJI

ai b

BH-

a + b = b + a, .HKa BHpamae nepecTaBHHH 3 8KOH ,n;o,n;aBa HHH.

BiiJ nepecmanoeKu iJoiJanKi6 cyMa ne ai.iinroembca.

Cnonyqnuif. 3aKOH ~o~aBaHHH. .D;o,n;aMo TPH 'tJHCJia 4, 3 i 6. Cno"tJaTKY .n;o cyMH "(nicen 4 i 3 .HKa .n;opiBHIOe 7, .n;o,n;aMO qucJIO 6. ,n:1u1 IJ;bOro Bi,n; cy MH 'll ttCeJI 4 i 3, T06TO Bi.n; q11c.na 7' Bi,n;Jii t.IMMO BnpaBO 6 "llHCeJI. .D:icTaHeMO lJHCJIO 13.

1~ ~ 8 9 10 11 12

® (4 + 3) + 6 = 13

Tenep .n;o "llHCJia 4 ,n;o,n;aMo cyMy 'tJHCeJI 3 i 6. 3 + 6 = 9. 0Tme, Tpe6a Bi,n; qucJia 4 Bi.n;Jii"lll1TM BIIpaBO 9 "l{MCeJI. ,D;icTaHeMO 3HOBY "tlHCJIO 13.

1 2 3 4

~ ~

9 10 11

4 + (3 + 6) = 13 B o6ox BMna,n;Kax ,n;icTaJIH o.n;:ny ii ·ry caMy cyMy. (4 + 3) + 6 = 4 + (3 + 6) TaK caMo .D;JI.H 6y.n;h-.HKHX HaTypaJibHMX qnceJI . BMKOHyeTbC.H plBHlCTb

a, b i c

(a + b) + c = a + (b + c), rqo BHpamae CilOJIY"l!HHH 38KOH ,n;o.n;aBaHH.H.

HKUJO iJo cyMu iJeox 11,uceJ1, nompi6no iJoiJamu mpeme 1£UCJ1,0, MO:J1Cna iJo nepmozo 'tUCJl,a iJoiJamu cy MY iJpyzozo i mpemboz.o. 3 nepecTaBHoro Ta cnoJiyqnoro aaKoHiB .n;icTaeMo ~e o,n;. ... HY BJiacTHBICTh .n;11 .n;o,naaaHH.H. Y cy Mi KiJl,bKOX iJoiJanKiB Mo:ncna nepecmaBJ1,Rmu iJoiJanKU i 6pa1nu ix y iJy31CKU 6yiJb-JlKUM 1tUHOM. Hanp11KJia.n;:

1+ 2+ 3=3+ 2+ 1 1 + 2 + 3 + 4 = (1 + 4) + (2 + 3) 34 + 249 + 26 = (34 + 26) + 249 = 60 + 249 = 309 302. (Ycno.) 237

+ 190 + 10

280 + 467 + 20 48

75 + 160 + 40 + 125 289 + 60 + 11 + 13

303. HKi 3 noJJ;aHHX 3aAa':i poaB 'H3YIOThCH Aiero ,n;o,n;aBaHH.H? 3anHllIH p03B' .H3aHH.H [(HX aa,n;a'l. ~e

BiA CMymKH Bi,n;piaaJIM 8 AM, a ITOTiM CKiJihKH BChoro caHTMMeTpiB BiApiaaJin?

,ZJ;M.

2) Ha raJI.HBnni pocJio 12 rpw6in. 3 u:nx 3 6iJinx, pernTa -

JIHCHtn<n. CKiJihKH JIHCMt.IOK pocJio Ha raJI.HBHHi?

3) y KOHBepTi 6yJIM Jil1CTiBKII. ~iBqJ1HKa B3.HJia 3 KOHBepTa 8 JllICTiBOK. y KOHBepTi 3aJIHIIIHJIOCH 4 JIHCTiBKH. CKiJihKM JIIICTiBoK 6yJio B KOHBepTi cnot.JaTKy?

Maca ,n;11Hi 2 Kr, a Maca KaByHa 3Haii,n;M Macy KaByHa.

Kr 6iJihma.

Ileprue t.IHCJIO a, JJ;pyre b. Ha cKiJihKH nepllle 'llHCJio 6iJihme, Him ,upyre? CKJia,n;H Bnpaa Ta 06t.1ncJIH iioro 3H8tieHH.ff, .HK~O a== 13, b = 7.

304. 4 + 5 7+6 305. 356

54 + 31 28 + 17

+ 49 + 188

340 + 120 584 + 175 107 + 285

+ 74 + 399

306. ,l(Ba noia,n;11 o,n;ttoqacHo BHHllIJIH HaaycTpit.1 o,n;nH OAHOMY 3 ,D;BOX MiCT. Ilepll1Hi1 TIOl3A npoiiwoB .no 3YCTpi l.Ji 245 KM, a APYrMii - Ha a KM 6iJihWe. HKa BiACT8Hh Mim U.HMII MicTaMH? CKJiaAII BHpaa )J;JI.H po3B 'H3yBaHHH aa,n;at.Ii Ta o6tIMCJIH i1oro 3Hat.IeHH.H, .HKI~O a.= 78.

307°. 3 o,n;Horo MiCTa B npOTMJiemHHX Hanp.HMKaX O,D;HOl.laCHO BH1xaJIH BeJioc11ne,n;HcT i MOTOU.HKJiiCT. Ao neBHoro MOMeHTY BeJIOCHrre.n:ncT IIOAOJIRB 42 ltM' a MOTOUHKJiiCT 3a u.eii caMHH qac - Ha 89 KM 6iJihIIIe. 3HRiiAH BiACT8Hh Mim HHMH B [(e:ii MOMeHT.

308°.34 + 25 34 + 20

57 + 28 57 + 1

340 + 200 340 + 20

458 + 249 307 + 127

309.

3 npHKJiaAy Ha AO,ZJ;aBaHHH CKJiaJin npHKJia,n; Ha Bi,n;ttiMaHHH. IT pol.I MT a ii [(i np11KJia,n;11.

8 + 5 == 13

13 - 5 = 8

310. Ilpot.IMTaii IlOHCHeHH.H rrpo AilO Bi,D.HiMaHH.H. Biih-tiMaHH.R.JU ttaauBa€ThC.H AiH, 3a )J;on0Moro10 .HKo1

. .

aa J(8HOIO cyMOlO )J;BOX JJ;OJ(aHKlB 1 OJ(HMM 3 HHX BlAllIYKYCThCSI .n;pyrHH .n;o,n;aHOK. qHCJIO, BiJJ; SI:Koro Bi,n;HiMalOTb, Ha311Ba€ThC5I 3Me1tLUytJaHLtM; quCJIO, .HKe BiAHiMaIOTb,BiiJ'€M1lllK0Jll, a peayJihTaT pi.1Hul{e10. HanpMKJia,ZJ;: 13 - 5 = 8. TyT 13 - aMeHrnyaaHe, 5 - BiJJ;'eMHHK, 8 pi3HMI.VI. 3Haxo.n;meHH.H pi3HMI1;i 13 - 5 MOmHa IIOKaaaTH aa ,D;OIIOMOrOIO HaTypaJibHOro p.H,n;y.

1 2 3 4 5 6 7

®9

10 11 12

IloaHaqMMO B HaTypaJihHOMY pa.n;i q11cJio 13. Bi,ZJ;JiitIHMO Bi.n; HbOI'O BJiiBO n' 51Tb qnceJI. ,IJJcTaHeMO tIHCJIO 8.

13 - 5 = 8 J];JI.H 3'.HcysaHHSI npHHOMiB Bi,n;HiMaHHSI samJIMBe 3HaqeHH5I Mae npanHJIO Bi,n;HiMaHHSI cyMH Bi,n; qHcJia.

11{06 aiiJ 1Lucaa eiiJnamu cyMy iJeox inmux 1Lucea, iJocmamnbo nocaiiJoeno eiiJnamu Ko:>1enuu iJoiJanoK OKpeMO. 28 - (8 + 9) = (28 - 8) - 9 = 20 - 9 11

3a IJ;MM npaBMJIOM q.HCJIO MOmHa Bi/~HiMaTH qacTHHaMH.

37 - 9 = 37 - (7

+ 2) = (37 -

7) - 2 = 30 - 2 = 28

311. HKi a rro;i;aHHx aa.n;a1:1 poaB'.n3y10ThC.H .n;iero si.n;HiMaHHsr? 3anHlllH po3B' SI3aHH.H IJ.HX aa.n;ac1.

1) Cepe.n;HLOA060B11i1 np11pic·r Macu 6H1:1Ka 800 r, a TeHa 70 r MCHllIHH. .HKMM cepe,n;Hh0,D;060BHM JIHtIKH np11picT MaCH TeJIHtIKH? 2) Ha ,n;Box OAHRKOBHX ;i;ocJii,n;1111x ,n;iJISIHKax nociSIJIH m11To i IlllleHHIJ;IO. m11Ta ai6paJIH 22 Kr, a IIIIIeHHUi 36 Kr. Ha CKiJihKH KiJiorpaMiB 6iJihllle ai6paJIH nrneHMIJ;i, Him )KHTa? 3) Heai,n;oMe tIHCJio 3MeHllIHJIH Ha 15 i B peayJILTaTi .n;icTRJIM 20. 3Haii.n;M HeBi,n;oMe l:IHCJIO. 4) CyMa ,n;Box l:JHCeJI 40, neprne 3 HMX 8. 3Haii.n;H ,n;pyre qncJio. 5) Y 6eHao6al(i aBToMo6iJISI 6yJio a JI 6eH3HHY. 3a .n;eHh BHTpaTHJIH b JI 6eHantty. CKiJILKM JiiTpiB 6eH3HHY aaJIHIIIHJIOCSI B 6eHao6au;i? CKJia,n;u s11paa .ZJ;JIH poaB 'H3yBaHHH 33,ZJ;al:li Ta 06l:IHCJIH lioro 3Hal:JeHHH, HK~O a = 80, b = 65.

6) YqeHh aa,n;yMaB qncJio. HK~o i1oro Bi,n;HSITH Bi,n; 80, ~e aaJIHIIIHThC.H 20. HKe qncJio aa,n;yMaB yqeHh? 312. 8 - 7 75 - 23 680 - 35'0 14 - 8 61 - 25 487 - 259 313. 857 - 509

834 - (400 - 218)

314. 3 950 Kr nrneHHQi

H8MOJIOJIH

834 - 400 - 218

818 Kr 6opOillHa,

a pern-

Ty cTaHOBHJIH BIICiBKII. Ha cKiJihKII KiJiorpaMiB 6iJibrne ,n;icTaJil1 6opOIIIH8, Him BMCiBOK?

315°. 3anHIIIH

pi3HHII;IO T3KHX qnceJI: 3MeHillyBaHe

b i 10. HKIIJ;O}?, = 200, b = 180.

Bi,n;'eMHHK BHpamennii' qacTKOIO 't.JHCeJI 3HaqeHH5I pi3HHI~i,

316°.65 - 23 • 81 - 47

380 - 200 380 - 20

317. yqHeBi Il0Tpi6Ho 483 i 255. + 483 255 738 IlepeBip, 't.!H

475 - 258 854 - 126

6yJio 3H3HTH cyMy

3HaH.n;H

356 - (104 - 87) 356 - 104 - 87 i

pi3Hll~IO qnceJI

483 255 228

rrpaBHJibHO yqeHb BHKOHaB 3aB,ZJ;8HHSI.

Ilo.HCHH, .HK Tpe6a 38IlHCYB8TH qncJia npH IlHCbMOBOMy

.n;o,n;aBaHHl 'l{H Bl,D;HlM8HHl.

fl UCbM06e OOiJa6anna i 6iiJniManna 6azam0"1Ul}Jpo6UX 1£ucea euKonyonbCR maK caMo, i eiiJniManna mpu"1u<J>poBux -iucen.

iJoiJaeanna

318. 1) BnKoHaH .n;i1 a no.HcHeHHHM. 45 374 + 8406 5478 - 2349 2) 06tIHCJIH 3Ha'lleHHSI a = 3575 i b = 75 431.

319. x 320. B

+ 34 013 = 764 354

BHpaaiB

a + b

b - a,

.HK~O

x - 20 244 = 45 645

ono-qecxoBM~i a6epiranacH KapTorrJI.H. KoJIH a oBo-

qecxoBnm;a BHBe3JIM

3240

7250 Kr KapTOITJii,

3aJIHIIIHJIOC.H Ha

Kr MeHIIIe, Him BHBe3JIH. CKiJibKH KiJiorpaMiB

KapTOITJii 6yJIO B OBOl..JCCXOBH~i?

321. 3 22 Kr 6aBOBH.HHOro HaciHH.H O'AepmaJIH 5 Kr OJlll. CKiJihKH HaciHHH IIOTpi6Ho, ni;o6 O'Ae~aTH

322掳. 76 032 + 13 452

28 340 + 2451

89 482 - 76 032 28 340 + 32 451

75 H:r OJii!?

913 452 - 13 452 5459 - 825

323掳. IliCJUI Toro .HK po6iTHHK11 B~peMOHTYB<lJil1 3650 M rnoce, 1M 3aJI11rnuJioc.H Bi,n;peMOHTyBaTn Ha 1270 M 6iJihme. CKiJihKH MeTpiB rnoce noTpi6Ho 6yJio ni,n;peMOHTyBaTn? TO b + c = a . .HK Bi,n;HiMaHHH rrepeBipHTH ,ll;O,A8B8HH.HM? 2) IIepeBip ,n;o,n;aBaHH.HM, qn npaBMJihHO BHKOHaHo Bi,ZJ;HiMaHH.H: 84 7 294 - 235 451 = 611 843. 3) HKni;o a + b = c, TO c - a = b. HK ,Ao,n;aBaHH.H nepeBip11Tl1 Bi,n;HiMaHH.HM? 4) Ilepenip Bi,n;HiMaHH.HM, l.JH npaBHJibHO BHKOHaHO ,n;o.n;aBaHH.H: 29 035 + 43 462 = 72 497.

324. 1) HK~o

a - b = c,

325.

48345 + 3328

40725 + 12944

78864 - 3562

50791 - 12375

326. Ha 3 MaUIHHM HaBaHTamHJIM 10 480 Kr nicKy. Ha rreprny i ,Apyry McUllHHH pa30M HaBaHT8.iKHJIH a na ,Apyry i TpeTro - 6180 Kr.

10 480 Kr {

8350 Kr,

1- ? l

8350 Kr II - ? f l 6180 Kr III - ? f

PoarJI.HHh BHpaa11 10 480 - 8350 i 10 480 - 6180, CKJia,n;eHi aa yMOBOIO 3a,n;aqi. II po ni;o ,n;iaHaeMOC.H, o6qncJIHBIIIl1 ix aHa-cieHH.H? BnKona:H o6qncJieHH.H.

327. Y 路rpbox uncTepHax 6yJio 10 720 JI naJlhHoro. Y nepmiii i TpeTiH UHCTepHax pa30M 6yJIO 78 70 JI, y .n;pyri:H i TpeTiH -

6020 JI. CKiJihKH JiiTpiB naJihHoro 6yJio B TpeTili

~HCTepHi?

328. Ha ,ABOX 6apmax 6yJio 18 600 KaByHiB. KoJIH a nepmoi 6ap.m.i BHB8HTa.m11JI11 2600 KaByHiB, Ha o6ox 6apmax KaByHiB cTaJio nopiBHY. CKiJihKH KaByHiB 6yJio Ha KOmHii1: 6ap.m.i CII0't{8TKy路! 52

329°. 1) 3Hai1,zvi cyMy ~HceJI: iJeicmi muca'l 'lOmupucma cop o1< Ci.:41 i iJec.Rmb mUCJl'l OBiCmi aici.M.

3MeHlllyBaHe

90 666,

Bi.n;'eMHHK

70 238.

3HaH,ZJ;H

pl3HMIJ;IO.

3) 3MeHlll 87 840 Ha 9535. 4)

PoaB'.HmH npttKJia.n;H i apo6u nepeBipKy.

28 540 - 6807 330°.

13 575 + 95 880

3a .n;aHMMH Ta6JIHIJ;i 3Haii.n;H, CKiJihKH TKaHHHH BHKO-

pHCTaJI ll ,ZJ;JI.H IIOlllH1'T H o.n;Hie1 HaBOJIOt:.IKM.

Ha3Ba

Ha o,zu1H

KiJihKiCTh

BHpo6y

BHpi6

llITYK

HaeonoqKa

3M 80

fl pOCTHp8,ZVIO

331.

163 250

8073

Bchoro

4 2

a- b

a+b

} 12

b·lO

a: 10

332. 1) Ilo.HCHH p03B'H3yBaHHSI. 9997 1000 1000 + 5 3 52 10002 997 948

40 CM

a + 7000

4004 - 328 3676

2) BHKOHa:H .n;ii IIHCbMOBO.

1998 + 8

2000 - 2

333. BnKoHa:H _n;ii i apo6n 307 857 + 84 408 334.

MiC.HIJ;i

10 008 - 125

100 000 - 37

nepeBipKy.

67 082 - 9556

38B0t( BHilyCTHB

4603

aBTOM06iJii.

CKiJihKH aBTOMo6iJiiB BHIIYCTHB aaBo_n; OKpeMo aa Kom"

•

HHH MIC.HIJ;b, rrycTHB MiCSIIJ;i -

335*.

.HK~O

2978 aBTOMo6iJiiB, 3093'!

,lJ;piT 38BA0B)KKH

•

38 rrepllllU:I I .n;pyrHH MIC.HI.I.I BIH BH-

250

nepIIIHH

TpeTiii

3 '-IaCTHHH. )];Bi TpeT.H qacTHH8 Ha 10 M ,ZJ;OBllla

M poapi3aJIH Ha

3 HHX piBHi Mim co6010, a

Bi.n; KO)KHOI 3 rreplllMX ABOX • .HKOI AOB)KHHH 6iJihIIIa qacTMHa ~poTy?

336°. Maca RBTOMo6iJiiB «TaBpi.H», «BoJira» i «HHBa» paaoM 4120 Kr. HKa Maca KomHo1 MamMH.Ji oKpeMo, .HKru;o Maca «Taapi1)> i «BoJirH» 2 020 Kr, a Maca «BoJirH» i «HHBH)> 3460 Kr?

rl,

4120 Kr

337°. 56 + 185 + 357

•

« aspl.H)> - • { «BoJira)> - ? «HHBa)> - ?

2020 Kr } 3460 Kr

121 393 - 65 850 69 760 - 23 580

375 + 109 - 251

68 000: 100 720 - 20. 7

338. (YcHo.) 1) 3MeHlll Ha 4 THC.Hqi KOmHe q11cJio: 55 778;

9000; 60 000; 4375. 2) 1·12 - 7 250. 100 + 1

60 000 : 100 - 10

339. Poaa'.HmH a KOMeHTyBaHH.HM.

25 + 43

+ 35 + 37 + 20

340. 30 001 - 7 341. IIepeBip,

2745 6549 + 275 9569

~1H

180 + 230 + 20 + 70

40 004 - 38

700 020 - 30 003

npaBMJihHO BMKOHaHo ,u;o,nasaHH.H.

945 45803 + 97 46845

342. 06'tIHCJIH cyMH, 3811HCyIOt.IH ,n;o,n;aHKH CTOBI1qHK8MH.

57 453 + 8480 + 876

3405 + 34 005 + 25 788

343. ,ll;osmMHa Ilin,n;eHHoro Byry 806 KM,

~HicTep HB

556 KM ,n;OBlllHH aa Ilia,neHHHH Byr. ,ll;Hinpo Ha 839 KM J(OBlllHH aa ~HicTep. 3Haii,n;11 ,u;oBmHHY ,ll;Hinpa.

344. IlepHMeTp TPHKYTHHKa 12 CM 6 MM. ,ll;onmMHa OJ(HieI CTOpOHH 4 CM 8 MM, }J.pyroi 3 CM 9 MM. 3HaH,UH ,lJ;OBmHHY TpeTbOI CTOpOHH.

345°. 240 - 80 < 300 - 80

240 + 80 D 300 + 80 54

350 - 70 D 350 - 40 350 + 70 D 350 + 40

346째. y neplUOMY OBOtJeCXOBU~i 6yJIO 3850 II. KanyCTM, a B ~pyroMy 4090 II,. y neprne OBOt.IeCXOBH~e npHBe3Jil1 ~e 358 II. KanycTH, a B ):(pyre 245 u;. Y .HKOMY oBoqecxoBH~i CTaJIO KanyCTH 6iJihIIIe ii Ha CKiJihKll l.(eHTHepiB?

347. (YcHo.) 35 - 7 - 8

42 + 8 - 14

40 - 8. 2 40: 8. 2

58 - 8 + 16 56: 8 + 17

348. 3anHllIH B MeTpax: 5 KM 600 M; 2 KM 80 M; 1000 CM; y caHTHMeTpax: 4 M; 8 M 20 CM; 10 M 5 CM; 300 MM.

349. 50 778 - 21 930 - 19 855

54 127 + (25 705 - 9777)

5888 - 3409 + 1758 1 7 788 - (94 73 - 6207)

350. PoarJI.HHh poaB'.HaaHHH aa~aqi a 6yKBeHHMM ~aHHMH. 3 a ~ a q a. KpiCJIO KOIIITye b rpH.' a CTiJieIJ;b y 3 pa3lf ~erneBrnni1. CKiJihKM I<OIIITYIOTh KpicJio i cTiJ1e1~h paaoM?

PoaB'513aHHH b - Ba pTiCTh KpicJia; b : 3 - BapTiCTh CTiJILIJ,H; b + b : 3 - BapTiCTh KpicJia i CTiJihl.(.R pa30M. y qoTHpH paa11: 6iJihme Bi~ neprnoro. 3uaif~H cyMy u;11x qHceJI. CKJia~H nHpaa Ta o6qHCJIH iioro 3HaqeHHH, HK~O a= 224.

351 . Ileprne qttcJio a,

~pyre -

352. BHaHaq Macy KOmHoro nTaxa.

353. 3 q11ceJI 1, 5, 20, 30 BHilHlllM Ti 3HaqeHH.H 6yKHH, ,D;JI.H

.HKMX npaBHJibHl HeplBHOCTl.

60 : k > 4

50 - k < 25

1 7 + k > 40

354°. 3 ,n;Box Kny6KiB rnepcTi cnJieJI11 3 rnano-crKH. CKiJibKH T8KHX manoqoK MOmHa cnJieCTl1 3 10 KJiy6KiB mepcTi? 355°. 72 420 - (11 725 - 9428)

7807 - (3655 + 977)

,ll;O,ll;ABAHHH I Bl,ll;HIMAI-IHH IMEHOBAHHX qlf CEJI 356. (Ycno.) 1 T - 250 Kr 1 M - 37 CM

10 T - 2 U. 10 ,[(M - 4 CM

2 Kr - 300 r 2 M - 30 CM

npaBH.TlhHO BHKOHaHO ni,n;HiMaHH.H, i . no.HCHM, tJMM p1att.HTbC.H no,n;aH1 aarrucII. 53 M 08 CM - 9 M 73 CM= 43 M 35 CM

357. 1) IlepeBip,

5308 - 973 4335 (cM)

l:{H

53 M 08 CM - 9 M 73 CM 43 M 35 CM

2) 3HaH,D;H CYMY i pi3HHU.IO 7 KM 080 Mi 5 KM 185 M. 358. 3a 10 c ,n;inqHHKa HaJii'lIHJia n ce6e 12 y,n;apiB nyJihCy. CKiJibKH y,n;apiB ttaJiiq11T1> ,n;iB'lIIIHKa aa XBMJIMHy?

359. 1) IlepeBip, q:u npaBHJibHO BHKOHaHO ,n;o,n;anaHH.H. 27 T 459 Kr+ 9 T 780 Kr= 37 T 239 Kr

27459 27 T 459 Kr + 9780 + 9 T 780 Kr 37239 (Kr) 37 T 239 Kr 2) 3HaH,[(H cyMy i pi3HHI.J.IO: 19 Kr 450 r i 7 Kr 080 r. 360. Maca rycKH 5 Kr 720 r, KYPKH - Ha 3 Kr 345 r MeHIIIa, Him Maca rycKM, a iH,n;MKa - Ha 4 Kr 390 r 6iJ11>IIIa, Him Maca rycKH :H: KYPKH paaoM. HKa Maca KypKM, rycKH Ta iH,n;HKa paaoM?

361 • Maca 50 o,n;HaKOBHX rraKeTiB a 6opoIIIHOM 1 .HKa Maca 100 T8KHX rraKeTiB? 56

u. 50

Kr .

362째. IlpH,n;6aJIH 180 JI 6eH3HHY. ,Il;JI.H aanpaBJieHH.H 8BTOM06iJI.H BMKOpMCT8JIH TpeTIO qacTHHY 6eH3J,niy. ,ll;JUI 38npaBJie:HH.H TpbOX MOTOIJ,HKJiiB BliKOpliCTaJIH no 9 JI 6eH3HHY. CKiJihKH JiiTpis 6eH3HHY aaJIHIIIHJIOc.H? 363째. 10u;9Kr - 5u;68Kr 5 Kr 708 r + 4 Kr 840 r

25 073 - (785 + 7 453) 49 507 - (4305 - 947)

364. Ilp0'lll1TaM TiJihKH Ti lIHCJia,

38KiH'llYIOTbCH HyJieM:

15;40;99; 100; 151;250; 1000; 1009; 1200. qHcJia, ~o anKiHtIYIOTbC.H HyJieM a6o KiJihKOMa HYJI.HMH, H8311B8l0Tb KpyzJtU.MU 'lllCJlll.JJUl. 40, 100, 250, 1000, 1200 - KpyrJii "lJHCJia. 365. Komne "l!HCJIO MOJKHa 3anHcaTH y BHrJI.H,n;i cyMH a6o piaHHUi KpyrJioro ii o,n;HOUHc}>posoro 'CJ:HceJI. HarrpHKJia,n;: 37=30 + 7

37=40 - 3

152=150 + 2 152=160 - 8

3arrHIIIH KO:>KHe 3 'tlHCeJI 76 i 379 y Bl1TJIH,ZJ;i cyMH i pi3HH[(i KpyrJioro Ta OJJ;HOI.J;HCpposoro l:IHCeJI. 366. PoaB' amn aa,n;a-ciy CKJia,n;aHH.HM snpaay. 3 MicTa B ceJio BHMlllOB TypttcT, a ia ceJia HaaycTpiq i1:oMY Bn1xaB BeJiocnne,n;11cT. ,l.(o aycTpi qi TypncT npoiiIIIOB c KM' a BeJIOCHne,n;HCT npo!xaB y 3 pa3H 6iJiblIIY Bi)J;CTaHb . .HKa BiJJ;CT8Hb Mi:>K MiCTOM i ceJioM? 424 888 - 285 099

367. 340 055 - 48 380

368. 3ttaii,n;H nepHMeTp KO:>KHOl ,n;iJI.HHKH aa IIJI3HOM. i' -

20M ~

KapTon1u1.

OripKH

I I

IloMiAOPH ~

369. ITeprnoro ,AHSI <lla6p11Ka Bnpo6HJia 13 750 M TKaHHHH, ,Apyroro ,n;H.H - cTiJihKH, cKiJihKH i1 IIPJlrnoro, a TpeTbOro - Ha 11 800 M MeHrne, nim neprnoro i ,n;pyroro pa30M. CKiJihKH MeTpin TKaHHHH <}>a6pH1<a BHp06HJia 3a 3 AHi?

370掳. 3i CKJia,Ay BHBe3JIH ByriJIJI.H Ha 15 8H1'0M06iJISIX, no 3 T Ha KomuoMy. Ha CKJia.n;i 3RJIHWHJIOCH 60 T ByriJIJI.fl. Ilpo ~o ,Ai3HaCMOC.H, .HKII\O 3Haii.n;eMO 3HaqeHH.H no.n;aHMX Bl1-

pa3iB?

3 . 15

60 : 3

3 . 15 + 60

371掳. 185 407 + 20 470 + 338 792 - 25 754 - (9457 - 7090)

60 - 3 . 15

15 + 60 : 3

75 Kr - 990 Kr { 2 n - 50 Kr) : 2 2

372. mo6 ,D;O,ARTH a6o Bi,lJ.H.HTH "CIHCJIR, iHO,D;i ,l\OUiJihHO KOpHCTyBaTHC.H cnoco6oM 01cpyZJU'Ull.H. PoarJI.HHh 3a1111c11 i rro.HCHH, .HK 3acTocoByeThc.H cnoci6 Ol{pyrJieHH.H.

586 - 299 = 287 57 + 28 = 85 586 - 300 = 286 57 + 30 = 87 87 - 2 = 85 286 + 1 = 287 373. 3aCTOCOBYIOt.IH cnoci6 OKpyrJieIIH.H, po3B'.H.mH YCHO npn:KJia.n;11, 3arrHcy10qH JIHllie yMoBy i1 Bi.n;rroBi,n;h.

38 + 18

47 + 99

360 - 37

92 - 46

485 + 198

374. 3 "CJHCeJI l, 3, 5, 8, 10 BH6epu Ti 3Hat.1e1-uu1 6yKBH X, ,D;JI.H

. .

.HKHX npaBHJibHa neplBHlCTb.

30路x > 100 240: x < 120 20 - x > 12 375. Y cnoprrnBHOMY Ta6opi 6yJio 217 J~iTei1. Ha 3MarattHH 3 <l>YT60JIY BHlX8JIO KiJihK8 KOMaH,l\, no 11 oci6 y KO:iKniiL Y Ta6opi 33JIHLUUJIOC.H 173 oco611. CKiJihKH c)>yT6oJihHnx KOMaH,n; BHlxaJio Ha 3MaraHHH?

376. rocno,n;apc路rno TIJiaHynano 3,ll;RTli 3250 Kr MOJIOKa. AJie BOHO 3,D;aJIO 3800 Kr, a noTiM ,D;O,A8JIO me _.!.._ :u.ici KiJibKOC. H a CKlJihKH . 6.l...1IhIIIe KlJIOrpaMIB . . MOJIORa Io rocrro.n;apcTTl. B03,D;aJIO, Him nnaHyBaJIO?

377. ,ll;oBmHHa ni.npi3Ka AB .n;opiBH1oe 6 CM. Pa,n;iyc KOJia 3 n;eHTpoM y To"ln.d A AOPiBH roe 2 cM 4 MM, a 3 n;eHTpoM 58

y Tot.1u.i B - 1 CM 8 MM. 3Hali_n;11 ei_n;cTaHh KM i CD. (Pe3yJihTaTH o6~HCJieHb nepeBip BHMipIQ,B3HH.HM.)

x.-~~~--~~~~-+-~~-+-~~~--~~__.l\f

378*. 'rapac KYIIHB 10 KOHBepTiB, a lOpKO -

8. ,ll;o HHX rrpH€tI;HaBC.H OJiech, i BOHH rro.n.iJIHJIH Bci 1toHnepTH rropiBHY. OJiech rroBepHyB IM 3a KOHBepTH 72 K. CKiJihKH rporneii i3 ~ie! cyM:n o,n;epm11Th Tapac i cKiJihKH - lOpKo?

379°. Po3B' Hm.H npHKJia,n;H ycHo, 3arrncyroqn JIHIIIe yMoBy ii Bi,n;rroBi,n;h. 218- 29 64 + 19 235 + 98 117 + 37 Jii~el HaBtia€ThC.H 8658 CTY,n;eHTiB. C1dJihKH cTy~eHTiR HanqaeThC.H oKpeMo B aKa,n;eMii' KOJietJ;»ti iI Jii~e!' .HK~O B aKa,n;eMii i ROJie.n;mi HaBqaeThCH 5087 CTy,n;eHTiB, a B KOJie,n;mi ii Jii~e1 - 4 756?

380°. y aKa)J.eMil, KOJie)J.mi ii

IlIBM,lJ;I\:ICTh. qAC. BI,ll;CTAI-Ib

381. PoarJI.HHh poaB'.HaaHn.H 3a)J.aqi Ta npot.IHTaii no.HcHeHH.H. 3 a ,n; a q a. 3a 2 ro.n. aBTo6yc npo!xaB 120 KM, npoYm. . . . ,n;malO'lllI ~OrO)J.HHH o,n;naKOBY KlJihKlCTh KlJIOMeTplB. CKiJihKH KiJioMeTpiB aBTo6yc npoYm,nmaB 3a 1 ro,n;? p 0 3 B'H 3 a H H .H: 120: 2 = 60 (KM). B i ,n; rr o B i ,n; h: 3a 1 ro,n; aBTo6yc npo!m)l.maB 60 RM. II o H c H e H H .H. HK~O aa KOmHy ro,n;HHY aBTo6yc npo1m,n;mae 60 KM, TO rOBOp.HTh, ~o BiH pyxaeThC.H 3i lllBH)J.KiC'l'JO 60 KM 3a ro,n;:nHy. Ue aanHcyIOTh TaR: 60 KM/ro_n;. mo6 3naiimu Ul6UiJKiCmb, mpe6a 6iiJcmanb noiJi.nu1nu ua 11,ac.

382. 3a ,n;aHJIMH 'ra6JIHIJJ o6tJJICJil1 lIIBH,n;KiCTb pyxy BeJIOCHrre,n;HCTa, nacamupcbKoro JiiTaRa, Jiac~iBKH.

illBH,D;KiCTb

"llac

Bi,ncTanh

ITncam11pcbKHH JJiTaR

. ?.

28KM 1500 KM

JiacTinKa

2 ro,n 3 ro.n 2 ro.n

PyxoMHH o6'e:KT

Bei1ocn11e'AHCT

180 KM

383. BeJioc11ne,n;HcT 6yB y ,n;opo3i 6 ro,n;, a MOTO~HKJiiCT 2 ro,n;. BeJiocHrre.nucT npoixaB 72 KM, a l\tOT0~11KJiicT 100 KM. Ha cKiJihKH lllnu,n;KicTb MO'l'O~HKJiicTa 6iJihIIIa 38 lUBH,ll;ldCTb BeJIOCHTie'AHCTa 'l IlJiaH poaB'srayBaHHH

1) qOMY ,n;opiBHIO€ IllBH,l\KiCTh BCJIOCHne,n;:ucTa? 2) qOMY ,[(OpiBHIOe IIIBH,D;KiCTb MOTO~HKJiiCTa? 3) Ha cH:iJibKH IIIBH,n;KiCTh MOTO~HKJiicTa 6iJihllla 38 llIBU,D;KiCTb BeJIOCHrre,n;HCTa?

384. Bi,n;cTaHh 400 M xJion~nIK npo6ir Ty,n;n :H Haaa.n 3a 4 XB. 3 HKOIO IIIBH,D;KiCTIO 6ir XJIOII~IHK?

385. Bi,a;cTaHh Mi.m yMOBHHMH rryHKTaMM K i M Ha op6iTi IIITyqHoro cynyTHHKa 3eMJii CTaHOBHTh 320 KM. 'lJeTBepTy 1.J8CTHHY ~ie1 Bi~cTaHi cyny'fHHK npoJieTiB aa 10 c. 3 .HKOIO lIIBH,D;KiCTIO BiH JieTiB '? 386. 1) 8000 ..------. 90 000

1500 -------. 1210 2000 - 300 5200 900 ....___ ______, 11 000

600 + 7000 23 000 60 - - - 45 000 2) 20 rpH. 8 K. - 59 K. 12 rpH. 70 K. - 8 rpH. 7 K. 3) 3a 3 Kr rpeqaHux KpyrriB aarrJiaTHJIH 9 rpu. 60 K. 3HaH,D;H ~iHy 1 Kr Kpynin. 387°. Bi,n;cTaHh Mim ,n;eoMa npHc1·att.HMH 320 KM. IloJioBHHY u.ie1 Bi'ACTaui MoTopnnii "tJOBeH npolillIOB aa 4 ro,n;. 3 .HKOIO IIIBM,n;KiCTIO HlllOB ~1oneH? 388°. Bil(CTaHb 20 KM BepllIHMK upoixaB Ty.nu i1 Haaa,n; aa 4 ro,n;. 3 SIKOIO lllBH,ZJ;KiCTIO !xa B BepllIHHK?

389. IIpoq11Taii 3a,zi;aqy Ta po3rJIHHh iI po3B'H38HHH. 3 a ,n; a q a. JIHmHHK 6ye y ,n;opoai 3 roA, pyxa10q11cb 3i lliBM,n;KicTIO 12 KM/rofJ... HKy ni,n;cTanh npoiillloB JinmHMK? p 0 3 B'H 3 a H HSI: 12 • 3 = 36 (KM). Bi 11. no Bi ,n; h: 3a 3 ro,n; JIH»<HMK npoi1rnon 36 KM.

IIJ.06 anaiimu BiiJcmanb, mpe6a m6uiJ1eicmb noMno31Cumu ua 11..ac.

390. Ilaca.mupcbKHH Ka·rep illIOB 4 ro,n;, a 6yKCHpHHH 7 ro,n;. HKHM 3 HMX npoi1llIOB 6iJihlllY Bi,n;cTaHb i Ha CKiJihKH KiJIOMeTpiB, Hl(I.IJ;O lIIBHJJ;KiCTb rracamHpChKOrO KaTepa 24 KM/ro,n;, a 6yKcupHoro 14 KM/ro,n;?

391. 3a ,n;aHHMM Ta6JinuJ

3H8H,ZJ;11

Bi,n;cTaHi.

PyxoMHH 06' £KT

lllBH,lJ;Ki CTh

t.Iac

Bi,n;cTaHb

Iliwoxi,n; TaKci EJieKTpono!a,n;

5 KM/rOA

4 rOA 2 ro.zi; 3 rOA

? ? ·1

70 KM/ro,n; 120 KM/ro,n;

392. 3a ,n;eHh TypHCTH MlllJIH rrirnKH 2 ro,n;, aBTo6ycoM ixaJI11 3 ro,n;. ITilllKH BOHM pyxaJIHC.H 3i IIIBH~KiCTIO 4 KM/ro,n;, aBT-o6ycoM ixaJIH ai mBMAKicT10 45 KM/ro,n;. HKHii lllJIHX no,n;oJiaJIH Typ.11cTn 3a 11.eHh?

393. 54 408 + 351 875 + 973 10 ~ 3 Kr - 4 ~ 12 Kr

48 350 - 9405 + 598 8365 - (2120 + 1080)

394. Ha rrTalll.11HoMy ABOpi 6yJio 16 KypqaT, a Ka"lleH.HT y 4 pa3H 6iJILllle. 3a YMOBOIO aa,n;aqi MOmHa IlOCT8BllTM TaKi 38IIHTaHHH: 1) CKiJihKM KaqeHHT 6yJio Ha nTalllHHOMY ,nBopi? 2) CKiJILKM 6yJio KypqaT i Ka"lleH.HT pa3oM? 3) Ha cKiJILKH 6iJILIIIe 6yJio Ka 1 1eHSIT, Him Kyp 1 1aT? BHKOHaii ycHo 06q11cJieHH.H i aanHI.llH BifJ..IIOBi,n;i.

395. IlpOT.HrOM 11.BOX ,n;HiB BeJIOCHrre11.11cT 6yB y ,n;opoai 12 ro,n; i aa qeii qac npoixaB 180 KM. CKiJihKH KiJIOMeTpi B npoi,n;e MOTO~HKJiiCT 38 20 rOA, HKI.IJ;O lioro lllBHAKiCTb Ha 36 KM/ro,n; 6iJibllI8 Bi,n; IIIBHll.KOCTi BeJIOc11rre11.11cTa?

396°. 10

u. 8 Kr -

4 u 12 Kr

12 KM 750 M + 4 KM 75 M

47 650 - 875 - 6588 3358 - (12 + 778)

397°. ABTOMo6iJih 1xaB 2 ro):J; ai lllBH,n;KicTIO 66 KM/ ro,n;.

•

IlicJI.H Qhoro noMy aaJIHlllHJIOC.H npolxaTH si,n;cTaHh y 3 paau 6iJihIIIY, Him Ta, ~o nitt yme npo1xas. HKy Bi,n;cTaHh MaB npo1xaTH 8BTOM06iJib?

398. IlpOtIHTaH 38,ZJ;81IY T8 p03rJI.HHh Ii'. p03B' .H38HH.H. 3 a ,n; a ti a. Ilacam11p npo1xas aeTo6ycoM 180 KM. IllsH,n;KiCTh asTo6yca 60 KM/ ro,n;. CKiJihKH tiacy ixae rracamup asTo6ycoM? Po 3 s'.H 3 au H .H: 180: 60 = 3 (ro,n;). Bi ,n; n o s i ,n; b: nacamnp IxaB aBTo6ycoM 3 ro,n;.

11{06 anaii1nu 11,ac, mpe6a 6iiJc1nanb 11,oiJi.numu na lU6UOKicmb.

399. 3a ,n;aHHMH Ta6nnu;i 3Haii,n;11 qac pyxy. PyxoMnli o6'eKT

lliBH,AKiCTb

'I.Jae

Bi.ACTai1b

JlIDKHHK

13 KM/ roJJ,

Iloia~

60 KM / ro11. 80 1<M/ ro11.

26 l(M 240KM 240KM

JierKOBHH aBTOM06iJib

400. Acc}>aJihTOBaHoro ,n;opororo aBTOMo6iJib rrpoi'.xas si,n;cTaHh 210 KM ai lllBH,ZJ;KiCTIO 70 KM/ ro,n;, a rpyHTOBOIO 90 KM 3i lIIBM,ZJ;KiCTIO 45 KM/ ro,n;. 3a .HKHH 11ac npolxaB aBTOM06iJib ycro Bi,n;CT8Hh?

401 . Bi,n;cTaHh Mim ,n;soMa 1IOBH8MH 15 KM. HKa ei,n;cTaHh 6y,n;e Mim HllMH, .HK~O o,n;nH 1IOBeH npoli,n;e 1 7 KM 250 M rrpoTH Te11i1, a ,n;pyr11ii - 19 KM 885 M aa Te11ie10'? Poa. rJI.HHb MO:>KJB1Bl BHII3,ZJ;KH.

402. qOBeH npOMlllOB 1KM3i lllBH,n;KiCTIO 100 M/ XB. 3a ueii qac IIJiaBen;h npOIIJIHB pyxaBCH IIJiaBeIJ;b?

400 M. 3 .HKOIO IllBH,ZJ;KiCTIO

403. BcTaB Hai1MeHyBaHH.H,

~06 pisttocTi 6yn:n npaBHJihHi.

6 ... = 6

4 AM

6 ... = 6

94 CM

3 T 320 Kr + 5 ... = 3

320 Kr - 5 ...

= 3 T 315 Kr

820 Kr

404. 12 T 70 Kr - 9 T 500 Kr 24 M 75 ClVI + 19 M 9 CM

~) : 2 (2M - 80~M)•4

( l 0 'r - 6

405*. IlapamyT11cT naARB, He poaKp11sa10qu naparnyT 3 c. 3a nepmy ceKYHAY BiH 3HH3HBCSI Ha 4 M 9 AM, a 3a KOmHy HaCTYilHY 3HHmyBaBC.H Ha 9 M 8 AM 6iJihlUe, ni.m aa nonepe,AHIO ceKYHAY. Ha CKiJihKM MeTpiB i Aen.nMeTpie 3HH3UBCH naparnyTHCT aa I..(i 3 c"? 406°. 3a .n;aHHMH T86JittIJ,i 3HaM,n;H HeBiAOMi BeJIH'CJMHI1. PyxoMHH o6'eKT

lliBM,ll,KiCTb

t.Iac

Bi.n.cTaHb

ropo6eu,b 3e6pa Ka Tep

'! 15 KM/ rop; 24 I<M/ ro.n.

2 ro.n.

120KM 45KM

4 ro)'\

407°. 0KeaHChKHii JI8HHep aa 6 ro.n; upoi-irnos 300 KM. CKiJihKH KiJioMeTpis npoii.ne aa n.eiii "(1ac naHTamtte cy.n;HO, HK~O iforo llIBllAI\:iCTb Ha 20 KM / ro.n; MeHUHl? 408. IlpO'tIHTaM IIOHCHeHH.H npo reoMeTpI1t.I1-d TiJia ii IIJIOCKi c}>irypH. Ha CTOJii CTO.HTb npe.n;MeTH: z,uJti.u.Dp, Kyd, KYJtJt, ICOHyc, napaJieJ1enineiJ, nipaMiiJa. Yee u.e - re o Me T p 11 "CJ: H i T i JI a. Ha MHJIIOHKY HH.iKt.Ie 306pameHo 1epyz, 1<BaiJpa11i, npa.MoKynittuK, mpuKy1nttu1<. ~e - n JI o c K i cl> ir y p 11. 3HaHAH u.i c}>irypn Ha reoMeTpHt.IHHX Tinax. Ha HKOMY reoMeTpHt.IHOMy TiJii e Kpyr? KBa,n;paT? npHMOKYTHHK? TpHKYTHHK? PoarJI.HHh Ha nepmoMy cI1opaan.i M8JIIOHKH reoMeTpnq. .. HHX 'rlJI, npO"CJHTaM IX H83BII. ~

[J ' 63

409. (Ycno.)

6·7 20·3

1·9 600·4

0·4 9000·3

7·0 10 000·8

41 O. 3arrnIIIn snpaa Ta ofrc.i11c11n iloro analleHH.H. Bi,n; q:HcJia 28 7 50 Bi,n;HHTH cyMy t.J.11ceJI ·7 50 i 1001. 411. opMy HKoro reoMeTplP-IHoro TiJia Mae BaJii3a? 6apa6aH'! pynop'! noBiTp.HHa KYJibKa?

412. 14 rpH. 96 K. + 6 rpH. 4 K. 20 KM 800 M - 4 KM 80 M

10 rpH. - 5 rpH. 8 K. 8 Kr 420 r - 3 Kr 80 r

413. BeJioc11rre,n;11cT, pyxaro~u-1cb 3i llIBH,D;KicTro 12 KM/ ro,n;, npo!xaB Bi,n;cTaHh Mim ,D;BOMa MiCT3MH 3a 5 ro,n;. IloBepTalOtIUCb, BiH npoixaB TY caMy Bi,n;cTaHh 3a 6 ro,n;. 3 HKOIO lllBll,z:t;KiCTIO 1xaB BeJioc11ne,n;11cT' IlOBepTalO'tJHCb Ha3a,n;? 414. 200 Kr Me,n;y p03KJI8JIH B 6i,n;OHM. y rrepIIIMM 6i,n;OH rroKJiaJIH 32 Kr Me,n;y. PeIIITY Me,n;y poaKnan11 nopiBHY B 6 o,n;ttaKOBMX 6i,n;ottiB. CKiJihKH KiJiorpaMiB Me,n;y B o,n;HOMY T8KOMY 6i,n;OHi? 415. 3a 3 ro,n; KapeTa MapKi3a ,n;e Kapa6aca 6pyKiBKoro npo!xaJia 7 5 KM, a 38 TaKHM caMMll qac r'pyHTOBOIO ,n;opororo - Ha 21 KM MeHme.

Ilpo rqo MOmHa ,n;iaHaTMCfl, 06~1MCJIMBIIIH BHpaaH?

75 : 3 (75 - 21): 3 75 + (75 - 21) 75 : 3 - (75 - 21): 3

416*. €

nHX 6i,n;OHiB Ha6p8Tl1 3

417°.

10 JI i 3 JI. HK pit.IKM 8 JI BO,ZJ;H?

,n;Ba 6i,n;oHH MicTKicTIO

3a IlJI8HOM npoT.HTOM

aa ,n;on0Moro10

n, .HTH ,n;HiB KOM6iHaT MaB BHny-

350 T nanepy. Ilo CKiJihKII TOHH nanepy Blipo6JI.HB KOM6iHaT ~O,UHH, .HK~O BiH BHnyCTHB Ha 50 T nanepy CTMTM

6iJihllie, Him nJiaHyBa.TIOCH?

418°. 8

B111<0Haii 06q11cJieHHH.

97 CM+ 2 M 5 CM 17 800 - (9753 - 8009)

Mta1·l•.\1h·tu~a.

·1

K.'f.

1000 - 1 1000 -10

640: 16 - 2 320 + 80· 2

MHO>KEHHSI I .0.IJlEHHSI 6ArATOU.M<l>POBMX lf MCEJl HA OAHOL\1'1¢>POBE l.IMCJlO

MHOmEllHH HA O}J.HOIJJ1<t>POBE qlfCJIO 419 . Ilpo 1 n1Ta:H I10.HCHeHH.H

npo ,n;ilO MHO:>ReHH.H Ta

IloMHO)KJ.1TH HaTypaJibHe "llHCJIO

iI 38KOHM.

3 Ha HaTypaJihHe l!HCJIO

5 oaua 1 rae anai1T11 cyMy n'HTH ,n;o,u.aHKiB, KomeH a HKHX e 3. 3 · 5 = 3 + 3 + 3 + 3 + 3. l.JHCJia 3 i 5 H83HBaIOTbC.H .+fHOJICUUKUMU, a BHpaa 3. 5 IX iJ06y1111<0.ilf.. IIcpecTaunnif. aaKon l\'IH0'1\:eHHH. ,lJ:JI.H 6y,n;h-HKHX HaTypa111>HHX "llI-JCeJI a i b BHKOHY€TbCH piBnicTh a· b = b ·a, ...

.HKa nnpa).Kae nepecTaBHH11 38KOH MHO.iKeHH.H.

Bio nepecniauoBKu MnomnuKia iJ06y1noK ne 3Min10C1nbca. CnoJI~1111ii 3a1~0H MHO~KeHHH.. ,ll;JI.H 6y,u.h-.HKHX HaTylJHCeJI BHKOIIyeThC.H piaHiCTb (a.. b). c " 38KOH MHO:>KeHH.H. .H:Ka nnpa:n\ae CIIOJiytIHH.H

paJILH ux

=a. (b. c),

II-{ 06 iJo6y nioK iJaox ttuce1t noMnomumu na mpeme MO:JICHU ne11me ttLLCJl,0 1lO.Mlt031CUmu na iJo6ymoK iJpyzozo i 11ipe1nbozo itucen. 'lltCJtO,

HanpHKJia)~:

JiiBii1

(3 · 5) · 2 = 3 · (5 · 2). i npan.i H: l:JacTn.nax piBHOCTi

caMHH ,n;o6yTOK

. nepeCT8BHOro

,l(lCT8€MO

MaeMo o,z1;11H i TOH

30. Ta cnoJiytIHOro 3aKOHiB ,u.il MHomeHH.H

....

O,ZJ;HY 11 BJiaCTlf BlCTb.

iJo6y 1nKy Kin bKOX inno:J1CnuKi6 Mo:>1ena nepecmaenarnu, Mlt031CHUKU i 6pa1nu ix y iJy31CKU 6yiJb-RKUM, 1lU1tOM. Hanp11KJia'A: 3 · 4 · 25 · 30 = (3 · 30) · (4 · 25).

420. 3ttaMAH

8·4·50 66

.n;o6yTOK apy 1n111M cnoco6oM.

2·4·5·15

421. Ilpot_I:HTaH IlO.HCHeHH.H npo poano,n;iJibHHH

381\:0H

MHO-

meHH.H. Poano)liJibHHii 33KOll MHOmCHIUI. ,ll;JI.H oy,n;h-HKHX HaTypaJibHHX t.llICeJI a, b i c Bl1KOHY€TbC.H piBHiCTb (a + b) · c =a· c + b · c, ~o BMpamae poano,n;iJihHH~i 3aKoH MHO»<:eHH.H. ,!1o6ymoK cy~iu iJaox 1tucea na 6yiJb-JtKe 'lLUCJLO iJopien10c cy Mi iJo6y 1nKi6 Ko:J1Cnozo iJoiJauKa na ~e ttUCJto. Poano,n;iJihHHii aaKOH BHK011yeThC.H AJI.H 6y,n;h-.HKOro 1111cJia ,n;o,n;attKiB. HanpnKJUl,n;: (1 + 2 + 3 + 4 + 5 + 6) · 7

= 1·7 + 2. 7 + 3. 7 + 4. 7 + 5. 7 + 6. 7. 3aCTOCOBYIOt.UI poano,niJibHHi1 3ClKOH MHO)KeHH.H, cyMy . . 1 qJ1CJIO MOmHa MlH.HTH MICIJ..HMH.

4·(5 + 8 + 10) = 5·4 + 8·4 + 10·4 4

. .HKi 3 IlO,l~aHHX aa,n;alf p03B '.H3YIOTbCH .DiieIO MHO.iKeHH.H? 1) Y KJiaci 15 napT. CKiJihKH napT y 5 TaKHX KJiacax?

2) Ileprne 1.JJ.ICJIO 8, a ,n;pyre Ha 4 6iJihIIIe. 3uaH:,n;11 ,n;pyre t.IHCJIO. 3) Ileprne 11ncno 8, a ,n;pyre y 4 paa11 6iJihIIIe. 3naii,n;H Apyrequcno. 1 4) BMiCT KPOXMHJIIO B KapTOTIJii CTaHOBMTb iI Macn. CKiJihKM KiJiorpaMiR KapTonJii rroTpi6no, n~oo BHiirnJio 200 Kr KpOXMaJIIO?

423 . .HKMH ,n;o6yTOK 6iJihlUHH i Ha CKiJihKH?

245·47

t.JM

245·45

468·25

l.JH

468·24

4 4. 207. 4 36. 23 1. 0 + 4. 1 200: 100 288 : 8 922 : 32 8 : 1+ 6 :6 230 : 10 425 . 3a ,n;aHHMH Ta6JIM~i CKJI8,D;H i p03B '.H.iKH aa,n;aqy.

426

PyxoM11ii o6'eKT

llIBK,ZJ; JdCTh

BeJiocune,n;HCT

15 KM/ ro,n;

BepIIIHiu<.

12 KM /ro,n;

t.Iac

B i.n;cTaHh .,

O,ZJJl8 KOBH H

30KM

Bi,n;cTaHh Mim ,n;BoMa MicTaMH 72 KM. TpeTHHY uJel Bi,n;cTaHi nola.Di npoiiIIIOB 38 12 XB. 3 .HKOJO IllBM,n;KiCTIO

tiu10B noi"a~? (Po3B' Simn 3a,n;aqy CKJia,n;anu.HM BMpaay .) 3

·... 427*.

Maca Kopo6KH ia u;yKepKaMH

550

r. KoJIH IIOJIOBHHY

u;yKepoK 3'1JI:n, Maca i<opo61tn cTaJia

300. r •

.HKa Maca

rropomHbOl KOp06K11?

428°. 203. 4 49·18 14 T 7 Q - 5 'r 9 Il 792: 24 12 T 70 Kr - 9 T 500 Kr 23·4 429°. Y rreprniii IIIKOJii a yqHiB, y ,n;pyrili Ha b y"(1HiB MeHIIIe, Him y rrepmif1. y TpeTiH IllKOJii Ha 119 Y1.IJiiB MeHrne, nim y ,n;pyrill:. CKiJihKH y'(1HiB y Tpe·rii1 IIJI<oJii? CKJiaJJ;H

Bnpaa Ta o6qncnH iioro anaLJeHH.H, .HI{IJJ;O a= 1758, b = 95.

430. Ilo.HCHII ycHHM i TII1ChMOBMll 263. 3 = (200 + 60 + 3). 3 = = 200 . 3 + 60 . 3 + 3 . 3 = = 600 + 180 + 9 = 789 431.

cnoco611 061.JHCJieHH.H.

263 x 3 789

IlHCbMOBe MHO.iKeHH.H 6araTOU.11CllPOBHX t.Il1CeJI Ha o,n;-

HOilHCppoBe "lJHCJIO BHKOHYIOTb TaK caMO, HK i TpHD;HC}>pOBllX.

PoarJI.HHh poaB'.HaaHHH npttI<Jia,n;y

•

201 852 · 4

l IIp0"llJ.1T8H IlO.HCHCHH.H. x

20 1852 II 4

o .H c n e H H H.

Ili,n;rrncyeMo "lJMCJIO

rri,n;

O,ll;HHMil.HMJ.1 nep1noro MHOlliHHKa. IlOMH0-

807 408 ~l1MO 2 o,n;1~.n11a;_i

Ha 4, 6y.n.e 8 O.ZJ;HHMD;b, n1,n;n11cyeMO IX Ill,ll; O.ZJ;MHHD;.HMH. IloMHOmH-

2 COTHL y po3p.H.n;i .n;ec.HTKiB y ,n;o6yTKY nnmeMO 0, a 2 COTHi 3anaM'.HTOBY€MO. 8 COTeHh IIOMHO)KHTH Ha 4, 6y,n;e

,n;ec.HTKiB Ha

6y.n;e

,n;eC.HTKiB, a6o

32 COTHi Ta I.Qe 2 COTHi, 6y,n;e 34 COTHi, i 4 COTHi. 4 COTHi 33IIMcyeMo rri,n; COTH.HMH, naM'.HTOBY€MO.

3 THCSPii,

6y,n;e

a6o

7 THC.ff"ll.

3anHCY€MO

THC.ffCJi

3 TllC.ff"Cii 3a-

1 THC.ff"llY IlOMHOmHTH Ha 4,

6y,n.e

7 TMCSit.I

4 Ta ~e

rri,n; THC.ff"lla-

0 ,n;ec.HTKiB TlIC.HY.J IlOMHO:>l<HTJ.1 Ha 4, 6y,n;e 0 ,n;eC.HTKiB THC.H"CJ. 3arrnmeMO "lfHCJIO 0 ni,n; )J.eC.H1'K8MI1 TMC.H'll. 2 COTHi THc.Hq IlOMHQjKHTH Ha 4' 6y.nie 8 COTeHh THC.ff"ll. 3arru1neMO 8 ni,n; COTH.HMH 'fl1CJI'lf. ,no6yTOK 807 408. MII.

432 . IlepeBip, t.IH e cepe,n; 'l!Hcen 351 462, 57 876, 362 278, 2304, 834 7 Bi,n;noBi,n;i no,n;annx npHK a,n;iB. 384·6 51754·7 117154·3 3.3 20·3 400·3 3tta:H,n;H cyMy ni,n;noBi.n;eli npHKJia,n;iB na MHomeHH.H Ta nopinn.H.i1 iI a Bi~noBi,n;,z:uo rrepu1oro npnKna,n;y.

433 . 423 + 423 + 423

434. PoaB'nm11 a noncHeHH.HM npHKJia,n;: 25 454 • 5. 6y,n;iBHH~'rBo ni,n;B03HJI11 u.erny aBTOMo6ineM i TpaKTopoM a upn~1erroM. Ha aBTOMo6iJib II.(Opaay HaBauTamyBaJIH 925 IJ;Cl'JIHH, a Ha np1P1in - 2075. 3a ,n;eHb

435 . Ha

aBTOMo6iJih apo6ua 6 peiiciB, a ·rpaK'l'OP 3. CKiJibKtt u.erJIMH 33Be3JII1 Ha 6y,n;iBHl1IJ.TBO npO'I'.HrOM ,D;HH?

436. 3 o,n;noro aBTOBOK3aJiy o,n;noqacHo BHpyn1nn11 B npoTMne.mHnx nanp.HMKax 2 RBTo6yc:u. Illn:u,n;KiCTh rrepIIIoro 65 KM / ro.n;, a .npyroro - 75 KM/ ro,n;. HKa Bi.n;cTaHb 6y,n;e Mim aBT06ycaM11 'l!epea 5 ro,n;? 3a anpaaaMH no.Hctt11 ).I.Ba cnoco611 poaa'SiaynaHHH aa,n;atii.

65·5 + 75.5

(65

+ 75)·5

~JI.fl BKPH'l'Tfl \JeperrHu.ero ,n;axy seJIMKoro 6y,n;MHKY

437°.

noTpi6no 2146 nJIHTOK, a Manoro 1428. CKiJihKH 110Tpi6no IIJIHTOK, ~06 BKpHTH qepenn~ero ,n;axM 6 BeJIHKHX i 7 MUJIHX fiy,ZJ;HIIKiB'!

438°. 2306 . 6

•

17 245. 8

684: 4

35511·7

439. (YcHo.)320 + 40 : 4

300 + 200

- 20

- 400

640 - 120 + 80

240 + 320

. 440. 3aKiH-CJM p03B H3yBaHHH rrpHKJia,n;iB.

4073

20073

9 x

... 92

441. 2306·6 442. IlapHi 20 756

20904

•.• 657

6 ..... 4

30 094. 7

40 801·9

~nicna

a6iJihIII y 6 paa, a nenaptti 3015 4006 17 201

40 059. 3 aMeHIII tta 6.

443 . y BeJIHKOMY 33Jii KiHOTeaTpy 1224 MiCI..\.H, a

MflJIOMY - 208 MiCIJ.L. CKiJih101 KiHorJI.H.n;aqiB Mome o6cJiymnTn KiHOTeaTp aa .n;eHh, .HKII\O y BeJIHKOMY 3aJii 6yJio k ceauciB, a B MaJioMy c? CKna.n;11 snpaa JJ;.TI.H poaB' .H3yBaHH.H aa,na qi Ta o6qHCJIH i-ioro 3Ha'-IeHH.H' .HKII\O ll = 5 i c = 4.

444. Bi,n; o.n;ttiei rrpncTaHi Bnpymn.Tin

o,n;ttoMy Hanp.HMKY K8Tep i 6yKCMp. lliBH,lI;KiCTh KaTepa 27 KM/ ro.n;, a 6yKCHpa 18 KM/ ro11... HKa BiJJ..CTaHb 6y.n;e Mim HHMll qepe3 3 ro.n;? (PoaB'.HmH aa.na"(1y .n;soMa cnoco6aM11.) B

445° . y IJ.MCTepHi 6yJio 3400 JI 6eH3HHY. IlicJI.H Toro .HK HaIlOBHHJIH 4 o.ntta KO Bi 60l:IKH' y UHCTepHi 38JIHllllfJIOC.H 2600 JI 6etta11tty. CKiJihKII JiiTpis 6eH3HHY HaJittBaJIH B KOmHy 6ot11ty'!

446° .40 037. 2

34 050. 4

80 015. 4

744: 24

447. 1) CKiJI.hKH BChoro B KomHoMy l:JHcJii coTeHh? THC.Hlf?

3400

7000

2404

140 000

2) 3anHlllll KO>KHe l:IHCJIO 3H .n;onOMOrOIO I..\Hc}>p.

5 COT.

240 COT.

180 JJ;ec.

3 .n;ec.

5 THC.

448. Ilo.HCIIH, .HK MipKyB8JIH npn 3H8XO)J;.meHni JJ;06yTKiB 1200. 4 i 7000. 4

1200. 4 = 4800 12 COT.· 4 = 48 COT.

= 28 000 7 'fIIC. • 4 = 28 THC.

7000. 4

449. 1) PoarJI.HHb, .HK MOmHa aanucysaTn .niro MHomeHH.H,

.HKI.QO O,lI;Hll 3 MHO)KH HKIB Mae HYJil B KlHI.I.1.

2300 x 7 16100

49000 x 4 --196000

2)6700·2

84000·6

450. 3HaH)J;H 3HaqeHH.H Bnpaay "lleUb 3MiHHOl a:

130000·7

760·5

a. 10 + 300 .D;JI.H TaKHX

3H8-

4, 40, 400, 210.

451. PoarJI.HHh qncJioRi .n;aHi Ha MaJIIOHKax (c. 71) i 3Haii11..n

BIJJ..TIOBI,nl Ha 38IIHT8HH.H. 1) HKa Maca 6 TaKHX KOHe:H:? 2 KOpiB?

10 oeeub?

2) Ha ·cKiJibKM Maca 2 Kopis 6iJihIUa Bi'A MaCH 1 KOHS!? 3) CKiJILKH Kia aa Maco10 aa MiH1oe t Kopoaa? t-IoMy 'AOPiBHIOe Ma ca 5 Kia i 4 oneu;h paaoM '!

KI'

•

J{l'

1• '

.. 480

KI'

0'AHH onepaTop na6upae 33 ,l.\eHh Ha KoMu'roTepi 20 cTopiHOK TeKcTy, a JJ;pyr11i1 - 24 cTopinK11. CKiJihKH CTopiHOK BOHH na6epyTb 3a k 'AHiB, .Hl{ ll\0 6yJJ;yTh npa~IOBaTH paaoM? CKJiaAH BHpaa 'AJJ.H poan 'sr3yaa11n.H aaJJ;a t:J:i Ta 061u1cJI11 :Horo aHaqeHH.H, .HH'.ll\O k = 5.

Tp11 'Aia1111HKH MaJibBa, Maprap11Ta i JliJii.H TpnMaJI11 B pyKaX KBiTu: M8JlbBH, MaprapHTIO-f '1'3 JiiJiiL iKO)J;.Ha 3 HllX He TPMMaJia KBiTM, Bi.A Ha3BM HI<HX IlOXO,lJ.HTb 11: iM' .H. MaprapuTa ynamHo po3rJI.H.AaJia JiiJiil, 1~0 Ix TPHMaJia noJJ;pyra. XTo .HKi KBiTn Tp11MaB'l

454°. 2300. 5 2140·5

14 n_ 9 Kr - 6 ~ 28 Kr 4 M 75 CM + 9 M 9 CM

2 Kr - 300 r 2

455°. Maca KYPKll 2 Kr 375 r, Maca rycK11 Ha 2 Kr 345 r 6iJibWa, nim Maca KypH:M. Maca iHJJ;HKa Ha 2 KI' 350 r 6iJihma, Him Maca rycKH i KYPKll pa30M. HKa 3araJihHa

Maca KYPKM, rycKM Ta iHJJ;MKa?

456. (Yetto.) 20 · 4 25·2

3·14 2·41

20·10·2 2 ·(3 + 30)

1200·5 101·7

457. Ilpo-cn1Taif 3a)J;aqy i po3rJI.HHb iI po3n'naaHH.H. 3 a JJ; a q a. y KOHJJ;HTepCbKHM I(ex XJii60KOM6iHaTy npnBe3JIH 2 7 56 .Hl~llKiB M8CJia, no 7 Kr y KOmHOMY. CKiJihKM BChoro KiJiorpaMiB Macna np11Be3JIH? P03B'.H38HH.H

7 · 2756 = 19 292 (Kr) Bi JJ; no Bi JJ; b: Bchoro np11Be3JIH 19292 Kr Macna.

2756

19292

7 .35 705 2. 240 756 458. 1) 4. 20 374 3·123 401 2) IIepeBip npaBMJibHiCTb 06"(111cJieHH.H B11pa3y. 4·65 701 - 867: 3 = 262 515 262804 _ 867~ 65701 x 4 289 6 1289 26 262515 262804 24 27 27 0 459. 4078. 8

+ 25 409

6·43051 - 28·35

460. 24 T BOAM nepllillM H8COC MO.me BllKaqaTII aa 6 rO)J;, a APYI'Hll - 3a 3 roJJ;. 3a cKiJihKM rOAMH BllKa""tJaIOTb ~ro BOAY o6HJJ;Ba Hacoc11, .HK~O 6yJJ;yTb npal(roBaTM OJJ;HoqacHo? IlJiaH p03B'SI3yBaHHSI

1) CKiJihKM TOHH BOJJ;M BHKaqye nepmnii Hacoc 3a 1 roJJ;? 2) CKiJihKM TOHH BOJJ;M BMKaqye APYrMli nacoc 3a 1 roJJ;?

•

3) CKiJihKM TOHH BO.D;M BMKaciyIOTh 0611,n;Ba Hacocu aa

1 ro.n;? 4) 3a CKiJihKH ro.n;HH 6y,n;e BllKaqaHo 24 T BO.n;M?

461 . AsTo6yc rrpo1xaB a KM aa b ro.n;. HKy Bi.n;cTaHh a TaKOIO caMoro IIIBn.n;KicTro BiH npoi.n;e 3a 3 ro.n;? CKJia.n;H BHpaa )l;JISI

p03B '.H3yBaHH.H aa.n;aqi.

462. 1) y SIKOMY rrp.HMOKYTHMKY KiJibKiCTb KJiiTMHOK 6irrbllla? 2) IIopiBH.Hii nepIIMeTpH np.HMOKYTHHKiB.

I- '

463°. 9. 75 046 200 275·4

3. 348 + 407. 7 5 . 280 - 280 : 10

2 Kr - 200 r 2 M - 200 CM

464°. Ilo6y.n;yli np.HMOKYTHHK ABCD ai cTopoHaMM 2 CM 5 MM i 4 CM 5 MM. 3Haii.n;H nep11MeTp np.HMOKYTHHKa. IIJIOIIJ.A IfYPli. OAMHMIJJ BMMIPIOBAHHH IIJIOIIJJ

465. PoaB'HmM npttKJia,n;M, y .HKHX nepwo10 e .DJ.H MHo:>KeHH.H. 6·60: 30 80 + 40· 7 12·2·3 + 28 6. (60: 30) (80 + 40). 7 800: (40. 2) + 100 466. Ha MaJIIOHKY aJiiBa Kpyr yMicTMBC.H Bcepe.n;11Hi qoTHPHKYTHHKa. Ue oaHaqae, ~o nJLow,a Kpyra MeHIIIa Bi,n; llJlOU{i llOTMpHKYTHMKa. Ilnom;a ~e BeJIH't!MHa, .HKY MO:>«Ha ue TiJihKH rropiBHIOBaTH, a ii BMMiproBaTM. IlopiBH.Hii Ha OKO nnom;i iHillMX <l>iryp Ha M8JIIOHKY.

OD V

0 73

•

467. ,ll;JI.H B.HMipIOBaHH.H BeJBil·IHHH o6HpaIOTb OtJ-HHHIJ.i BHMiplOHHHH.H. € OAHHHIJ.i BUMipIOBRHHH i ,n;JI.H rrJio~i. HeeeJIMKi nJio~i BllMipIOIOTL KBa.npaTHHMH caHTllMeTpaMH. Kaaapaniuuu ca111nu.iw.e1np - qe nJtou,a K<Jaapanza ai c1nopo110KJ 1 CM. TipH "LIJ.ICJiaX «ICBa.npaTHHM caHTHMeTp» aan11cy10Th cKopoqeno TaK: 1 cM 2 , 7 cM 2 •

IloJii~n1

i aannIIIH B 30llllITi, CKiJihKll KB8JJ;p8THl1X caHTHMeTpiB y KOm.Hiii c}>irypi.

468. 6700·6 270 000·3

8·83 201 5·3020

1 7 005 . 8 + 28 786 4207-6 - 3019·2

469. O.n11H onepaTop Ha6Hpae Ha KOMII'IOTepi 100 CTOpiHOK 'feI<CTY aa 5 AHiB, a .n;pyruii - 38 4 )];Hi. 3a CKiJihKH .nniB Ha6epyTh u.i onepaTOpH 90 CTopiHOK, .HK~O npHlVOBHTRMYTb paaoM?

470°. BeJioc11ne.n;ucT npoixan 67 KM. 3 ro.n nin lxaB .no o6i.ny i 2 ro.n rricJIH o6i.n;y. ,ll;o 06i1~y senoc11ne.n;11cT 1xas ai llIBHAKiCTIO 15 KM/ rOlJ.. 3 .HKOIO lllBH,ZJ;KiCTIO BiH lX8B nicJIH o6i.n;y?

471°. 203 000 - 43 500. 4 800 000 + 50 500 . 3

IT e p e

40 000 - 250·3 + 985 5500 + 2. 370 - 4800

i p c e 6 e: 1440; 29 000; 40 235; 951 500.

472. ,[(JUI .HKMX 3HaqeHb 6yKBH npaBHJihHi HepiBHOCTi'!

x + 40 < 45

x. 70 < 280

120 : x > 24

473. Ilp.HMOKYTHHK, AOB:i:KHHa .HKOro 5 CM, a IIIHplIH8 3 CM, noAiJIHJIH Ha KBaApaTHi caHTHMeTpw. ,ll;icTaJIH 3 P.HAM, no 5 CM 2 y KO:i:KHOMY, a6o 5 CTOBil'l!MKiB, no 3 CM 2 y KOm.HOMY. 'l{11cJIO KBa,n;paTHHX C8HTHMeTpiB ,n;opiBHIOe }J.06yTKY qnceJI 5 i 3: 5 · 3 15 (cM 2 ), a6o 3 · 5 = 15 (cM 2 ).

:sCJ -4

1-----t----t---+---+----I

)1 CJ

1 CM 1 CM 1 CM 1 CM 1 CM Il.{06 o6ItUCJl,Umu ltlLOUfY tipRMOKymnuKa, 11ipe6a BUanaitumu uozo iJoB31Cuny i mupuny ma anau1nu iJ06y1noK qux 11,uce11,.

47 4. 06-.:nICJIH

IlJIO~y KO.iKHOrO np.HMOKYTHHKa.

"--"""tJ... (_ __;..-

475. 1) CyMy 1:111ceJ1 27 404 i 129 844 36iJihIII y 6 pa3. 2) Pi3u11u;10 qHceJI 5308 i 4546 3MCHIII y 3 pa311.

476. 48 000 - 3 • 275

+ 5000

26 400 · 5

T -

3 Kr

477. 72 ~ ciua KOpOBaM BHCTaqHTb Ha 12 JJ;HiB, a BiBIJ.SIM Ha 24 JJ;Hi. Ha cKiJihKH BMCTaq11Th IJ.horo cina AJISI KopiB Ta oneu;h pa3oM?

478. AeTo6yc B111xan i3 ceJia o 8 roA paHKy i rrpn6yn y MicTo 06 11 ro.n paHKy. 3a u;eM t.1ac BiH no,n;oJJaB 3 .HKOIO IIIBH,AKiCTIO lX8B aBT06yc?

192 KM. 75

479*. € Ilp.HMOKYTHHKH 3i CTOpOH8MH 1 CM i 7 CM, 2 CM i 6 CM, 3 CM i 5 CM, 4 CM i 4 CM. flKHH i3 I.J.HX Ilp.HMOKYTHHKiB Mae naii6iJihIIIY IlJIO~y?

480°. Y Mara3MHi 6yJio 500 Kr 6opollIHa. Ao nepepBH npo,n;aJIH a Kr 6opornHa, a rricJIH rrepeps11 - b Kr. CKiJII>KH KiJiorpaMiB 6opoII.IHa aaJIMlllHJIOC.H? CKJia,n;11 nwpa3, 3a ,ll;OilOMOrOIO .HKOrO p03B '.H3yeThC.fl aa,n;aria.

481°. x - 3540 = 48 580

24 085

+ x = 94 817

x: 6 = 36 048 57 083 - x = 9075

482. 3a ,ll;8HHMH ManIOHKiB 3Han,n;H IlJIO~Y i nepnMeTp KO»<HOro rrp.HMOKYTHHKa.

,i,

-- 2 CM

CM.

483. 1Io6y,n;yi1: np.HMOKYTHHK 31 CTOpOH8MH 2 CM i 8 CM, ....

....

3Ha:H,n;H noro

nJio~y

1 nepHMeTp.

484. Ilp.HMOKYTHHK no,n;iJieHO Ha 3 np.HMOKYTHHK11. 3po611 Heo6xi,u;Hi Bl1MipIOB8HH.H Ta 06 1 IHCJIH IIJIO~Y KO:>KHoro np.HMOKYTHHKa.

485 . 90 6yJioqoK KapJICOH Mome a'!cTH 3a 10 .n;HiB, a peKeH BoK - aa 15. 3a cKiJihKH ,n;HiB 3 '1,n;.HTh u;10 KiJihRiCTh 6yJIO'tl OK KapJicoH i cI>peKeH BoK, HK~o 1cTHMYTh 1x pa1oM?

486.

487.

CKJiaAH 3a,n;aqy 3a KopoTKMM 3anHCOM i po3B'.H:>KH

llIBHJUdCTh

1Iac pyxy

60 I\.M / ro.n; ?

o.n;naKOBHM

Bi,n;CT8Hh

180 .KM

HeBi'AoMe qHcjIO 36iJihllIHJIH y

11.

48H:M

pa3 i .n;icTaJIH

98 7.

3HaHAH HeBi,D;OMe qHcJIO. (CKJI8,D;H piBH.HHH.H i p03B' SimM iioro.)

2. 7766 + 83 030. 6 220 - 200 : 2 - 50

488. 2075. 9 - 11 307

100 489掳.

+ 24路4 - 18

Ilo6y.n;yii IIP.HMOKYTHHK 3i CTOpoHaMH

3 CM i 10 CM

06q11cn11 11oro nepHMeTp i rrno~y.

490掳.

Ileprnoro ,D;H.H y IIIKiJibHY i)~aJibHIO npHBe3JIH

CH 3 BHniqKolO, BCboro

Be3JIH

108 TiCTffCJOK.

ni,nHO-

,IJ;pyroro ,ll;H.H npII-

T8KHX rri,n;Hocn 3 s11rri t.11<010. CKiJihKH TiCTeqoK

npnBe3JIH .n;pyroro .D;H.H?

491.

Ilpoq11TaH nO.HCHeHHSI npo OAHHHD;i BHMipIOB8HH.H

IIJIOII.\l.

llllout,a -

MaTeMaTHt.IHa seJIHtJHHa.

BHMipIOIOTb He

TiJibKll B KBa,n;paTHMX C8HTHM路eTpax, a ii y iHIIU1X O.D;HHIUJ;.HX.

( C. 78) Il0'A8HO O.D;HHH~i BHMipIOB8H. T86JIHIJ;i . .... .

H.H IlJIOI.Ql, .HKl 38CTOCOBY10Tb Half'lI8CTlllle.

1 MM 2 -

IlJIO~a KBa,n;paTa, CTopoHa .HKOro 1 MM. 2 1 CM - IlJIOll\8 KBa,n;paTa, CTOpOHa .HKOrQ.1 CM. 1 .n;M2 - IIJIO~a Kna.n;paTa, CTOpOH8 .HKOro 1 JJ;M. 1 M 2 - IIJiora;a KBa.n;paTa, c路ropoHa HKoro 1 M. Ap (a) - IIJIOIIJ.8 KBa,n;paTa, CTOpOHa .HKoro 10 M (COTKa). feKTap (ra) - rrJiom.a KBa,n;paTa, cTopoHa .HKoro 100 M. 1 KM 2 - IlJIOIIJ.8 Kna.n;paTa, CTopoua HKOro 1 KM.

492. Ha MaJIIOHKY B HaTypaJihHY BeJI11q11Hy noKa3ano 1 cM 2 i 1 ,n;M 2. CKiJihKH Kaa.n;paT1111x canT11MeTpiB MicTHTb 1 ,n;M 2?

1 CM2

. . IlJIO~Y HHX MlJilMeTpax.

493. Q6qHCJIH

,nM 2

KOmHoro rrpHMOKYTHHKa y KBa,n;paT-

494. PoaB' .Hm11 aa,zvt'Lfi Ha nopiBH.HHH.H nJI011~. 1) IlJIOI.1\a ca.n;oBOl .n;iJUiHKM 6 a, a IlJli>tna npHC8AM6HOl .n;iJI.HHKH 25 a. fla CKiJihKH apiB IlJIOI:Qa rrp11ca11.116HOI .n;iJI.HHKH 6iJihllia Bi.n; IlJIO~i ca11.y? 2) IlJioI:Qa YKpaYHH 604 000 KM 2 , a nJiou~a <l>paH~ii 551 000 KM 2 • Ha CKiJihKH KBa11.paTHMX KiJIOMeTpiB IlJIOI:Qa YKpaiHH 6iJihIIla aa IIJIOI.1\Y paH1d1?

495. 10 000 - 604. 5 - 910

37·14 - 693: 21

50 507. 6 + 14 850 936 : 26 + 35. 22

496°. II06y11.yi1 np.HM0Ky1·tt11K 3i cTopoHaMH 2 cM 5 MM i 9 CM 5 MM. 06t.HICJil1 iioro nep:nMeTp i IlJIOI.1\Y. 497°. IlJiorQa npHca.n;n6tto1 .n;iJIHHKH 25 a. By11.iBJJi i1 11.Bip 3a.ftM8IOTh 4 a, ca.n; - 6 a . PellITY nJio~i 3attMae ropo.n;. Ha c1<i.nhKM apiB rrJJOII\a ropo11.y 6iJihrna Bill. nJio~i ca.n;y?

498. HKy o.n;MHHI\IO nJioI.Qi 3PY'LfHO B3.HTH lJ.JI.H BHMipIOBaHHH IlJIO~i IllKiJlhHOro Kop11.n;opy? IIJIOlQi CTOpiHKH y~1HiB

CbKoro 30IllHT8? IIJIOI.Qi nonepxHi CTOJI8?

499. 3a IIJJaHaMH .n;iJI.HHOK 3HHM)J;M, llKY IIJIOI.1\Y BilJ.Be.n;eHO OKpeMO .ZJ;Jl.R BHpo~yBaHH.H u.116yJJi, MOpKBH i pe.n;l1CKH. -

Mop Kea

~H6yJIH r

Pe~HcKa 1

-- --

10M

500. IlapKeTHY ni.n;Jiory BRPMJIH JIHKOM ABa paa11. Ilepmoro paay

Ha KO)l{Hl1H KBa.n;paTHllii MCTP BHTpaTHJIH 120 r JlaKy, fl 11.pyroro - 80 r. CKiJihKtt BHTpaT11JI11 KiJiorpaMiH JI8KY, .Hl{~Q .ZJ;OB.)KHHU KiMHaTH 5 M, a IIIHpllHa 4 M?

501. AoB.mMHa ca.n;y 40 M, IIIHpHHa - Ha 16 M MeHrna •

.!. ca-

11.Y aaiiMaJOTb .H6JiyHi, a pellITY - iHllli Cl> y1<:T0Bi .n:eteBa. HKy nno~y aaliMaJOTb iHmi <llPYKTosi AepeBa?

502. 12 037. 5 - 8984 - 457 1200·100 - 900: 10

12 037. 5 - (8984 - 457) 23 • 23 + 954 : 3

503. 1) CyMy qHceJI 9407 i 5080 3MeHlll Ha pi3HUU.IO u.ux t.JHCeJI. 2) ~o6yTOK qHceJI 9485 i 9 3MeHilI Ha \x pi3HHU.IO. 504°.

BHaHa~1 BilJ.CTaHb Mim MicTaMH JlhBiB i XapKiB T.Iepea

Kn1B, jJK~O

1 CM Ha M8JIIOHKY BiAilOBiA8€ 100 KM • •

X apldB

JlhBi:Q

•

505°. 36 Kl' 3epHa Kypu,i BHCT81:JHJIO Ha 12 MiC.HIJ,iB, a ryc u.i - na 9 Mic.HU.iB. Ha CKiJihKM MiCSIU.iB BHCTaq11Tb IM e o6oM 42 Kr aepHa? 506. (YcHo.) x·2 = 24

4·x=8

lO·x = lOOO

507. y aoonapKy ae6paM' KpiM iHililfX KOpMiB, 38 TH.>K.n;eH b aro,n;oByBaJIH 14 Kr citta. JlaMaM 8 Kr ciHa BH~aBaJIH Ha JI.Ba ,n;Hi. Ha CKiJihKH ,n;HiB BHCTat.JHTh yciM U.HM TBapnHaM 450 Kr ciua?

JI a Ma

508. 1) IlJio~a npHMOKYTHHKa ,n;opiBHIOe ,n;o6yTKY ,D;BOX 'llRceJI (HKi Il03HaqaJ01'b ,n;oB.mHHY i IIIHPHHy), TOMy, 3HaIO'C{ll IIJIOI.QY (,n;o6yTOK) i o,n;Hy ia c1·opiH, MO.mHa 3H8HTH ,n;pyry fioro cTopoHy. HanpHKJia,n;, .HKil\O nJio~a rrpHMOKYTHHtca ,n;opiBHIOe 30 CM 2 ' a o,n;Ha 3 iioro CTOpiH 5 CM' TO ,D;JI.H 06q11cJieHHSl ,n;pyroi: CTOpOIIl1 Tpe6a 30 :

5 = 6 (CM).

2) 3HaM,ZJ;H p03Mip HeBi,D;OMOl crropOHH KO.mHOrO Ilp.HMOKYTHHK8, SIK~O IIJIOil\8 neprnoro 12 CM 2 ' a ,n;pyroro 8 CM 2 • '~

. ••

509. 3Haf1,n;n anaqeHHfl Ko.mHoro BHpaay, HK~o a = 1095. a· 7 - 500 3404 • 8 - a 510. 36 T 9 ll_ : 3 L\ 4 1~ 8 Kr: 8 Kr

15 KM 250 M

M 24 CM:

511 *. IlepHMeTp np.HMOKYTHHKa 24 ,n;M. Moro IIIHp11na Ha 4 ,n;M MeHU18 Bi,n; )J;OB)KHHH. 3HaH,ZJ;ll IlJIOI.QY np.HMOKYTHHKa.

512°. IlJio~a npHMOKYTHOI ,n;iJISIHKH 600

2 M '

ii ,D;OB>KHHa

30 M. Ha cKiJihKH MeTpin m11pHHa [\iei ,n;iJISIHKM MeHma Bi,n; iI ,D;OB.)KHHH?

513° . 10 000 - 690 : 3 • 7 2·27 069

+ 92 405

2 rpH. 80 K.:7 K. 25 rpH. 5 K. •4

514. ~JI.H 3H8Xo,n;.meHH.H IIJIOmi HeBeJIMKUX c}>iryp, .HKi He e np.HMOKYTHHKaMH, 38CTOCOBYIOTb naJLemKy - rrpoaopy IlJI8CTMHKY (a6o narrip), no,n;iJieHy Ha KBa,n;paTH ai CTOpoHOIO 1 MM a6o 1 CM. Ha MaJIIOHKY ( c. 82) naJieTKy HaKJia,n;eHo Ha JIHCTOK ,n;epeBa. IIo.niqHMO, cKiJihKH KBa~paTHHX caHTHMeTpiB yKJiano. C.H BCepe,n;:UHl JIHCTKa.

IlOBHHX KBa,n;paTHMX C3HTHMeTpiB 3. HenoBHHX KBa.n,paTHHx caHTnMeTpiB 10. 10 HCTIOBHHX KBa.n;paTHMX caHTHMeTpiB - ue npH6JIH3HO 5 IIOBHHX KBa,n;paTHHX caHTHMeTpiB. 0Tme, TIJIOI.Qa JIHCTKa: 3 + 5 = 8 (cM 2).

515 . 3uaAAH TIJIOIQY Kpyra i n'HTHKYTHMKa. ~

I \

,...,_

/ ............

( \

516. 06tIHCJIH nepHMeTp i IlJIOII.\Y npHMOKYTHHKa ai CTOpoII8MH 5 JJ;M i 3 JJ;M i KBa.n,paTa ai CTOpOHOIO 4 ,n;M. TiopiBHHH nepuMeTpH lVfX cpiryp, a IlOTiM -

TIJIO~i.

517. 3anHllll1 s11paa11 i 3Haii.n;n ix ana 1 1enn.H. 1) ,[(o cyMH '-U1CeJI 134 i 6 .n;o.n;a11.n;o6yTOK I.J,HX 1 IHCeJI. 2) qaCTKY 'lHCeJI 966 i 23 3MeHlll y 7 paa. \

518. (1270

519 .

+ 1856 : 4). 7

(8240 - 294. 7). 3

~Ba IIOI3JJ;ll O,ll;H0l-J8CHO si.n;iiillIJIH Bi,n; CT8Hll_il

y npoTM-

Jie)KHHX HanpHMKax. llIBH,n;RiCTh nep111oro rroia.n;a 90 KM / ro.n;, ,n;pyroro - Ha 5 KM / roll. 6iJibllla. .HKa Bi,n;cTaHh 6y,n;e Mim noia.n;aMH t-1epea 3 ro.n;? 82

520.

Po3rJI.HHh 3a)l.a-c.ri Ta Bnpa311. Tio.HCHH, JJ,O SIKo1 3a)l.aqi

CKJia~eHO KO:>KHHii BHpa3 o6'lIHCJIHBillH iioro. 3 all, Ha y

npo ~o MOmHa ,u;iaHaTHC.H,

a 'l{ a 1. ,il;oBmHHa np.HMOI<YTHHKa 32 MM, a IIIHPH4 pa3H MeHrna. 3Haii,u;n nepHMeTp i TIJIOII~Y np.HMO-

KYTHHKa. 3

a ,lJ. a

Ha Ha

'l} a

2 . .IJ:o1nKHHa

np.HMOKYTHMKa

32 MM,

a lliHpH-

MM MeHilla. 3Haii,n;H nepHMeTp i IlJIO~y np.HMO-

KYTHHKa.

32. (32 : 4) 32·(32 - 4)

(32+32:4)·2 (32 + (32 - 4)). 2

521°. Ilnoma np.HMOKYTHHKa 640 M 2 , a 40 M. 3Haii,u;H nJio~y KBa,u;paTa,

,n:oBmHHa CTOpOHH nep11Me·rp .HKoro

,u;opiBHIOe rrepHMeTpy np.HMOI<yTHHKa.

522°. 8. 50 725 57 100 • 7

6 T 305 Kr - 2 13 M 64 CM• 5

877 Kr

600 - 600 : 20 (1006 - 265): 3

,Il;IJIEHH.H HA OJ:(HOUJ1cI>POBE qMCJIO 523. 1) IT poq11Taii

noSicHeHH.H npo .n;iro ,n;iJieHH.H.

j{iJleHHR..l'tt Ha3HB8ETbCSI ,n;i.H, 33 ll,OilOMOrOIO RI<Ol 3a ,lJ.06yTKOM ,ll;BOX MHO)KHHKiB i O,ll.HHM i3 ~HX MHOmHHKiB 3H3XO,lJ..HTb ,lJ.pyrHH MHO)KHJIK.

80· 3 = 240 240: 3 = 80 "C.J:HCJIO

80 -

240

Ha3HB8€TbC.H iJiJLellUM'

1lacnuco10.

3 -

iJiJlbflUICOM.,

MHO)KHHi HaTypaJihHHX qnceJI ,D.i.H

,n;iJieHH.H tte 3aB:>K,lJ.M

BHKouyeTbC.H. Hanp11KJia,n., I.Qo6

50 Ha 6, Tpe6a 3HH MTH TaKe q:ucJIO x' .D:JIH SIKOro 6 · x = 50. TaKoro HaTypaJibHoro q11cJia He icHye, 60 6 · 8 = 48, a 6 · 9 = 54. no,n:iJIHTl1

MHO)KHHi HaTypaJibHHX

,n:iJieHH.H 3 OCTa'lleIO:

'l{HCeJI 38Bjl{ll,J1

50 : 6 = 8

(OCT.

MO)KJIHBe

2).

HaBe,n;H 11p11KJia,n;n Ha ,u;iJieHH.H 6ea ocTaqi Ta 3 ocTa-

qero.

524.

Ilpo 1 111Taii BJI8CTHBOCTi qacTKH i

poarJI.HHb no,u;aHi

npnKJia,u;n.

1. ll(o6 noiJinumu 11,ucno na iJo6ymoK iJBox 'lucen, iJocmamnbo noiJi.numu q,e ttuc.no na <¥Jun 3 MU031CUUKi6, a nomiM pe3ynbmam noiJinu1nu na iJpyiuu inno:>1enuK.

120 : (2. 3) = 120 : 2 : 3 = 60 : 3 = 20 2. 1Qo6 noiJi.numu cyMy 'lucea na iJane 'lucao, iJocmamnbo noiJi.nuniu KO:J1Cnur1 iJoiJanoK ua q,e 'lucao i iJoiJamu 3iJ06y1ni 'lacmKu. (48 + 36): 6 = 48: 6 + 36 : 6 = 8 + 6 = 14 3. mo6 noiJinumu pi3UUtflO 'LUCe.n 1ta iJane 1LUC/l,O, iJocmamnbo noiJinumu na ite 'Luc.no aMen1uy6ane i BiiJ' eMnuK, a nomiM BiiJ nepmoi aiJo6y moi 11,acmKu eion1unu apyiy. (90 - 21) : 3 = 90 : 3 - 21 : 3 = 30 - 7 23

BJiaCTHBOCTi l.J8CTKH 38CTOCOBYIOTb rrpn BHKOHaHHi

o6t.JHCJieHb.

144 : 6 = 144 : (2. 3) = 144 : 2 : 3 = 72 : 3 = 24 216: 4 =(200 + 16): 4 = 200: 4 + 16: 4 = 50 + 4 = 54 196 : 4 = (200 - 4) : 4 = 200 : 4 - 4 : 4 = 50 - 1=49

525.

IIo.n;ali .n;iJieHe y BliTJUIAi CYMH 3pytlHHX AO,l\3HKiB i BHKOu

•

HaH )J.lJieHH.H.

846: 2 693: 3 65: 5 450: 6 526. HKi 3 no.u;aHnx aa.n;aq poaa'.a3y10Thc.H ,n;iero .n;ineHH.H? 1) Y 6 OAHRKOBMX 6i,n;oHax 186 JI so.n;n. C1<iJibKM JiiTpiB BO)J;H B O.TJ;HOMY 6i,n;oHi?

2) y

KiOCKY 6yJIO

a KpaeBH,n;aMn y

HaCTiHHHX KaJieH,n;apiB 3 KBiTaMH, a

paa MeHme. CKiJihKM 6yJio KaJieH-

,n;apiB 3 .K paeBn,n;aMn·? CKJia,n;H BHpaa AJUI po3B '.aayBaHH.H 3aAa 11i Ta o6t.JHCJIH lioro 3Ha 1 1eHH.H, .HKI.IJ;O

3) y

b = 126 ill= 3.

180 6iJihllie Bi,n; qJicJia 20? no,n;iJIHJIH Ha 4 i ,n;icTaJIH 24. 3Hai1.u;n

CKiJihKH paaiB '1MCJIO

4) HeBi,n;oMe t.u1cno

HeBl.ZJ;OMe l.B.fCJIO.

5) Y

IIIKiJILHY 1.u;aJibHIO npHBe3JIH

roTyBaHH.H

cHi,n;aHKY

72 JI

BMTpaTHJIH

MOJIOKa.

TpeTHHY

npu-

MOJioKa.

CKiJihKH JiiTpie MoJioKa BHTpaTHJIH?

527.

IlpOl.IHTaM npIIKJia)J;H Ha Ta6JIIflIHi BHII8,Zl;KH ,n;iJieHH.H.

Ilo.HCHH rrpHMOMH 06~n1cJieHH.H iHllIHX npHKJia,n;iB.

72 : 8 84

48 : 3

54 : g

64 : 16

240 : 3

528. Ilo.HCHH p03B'.H38HH.H KO:>K.HOro rrpHKJI8.l(y. _ 988 L!_ _ 216 LL 8 I 247 24 146 18 36 16 36 28 0 28 0 529. CKJia.n;n i poaB' .Hm11 piBH.HHH.H: .HKI.I.J;O Hesi.n;oMe qHcJio a6iJihllIHTJ.I y 7 pa3, .n;icTaHeMO 168. I

530. CKJia,n;H aa Ta6Jin:u;e10 npocTi aa~aqi Ta po3s'.nm11 ix. ,l(on.mnHa

IlJio~a

IllupHHa

npSIMOKYTHHKa

npSIMOKyTHJU<a

? 20 CM 15 M

7 CM ?

70cM2

120 CM 2

....,

531. 3a .n;eHb TypHCTH IlO.l(OJiaJIH 31 KM. 4 ro.n; BOHM llllIJIH ai llIBif.l(KiCTIO 4 KM/ rOP., a pernTy IllJI.HXY - ai IIIBll.l(KiCTIO 5 KM / ro.n;. CKiJihKII t.1acy TypncTH 6yJIM s .n;opo3i?

532째. 48 : 3 . 4

48 : 4. 3

624 : 3

6000 . 3 - 600 : 2

533째. llIHpHHa np.HMOKYTHHKa 8 CM, a 'fJ.OB:>K.HHa - y 4 pa3H 6iJibIIIa. qOMY .n;opiBHIOe IlJIO~a np.HMOKYTHllKa?

534. (YcHo.) 8 : 3

24 .n;ec. : 5

9 COT. : 4

17 THC. : 5

535. Poas'.Hmn a no.HcHeHH.HM: 882 : 7, 378 : 7. 536. PoarJI.HHb aannc i npoq11Ta:M: no.HcHeHH.H. _ 20736 LL_ 16 I 2592 II o H c H e H H .H. Ileprne ttenonHe 47 P.iJieHe 20 THC.Ht.I. y qacTu;i 6yP.e 4 IJ;H- 40 c}>pH. 20 THC.Hq IIOP.iJIHTH Ha 8, 6yP.e 73 2 THC.Hqi i B OCTaqi 4 THC.H1li. 72 ,IJ;pyre HeTIOBHe P.iJieHe 4 7 COTeHh. 16 4 7 COTeHh no.n;iJIHTH Ha 8, 6y.n;e 5 co16 Tellb i B OCTaqi 7 COTeHh. 0 73 .n;ec.HTKH - TpeTe HeIIOBHe P.iJieHe. 85

73 .n;ecHTKii rro.n;iJIHTI1 Ha 8, 6y,n.e 9 ,n;ecHTKiB i B OCTfflii 1 .n;eCHTOK. 16 O,ll.M:Hlll~h - t.IeTBepTe HeIIOBHe ,n;iJroHe. 16 rro.n;iJIHTl1 na 8, 6y.n;e 2. OcTacii HeMae. (_lacTKa 2592. 537. IlOHCHH p03B '5138IIH.H RO:>KHOro rrpHKJia)J;y.

_ 8235 L_a__ 6 I 2745 22 21 13 12 15 15 0

5264 l1_ 49 I 752 36 35 14 14 0

538. PoaB'HjKH a rro.ncue1n-1HM: 24 7 668 : 6, 65 559 : 3.

250 : 5 + 800 : 8 20. 9 - 80 + 800 : 100

539. 360·10: 100: 18

120 . 100 : 10 : 6

540. ,n:na ·rpaKTOPH aa 4 ro.n; po60TH BHTpaTHJIH 200 JI naJibHOro, KomHn.H nopinny. CKiJILKH rraJihHoro B11Tpa1.1an O)J;HH TpaKTOp 38 1 ro,n;'! (Po3B 'JDKI'I aa,n;atiy CKJ18JJ;ClHHHM BHpaay.)

541 . .l1:JIH KpOJiec}1epMH aaroTOBHJIH Ha 3IIMY 20 I\ 40 Kr JiyqHOro cina, a KOHIOWHHH y k paa MeHme. CKiJibKH paaoM citta i Kon10IIn1Htt 3aroTOBHJIH Ha 3HMy? CKJia,n;u BHpaa Ta o61.U1CJIH iioro anaqeHHH, HKill;O k = 3.

330. 3 - (690 + 125) 240 : 8 + 70. 3 - 100 7406: 7 II e p e Bi p c e 6 e: 140; 175; 1058; 41 279.

542°. 288 953 : 7

543°. Ilo6y,n;yii ,n;Ba pi3HHX npHMOKYTHHKH, aJie TaKi, m;o6 •

IIJIOm;a KOmHoro ,n.opiBHJOBaJia

12 CM 2•

544. BnKonaii ,n.iJieHH.H 3 ocTat.IeJO.

9 :4

26 : 8

32 : 5

55 : 7

45: 6

545 . PoarJI.HHh MaJIIOHOK, tIHCJIOBi J];aHi Ta BHpaatt. IloHCHH, m;o ana:H.n;eMo, .HKID;O 061.JMCJIHMO KO»(HHll B11pa3.

30 JI

60 JI

120: 30 120 - 30 546.

120 JI

120 - (30 + 60) 120. 3 + 30. 4

60·6 60: 30

3Hai1:,n;H qaCTKH

547. 19 187: 7

34104 : 6 i 94056: 4

120 865: 5

3 noncHeIIH.HM.

57 128: 8

148 460 : 4

548. )l:soMa cinaJIKaMH 3a 12 ro~ po6oTH aaciHJIH 96 ra nu1eHMIJ,i.

CKiJihKH

reKTapin

o,n;ttieIO TaKOIO ciBaJIKOIO 38

7 ro,n; po60TH? 6

j3 720 OBeIJ,b no 4 Kr non11u. CKiJibKH BCboro KiJiorpaMiB BOBHH HfiCTpl1rJIH? (P03B'.H:IJ\H aa,n;ac1y CKJI8,ll;8HH.HM BHpaay.)

549.

1240

nIIIeHnlJ,i MOmHa aaciHTH

6apaHiB H8CTpHrJIH no

10 M: 4

550. 5 H:r: 2 551 °. 58 216 : 8 26 364 : 6 552°.

1 ~M: 5 CM

1 rOA: 3

4 7 000 : 100 . 5 - 3 70 10 000 - 24. 5 . 7

,[(0Bm1u1a IllKiJibHOro KOpH,u;opy

,u;opiBHIOe

553.

Kr BOBHI1,

11oro ,ll;OB:/KHHH.

24 M, a

1U11pHHa

3HaM~I1 IlJIO~Y KOpH,n;opy.

CKJI8AH KiJihH:a 3a,n;aq 38 BHpa30M

a : 4.

554. qOTHpMa 0'AH81\:0BHMII ciBaJIKaMH 33 9 ro~ aaciSIJIH 108 ra .Ht.IMeHIO. 3a CKiJihKll ro,n;HH MOmHa aaci.HTH 60 ra o,n;Hiero TaKOIO ciBaJIKOIO?

4 c., 9 ro)\ 1 c.,?

108 ra 60 ra 87

555. PoarJUIHb Ta6Jin:a;10. 5 4 ··~ 0 7

III

70 20 90 100

10 6 8 1

12 13

16 14

27 56

1) JJ:o,n;ai1: q11cJia IV i V cTosrr~111Kin. 2) IlepeMHO.iK 'lIMCJia I i V CTOBnqHKiB, III i IV CTOBnqnKiB, II i IV CTOBiltll·I KiB. 3) Bi.n; l:JHCeJI II cT0Bn~1HKfl si,n;HiMM q11cJia IV cT0Bnt1HKa. 556. x. 9 = 4599

x: 9

= 999

x - 9 = 9000

557. 31-1ai1,n;M qacTKM i BMKOHaH rrepeBipKy MHO.iKeHH.HM. 2548 : 2 8486 : 3 25 048 : 4 8105 : 5 558. 3 ,n;iJI.HHKM ai6pa.11n 248 u. KanyCTH, 6yp.HKiB - y 2 pa3H Menrne, Hi.iK KarryCTM, MOpKBM - Ha 84 I( MeHI.IIe, Him 6ypsrKiB. CKiJihKH BChoro u.eHTHepiB onoqin ai6paJIM 3 ,n;iJI.HHKM?

559*. Maca 9 KYJihOK 'raKa caMa, HK Maca 2 Ky6nKiB i 2 maii6. Illaii6a y 2 paaH Jierrna, Him Ky611K. CKiJibKH KyJibOK Tpe6a B3.HTH, ~06 Ix Maca .n;opiBHIOBaJia Maci 1 Ky6HK8?

0000 00000 560°. 3a 2 ro,n; 8 IOHHaTiB apo6HJII1 48 ro,n;iBHHIJ.b ,ZJ;JI.H rrTaxis, rropiBHY KO:>KH11ii. CKiJihKH ro,n;iBHHI.J;b Mome apo6HTH O,ZJ;HH IOHHaT aa 5 ro,n;?

561°. 3Haii,n;M qacTKY i BHKOHaM nepesipKy MHO:IKCHH.HM. 2310 : 6 2905 : 7 61 712 : 8 67 455 : 5 562. 3Haii.n;n tiaCTKY q11ceJI 918 i 3 3 IIO.HCHeHH.HM. 88

56..., . PoarJUIHh aanHc poaa' .HayBaHHH i npo-

_ 12282l§_____ 12 12647 28 24 42 42 0

'(_IHTaii TIO.HCHeHHS:I. Il 0 SI C H e H·H .H. IlepIIIe HeTIOBHe ,n;iJieHe 12 THCSI1I. y qaCTUi 6y.n;e 4 U.Hc}lpH. 12 THC.Ht.I no.n;iJIMTII Ha 6' 6y.n;e 2 THC.fl'Ii. OcTatii HeMae. ~pyre 11enOBHe ,n;iJieHe 2 COT Hi' 2 COTHi He ,n;iJI.HTbCH Ha 6 'l'aK, ~06 y t.IaCTIJ;i 6yJIM COTHi. y qacTu;i Ha Micu;i COTeHh IlHIIIeMO 0. TpeTe nerroBHe ,n;iJieHe 28 .n;ec.HTKin. 28 .n;ec.HTKiB no.n;in11TH Ha 6, 6y.n;e 4 ,n;eCHTl~H i B OCTalli 4 .n;ec.HTKH. l.JeTBeprre HenOBHC ,n;iJieHe 42 OJ);HHHIJ;i. 42 no_n;iJIHTH Ha 6, 6y_n;e 7. OcTatii H~Mae. qacTKa 204 7.

564. 3ttaii.n;H 'lJaCTKlf. Bi.n;noni.n;i nepesip MHomeHH.HM. 453 905: 5 217 301 : 7 377 232: 4 565. 3annIIIH rroTpi6Hi aupa3H i 3Hai1.n;11 i:x 3H8"CJeHH.H. 1) ,ll;o6yTOK llllCCJI 2008 i 8 3MeHIIIHTH Ha 800. 2) qaCTKY q1-1ceJI 33 000 i 100 a6iJihlIIHTH y 3 p83H. 566. 3a 6 XB 3 Kyxapi 3JiiTIHJIH 72 BapeHHKH, nopiBHY Ko.men. 3a CKiJihKH XBHJIIJH O)J;lIH Kyxap MO.me 3JiiTIHTI1 28 BapeHMRiB?

567. Ha Marn11Hi 6yJio 2 T 4 r~ rpel'.IaHHX Kpynis. Y Mara3HHi 3 He! BMBaHTa.mHJIM 4 O,ZJ;H8KOBHX MilIIKH 3 KpynaMH. 3aJIHIIIHJIOC.H Ha MaIIIHHi 2 T 80 Kr. CKiJihKH KiJiorpaMiB KpyrriB 6yJIO B KOmHOMy MiIIII<y?

568 . 2842: 7

52 260: 4

10 032 : 3

20 04 7. 6

569°. 3a 4 ro.n; po60TH 3 O)J;HaKOBHX TpaKTOpH BHTpaTHJIH

240 JI naJihHoro. Ha cKiJihKH ro,n;HH po6oTH BIICTatIHTh 400 JI naJibHOro O,ZJ;HOMY TaKOMy TpaKTOpy? , 570. 81 14 7 : 3

27049·8

183 318 - 183 318 216 392 + 48 073

148 420: 4 23·3i

571. 42 036 : 4

846 027 : 9 720 136 : 4 60 006 : 3 572 . ):(Bi CHHHII,i 33 4 ,n;Hi 3'lJIH 576 ryceHHIJ;h, nopiBHY I<OmHa. CKiJILKM ryceHHIJ;h 3'i:cTh o.n;na CHHHIJ;.H aa 6 .n;JiiB? 89

573. PoarJUIHh aan11c i 110.HCHM poaB'.H3aHHSI.

282024 1-=6_ _ 24 47004 42 42 24 24 0

_ 21056 17 - !3008 21 56 56 0

- 656024 Ill_~_ 64 f82003 16

- 16

24 24 0

574. CTopoHa pinHOCTopoHHhoro TPHKYTHHKa ,n.opiRHJOe 8 CM. 3Haii,nH IlJIOll~Y KBa,n;paTa, nep11MeTp SIKOrO ,n;opiBHIOe nepHMeTpy U.hOrO Tpl1KYTHHK8.

575 .

MoTo~HKJiiCT 6yn y ,nopoai

csi npoixaTH

4 roA, i iloMy ~e aaJIMIIIMJio-

130 KM. 3

.HKOIO llIBHJi:KiCTIO pyxaBC.H MOTO~IIKJiiCT, SIK~O Bech IIIJI.HX CTaHOBMTb 390 KM?

204 012: 6

49 023: 9

7路27004

577. {YcHO). 3HaH,ZJ;l1 HeBi,n;oMi llHCJia. u

b a:b

18 1

100 4

10 100

578. 3Hati,n;11 qacTKM. Bi,n;noBi,n;i nepeaip ,n;ie10 MttomeHH.H. 563 528 : 7 121 824 : 6 98 765 : 5 162 432 : 8 5 79. Q6qIIcJI 11 ycuo Ta 110.HcHu cnoci6 o6l.JHCJieHHH.

180 000 : 6 3 pa 3 0 K.

2400: 2 50 000 : 2 160 000: 6 36 000 : 3 = 36 THC. : 3 = 12 THC. = 12 000.

580 . PoarJI.HHh aarrHc i npo'ln1Tai1 rro.HcHeHH.H. II o .n c H e H H H. fleprne HerroaHe _ 67000 LL_ ,n;iJieHe 6 ,n;ec.HTKiB THC$Jt-l. y l.JaCTUJ 5 I 13400 6y,n;e 5 IJ.HC}>p. 6 ,n;eC.HTKiB TMcnq rro,n;iJIHTH Ha 5, 6y,n;e 1 ,n;eC.HTOK THC.Ht{ i B OCTal.Ji 1 J,J;eC.HTOK THCSlq. ~pyre HeIIOBHe ,n;iJieHe 17 TMC.ff"lJ. 17 THC.H"ll no,n;iJIHTH Ha 5, 6y,n;e 3 THC.ff'lli i B OCTaqi 6y,n;e 2 THC.Hlli.

17 15 20 20 0

TpeTe HenoBHe .n;iJieHe Ha

6yAe

AecHTKiB

coTeHh.

coTeHh no.n;iJIHTH

COTHi. o.n;11HHIJ.h y p;inettoMy

HeMae.

Ha Mic~i .n;e-

C.HTKiB i

O)l;HHHI.I_b 3aTIHCY€MO B tiaCTU.i HyJii. qaCTKa

13 400.

581.

198 000: 3; 681 628: 4.

3Haiip;u qaCTKl13110.HCHeHII.HM:

582. 3a 6

ro.n; po60TH

1560

BHJIH

CHJIOC030Mp8JihHi ROM6ai1HH aaroTo-

T 3CJieHOl MaCH COlUillIHMKY.

520

ro,[(HH MO»te aaroTOBHTH

CKiJibKM

T 3CJieno1

MaCH COHHlllHHKY O)J;HH T3KHM KOM6ai1H?

083 . ,ll;oBmHHa

pe6pa Kyua

cM. CKiJihKH

KBa.n;paTHHX caHTIIMeTpiB nanepy 6y.n;e Il0Tpi6HO,

~06

o6KJieITH

BCi

rpaHi

2cM

Ky6a?

584°. I-la

6y.n;iBHHl~TBO aaBe3JIH

300

Toro .HK BHTpaTHJIU

c MillIKiB. Ilpo

MimKiB n;eMeHTY. IliCJI.H

Kr u.eMeHTY'

33JIIIlllHJIOCSI

~o .n;iaHaeMOC.H, KOJIH 3Haii,n;eMo 3H8lleH-

H.H no,n;aHMX BHpaaiB?

k- c

300 : (ll - c)

300: (k - c) · 20

361 809: 3

10 025: 5

586.

(YcHo.)

IlpotHiTaM aap;aqy Ta p03rJI.HHb

3 a

,n;

2 T 7 u_: 3

a q a.

50 CM

5 ,D;M : 5

TKHHHH11

qacTIIH. CKiJibKU TKaHHHH y

300 : (k - c) · 14

6·2030 CM

1 MM: 9

11 p03B'.H38HH.H. poapiaaJIH Ha 6 piBHHX

tIOTI1phOX TaK11x qacT11 -

Hax? P03B'H38HH.H

1) 19

50 CM : 6 = 3M 25 CM _ 1950 l!L_ -18- 1325 15 1230 30

B O,D;Hiif tJaCTHHi.

0 91

2) 325. 4 = 1300 (cM) = 13 (M) - y qoTRpbOX 'IaCTMHaX. Bi .n; no Bi .n; h: y qoTnphox qacTnHa 13 M TKaHHHll. 588. 5 rpH. 76 K. 5 rpH. : 10 50 K. • 10

10 M: 4 10 T : 4 5 IJ, : 10

13 CM 5 MM : 5 7 ,ll;M 8 CM : 3 8 T 1 U. : 9

589. 1 Kr u.yKepoK KOlllTye 9 rpH. 50 K. CKirrhKH KOlllTye ;:)~Kr U.IIX ll,yKepoK?

590. 3arrIIIIIll BHpa3 Ta o6"tU.YCJil1 iioro 3H3t.IeHH.H. JJ:o6yTOK qHceJI 2080 i 8 a6iJihlllHTH Ha lX qaC'l'KY. 591. TpboMa KocapKaM11 3a 7 roJJ; CKOCHJIH TpaBy a IIJio~i 42 ra. 3 .HKOI IlJIOw;i CKOCMTh TpaBy O,n;Ha TaKa KOCapKa aa 4 ro.n;? 592. jl\IfTO npMBe3JIM Ha ,ll;BOX Tii.D;BO.n;ax, ITO 3 U. 56 Kr Ha KO:>KHiii. Yee jf01TO poac11rraJI11 nopiBHY y 8 MiwKiB. CKiJihKH KiJiorpaMiB m11Ta B o.n;ttoMy MilllKy?

593°. 97 M 20 CM : 9 3 U. 4 Kr: 8

10 T 5 U: 5 1AM8 CM: 2

42 KM 40 M: 4 2 KM 50 M • 8

594°. Y pit.IKOBHM rropT ,n;ocTaBHJIH 24. 168 T rrllleHttIJ,i. Yc10 IlllleHHU.IO BHBaHTa:>KHJIH aa 4 .n;ni, KO:>KHOro ,D;H.H nopinHy. TpeTHHY nllleHHIJ.i, HKY BUBaHTamHJIH nepworo ,n;HH, Bi.n;rrpaBHJIH .n;o MJIHHa. CKiJihKH nlllett11u.i Bi,n;npaBMJIM ,n;o MJIHHa?

595. (YCHO.) 1 AM: 2 CM

1M 596. 36 KM : 5 M 39 IJ. : 5 Kr

5 CM

1 KM: 100 M 2 CM : 20 MM

12 Kr 40 r : 8 r 12 ,D;M 6 CM : 9 CM

1 T: 5 U 1 Kr: 10 r 4 M 8 CM: 3 10 M: 4

597. 3 o.n;Hiei ,n;iJI.HHKlf II OJI.ff cpepMep 3i6paB 12 7 T 8 u. IJ.YKpOBHX 6ypHKiB, a a .n;pyroi - y 3 paan MeHllle. Yci 6yp.HKH BiH Bi.n;Bi3 Ha U.YKPOBMR aano.n;. CKiJihKH 3 HUX Bllll,D;e IJ.YKPY' .HK~O Maca IJ.YKPY CTaHOBHTh l Bi,n; M8CH 6yp.HKiB? 6

598. IIpot.1nTaiI aa.n;aciy Ta po3rJI.HIIh iI po3a'.HaaHH.H. 3 a .n; a "tJ a. 3 ,n;iJI.HHKM 3i6pa.rrH 34 u. 16 Kr oripKiB. Yci 92

oripKH poaK.na;111 B .HllVII<U, no 8 Kry KO)KHHH. CKiJibKH Il0Tpi6tto 6yJio SII.l~HKiB? Poaa'.H3aHH.H

_3416 Ls__ 32 1427 21 16 56 56 0 Bi .n; no Bi JI. b: 427 .H~HKiB. 599. y TpbOX cyBOHX 249 M 90 CM caTHHY. lIIOBKY B 0,ZJ;HOMY cynoi y 2 pa3H 6iJibIIIe, Hi)K caTHHY B O,ZJ;HOMY cyBol. CKi.nhKH IIIOBKY y .n;aox cyao.Hx?

600. 360 : 6 + 72 : 3

252: 42

+ 54

360 : (6 + 72 : 3) (360 : 6 + 72) : 3 672 : 42 + 24 42. 23 - 43. 16

601 °. 3a 7 .D;HiB po60TII 2 onepaTopH Ha6paJI1'J Ha KOMil'IOTepi 294 CTOpiHKH TeKCTy. ~OAH.H o6HJI.Ba onepaTopH na6npa.nn o.n;HaKOBy KiJihKicTh cTopiHoK. CKiJihKH CTOpiHOK Ha6epe O,ZJ;HH onepaTop 3a 6 .n;HiB?

02°. 29 M 60 CM : 4 CM

9 T 48 Kr: 4 Kr

•

4 9 rpH. 5 K. : 3

10 rpH. - 10 K.

S03. (YcHo.) 40 + 20: 5

40: 5 + 20

(40 + 20): 5 40 + 20- 5

8 Kr: 5 K.

5 rpH. : 4

3·6-4·2 3·(6-4)·2

604. 540 042 : 3 . 2

100 640 - 2048: 8 2 T 16 Kr: 8+ 5 T 540 042 :(3·2) (100 640-2048) :8 1 T - 1 I(: 2

605. 3 TepHonoJI.H 11.0 KneBa BHixaB aBTo6yc. 0.n;HoqacHo HaaycTpi~1 iioMy a KneBa BHIXaB 11.pyrHii aBTo6yc. IIep-

lllHH 8BT06yc lxaB 3i llIBM,ZJ;KiCTIO 60 KM/ro.n;, .n;pyrn:H 62 KM/rOJI.. 11epe3 3 rOA BOHM aycTpiJIMC.H . .HKa BiACTaHb Mim MiCTaMtt'! PoarJUIHb poaB'HaaHH.H aa11.aqi JI.BOMa cnoco6aMH. Ilo.R.c. . HH, npo ~o Al3HaJIHCSI KO)KHOIO ,ZJ;l€10.

Poaa'.aaattH.H

2-:H cnoci6

1-ii crroci6

1) 60· 3 = 180 (KM) 1) 60 + 62 = 122 (KM/ roll.) 2) 62 · 3 = 186 (KM) 2) 122 · 3 = 366 (KM) 3) 180 + 186 = 366 (KM) Bi 1l. no Bi 1l. h: 366 KM - BilJ.CTaHh Mim MicTaM11. 606. Bi,n; npncTaHi «Kn1B» 11.0 npncTaHi «KpeMeHqyK» Bi,n;qaJnfB TenJioxu, i O.AHOl.Jactto iioMy naaycTpil:I Bi,n; rrp11cTatti «KpeMeH'(IYK» Bi,n;t.HlJIHB KaTep. TenJioxi11. imon ai IIIBHlJ.KiCTIO 30 KM/ rolJ., a KaTep - 24 KM/ r01J.. qepe3 5 roll. BOHM aycTpiJIHCSI. HKa Bi,n;cTaHh Mim np11cTa1uIMH?

607. l)x·2 = 14850 x:2 = 14850

x - 2 = 14850

2) B11:K0Hali ,n;i1 i apo6w nepeBipKy o6epttettoro 1l.ie10.

20 700 - 9478

817: 43

36. 23

9765 + 91 807

608°. ,lI;BOMa KOCapKaMH 38 4 rOlJ. CKOCHJIH TpaBy 3 IlJIOll.li

24 ra. 3a CKiJihKH rO,Z:V1H CKOCUTb Tpaay O,n;Ha KOCapKa a ITJIOII\i 138 ra? 6 09°. 3 XapKoBa Ta 3anopimm.H HaaycTpiq O/J.HH Oll.HOMY .. .

OJJ;HO"t.JfiCHO BH1X8JIH )lBa TYPHCTH: Ha MOTOU,llKJil TH Ha MOTopoJiepi. lliBH)1-KiCTh MOTO°'Hl{Jia 55 KM / ro11., a MOTOpoJiepa - 30 KM/ rOlJ.. qepea 3 ro,u; TYPHCTH aycTpiJIHC.H • .HKa BiACTaHb Mi:>K MiCTaMH?

6 10 3400·100 + 100

900 - 10·10 61

35 - 12 + 20 - 18 78 + 12:3 - 36:9

612. 5·4207 ·3

(80 + 20) · 100 80 + 20·100

480: 4. 3 480: 3. 4

24 : 3 : 2. 4 : 8 34 - 2·(16 - 6)

4· 145 397: 7

27 801: 3 + 73100·6

1) Po3rJI.HHh aanHCH i no.HCHH 06q11cJieHH.H. 24 000: 4 = 6000 3600: 3 = 1200 24 THC. : 4 = 6 THC. 36 COT. : 3 = 12 COT. 2) 16 000: 2

4800: 3 150 000: 5 90 000: 6 (8706: 6 + 107)·9 12 087: (3 + 30: 5) (6018·2 - 540): 6 27 018 : (9 - 30 : 5)

615. BiA AROX npoT1111emtt11x 6eperiB 03epa OAHO'llaCHO noITJIHBJIH Ha.aycTpitI OAHH O~IJOMY ;:(Ba ~10BHl1. Ilep111Hii t.IOBeH IIJIHB ai lllBH'AKicTIO 7 1<.M/ ro,z:(, a Apyrnii 8 KM / rOA. qOBHH aycTpiJIHC.fl qepea 3 rOA. 3ttaiiJJ;M BiJJ;CT8Hb Mi)J{ 6eperaMH 03epa.

616. (YcHo.) 22 : 5 49: 6

40: 8 52: 7

40: 6 23: 5

36: 5 82: 9

70: 8 60: 8

617. 3a AfiHHMII MRJIIOHl\.a o6t.UfCJIH IIJIOIIJ;Y noncpxui poa-

ropTKH np.HMOKYTHoro napaJieJierr1neAa.

618°. 3 ,ll.BOX HaceJieHHX nyHKTiB, BiJJ;CTaHb Mim

.HJ{.HMH

KM, BH1xaJIH o~HO'llacuo Ha3yCTpitI OAHH OAHOMY .n;na

BeplllHMKM. Ilepuu-d1 i'.xan 3i IllBHJJ;H:icTIO 9 KM/ ro,n, a Apyrui'1 -. 12 KM/ rot(. qepea cKiJihKH rOJ(HH noHH aycTpiHyTbC.H?

619°. 2600: 10 + 27 840

90 + 348·100

8244 : 9 + 4 708 . 7 (8244 : 9 + 4 708). 7

620. 3HaHJ(I1 t.IaCTKH i 3p06H rrepeBipKy. 44 824 : 8 34 521 : 3 621 . 24 708. 4 - 24 708 : 4

(24 708. 4 - 24 708) : 4

622. 3 ;:(BOX acpo.n;poMiB, ni.n;CT8Hb Mim HKUMH 2560 KM, Hl1JieTiJIH O,ll;HO'llaCHO HaaycTpiq O.D;HH O,AHOMY ,ABa JiiTaKH i 3ycTpi1n1cn qepe3 2 roA. IIeplllHii JiiTaK JieTin ai lllBHAKiCTIO 620 KM/ roA. 3uai1.n;11 UIBH,AKiCTh ,Apyroro JiiTaKa.

623. Po3rJIHHh MaJIIOHOK (c.96) i 1 111cJIOBi .n;aui Ta ana:ti.AH Bl~ITOBl,Al

Ha 38Ill1TRHH51.

1) .HKa Maca 3 T8Kl1X OBeU.h? 2) .HKa Maca 2 TaKHX 61rc1KiB? 3) 4) 5) 6)

y CKiJihKM paaiB BiBU.H Ba:>K'lla Bi,n; IIOIJ)CHTH? HKa Maca 8 TaKHX osen.h i o,n;Horo rropocHT11? Ha cKiJihKH KiJiorpaMiB BiBU.H Bam'(1a BiA nopoCH'rH '! H1(a Maca 3 TRKIIX nopOC.HT?

30 KI'

KI'

4 U. 80 Kr

624. Bi,n;cTaHh M.i:>K ABOMa ceJiaMH 48 KM. 3 o,n;Horo ceJia BH1xas BeJioc11rre,zi.:ncT. O,n;ttoIIacHo Ha3YC'rpi'(1 ifoMy a iHrnoro ceJia s111xaB ryceH1rqu11i1. TpaKTop. lliBM,n;KiCTb BeJioc:nne,n;11cTa 14 KM/ ro11., a TpaKTopa 10 KM/ ro,n;. qepea CKiJibKH ro,n;MH BOHM aycTpiHyTbCH?

625. 3naH,n;H 3Ha'lleHHH Bttpaay 15 750: k,

HK~O

k = 3, h = 7.

626 *. Ana neJioc:nrre,n;ncTa BH1xaJIH o,n;Ho'llacHo a MicTa ,n;o 6a3H Bi).l;ITO'CJFIHKy. 0,n;HH 1xaB ai llIBH,ZJ;KiCTIO 10 KM/ ro,n;, a ,n;pyrnii - 13 KM / ro.n;. qepea 2 ro,n; ,n;pyr:nii BeJiocnrre,ZJ;HCT npOKOJIOB KaMepy' TOMY ,n;aJn HllIOB IlllliKH 31 IIIBH,ZJ;KiCTIO 4 KM/ ro,n;. Ha .HKiii BilJ.CTaHi Bi,n; MiCTa rrepllIHii BeJiocnrre,n;McT .n;omeHe ,n;pyroro? •

627. 2312: 8

44 268: 3. 7

903 : 21

44 268: 7. 3

•

14 301·2 - 777: 7 (14 301 . 2 - 777) : 7

628 . Ills11,n;KicTh seJiocune,n;ncTa 12 KM / ro,n;. [(e B 3 pa311 6iJihIIIe Bi,n; lllBH,ZJ;KOCTi rriIIIoxo,n;a, aJie B 6 paa MeHIIIe Bi,n; IlIBll,ZJ;KOCTi aBTo6yca. 3Haii,n;H IIIBI1,ZJ;KiCTh rrirnoxo.n;a ii •

anTo6yca.

629. (Yetto.) 45 000: 100

630. (YCHO.) 25 : 3 96

14 : 5

250. 100 20 : 7

10 000 : 1000 30 : 4

45 : 6

631. TipotIHTai1 noncHeH1u1 npo )liJieHHn na 10, l 00, 1000

a oc ra'-1e10. 1

1) 73 : 10 = 7 (OCT. 3) 2) 184 7 : 100 = 18 (OC'f. 4 7) Il 0 n CH CH H SI. 1) Y qncJii 73 Haii6iJihll1e '-IIICJIO, Hl\C ,niJIIITbCSI Ha 10, u_e 'LJlJCJIO 70. 73 no~iJIHTU na 10, 6y,ne 7. 3 UAMH HU.i CTflHOBMTMMYTb OCTaqy. 2) Y qncni 184 7 Haii6iJibUie q11cno, .HKe ,niJinThCH na 100, t\e "lJHCJIO 1800. 184 7 IlO,l\iJIHTH Ha 100, 6yAe 18. 4 7 OJU-1Hl11.J.b CT8HOBHTHMYTh OCTaqy.

633. 724 036 : 4

83 450: 10 83 450: 100

12 700: 1000 8400: 1000

632 . 254: 10 254 : 100

+ 40 850

2·843 - 4·343

634. I-Ia 3 rn aeMJii rrocinJIH 500 i<r 11u1e111u.J.i. CKi..TihKH aepHa noTpi6uo, ~06 aaci.flTH 300 ra aeMJii? 635. AnTOM06iJieM r A3 Mom.Ha nepcBe3TH 600 IJ. ByriJIJUI aa 24 pei1cH, a HBTOM06iJieM 6iJJhlllOi B8HT8i1\IIOCTi - 3a 12 peiicin. 3a CKiJILRH peiicis Mom.yTb nepeBe3TH Bee ayriJIJISI o6H]\Ba aBTOM06iJii?

636. AnToMo6iJIL KpA3-237 n11Tpal'.1ae aa HopM010 Ha 100 KM IJIJIHXY 36 JI naJihHOrO. AJJ.e llIOc}>ep o6Hpan apyqHHH pemuM po60TH MallIHHM i AOMirc.H BHTpaTH 31 JI naJibHoro Ha 100 KM. CKiJihKH JiiTpin naJI1>Horo ae1toHoMHTb llIO<}lep Ha llJJISIXY B 1000 KM? 637*. lJepea 16 poKin CeMeH 6yAe

BTp11~1i cTapu111if, uim

Tenep. CKiJihKM poKiB iioMy Tenep?

638°. 3 ABOX TYPHCTHqHJIX 6aa, Bi'ACT8Hb Mim SIKHMH 34 KM,

...

Bl1HllIJIH O,l\HOqacno Ha3ycTpPI O,l\HH O)J;HOMy IllillOXIA

i JIHmHHR. IIiinoxiA i1uon ai IllBHAKiCTIO 5 KM / rOA, a JlfDl<HHK - 12 KM/rOA. qepe3 CKiJihKH rO/\HH BOHH aycTpiHYTbCH?

639°. PoaB'HmH rrpHKJI8AH a nepenipKOIO. 7023·5 34 456: 8 621150: 3

4. M11-rer.saTn Kn. 4 1<11.

AMoMnEHHSI 3 AP06AMM. HHSI I AlnEHHS1

"IMCEn, ...""..-.TbCSI HYnSIMM

~,,_.oaMX

,l(POBli 640. Ha MaJIIOHKY ao6pameHo ~iJIHM Kpyr i Kpyr, rro11.iJieHnii Ha 2 piBHi qacTHHH. 011.Ha TaKa "CJ8CTHHa - ~e IIOJIOBHHa, a6o O,lt;Ha 11.pyra. IloJIOBHHa II03Haqa€TbC.H 11.BOMa 1 l\IH}>paMH - - • HK~o npnKJiacTn noJIOBMHH 011.Ha 11.0 O)IiHOl,

,ZJJCTaH~MO ~iJIHH Kpyr. y

IOThC.H CJIOBOM

llOJW6U1ta,

no6yTi 43CTO KOpHCTY-

a6o nia. IliBKiJiorpaMa (!Kr),

1 rriBJiiTpa (_!.JI), niBTOHHH ( 2 T). 3HaM,n;H _!_ Bi,n; "CJHCeJI

100, 1 Kr.

641. Ha MaJIIOHKY ao6pameHi Kna11.paTn, no11.ineHi Ha piaHi 'tHlCTHHH. HKa 3 ~nx qacTHH Haii6in1>ma? HaiiMeH11Ia? 3arrHIIIH BCi qacTHH11 BiA Haii6iJiblll0l 11.0 HaHMeHllIOl.

642. PoarJI.HHb aa11.aqi Ha aHaxo11.meHHSI qacTHHH 1IHCJia i tJHCJia aa iioro qacTHHOIO. CKna11.1I ,n;ai rro11.i6Hi aa11.aqi. 3a11. a q a 1. Bi11. 12 M APOTY Bi11.piaaJIH 'tJeTaepTy 'tJaCTIIHY. CKiJILKH MeTpia 11.poTy ai11.piaaJIH?

p 0 3 B'.H 3 a H H .H: 12: 4 = 3 (M). Bi /1. II o B i /1. h: BilJ. 12 M 11.opimnoe

3 a ,n; a 'll a 2. Ileprnoro .D;HH 'l1YPMCT rrpOMIIIOB 24 KM,

cTanoBHJIO .! nchoro IIIJI.HXY. HKu:H ysecL llIJI.Hx? 4 p 0 3 B '.ff 3 8 H II SI: 24 • 4 = 96 (KM). Bi Ano Bi A 1>: yBeCh mJI.HX cTaHonttTh 96 KM.

643. 1) PoarJI.HHh poaB'.H3aHHSI aaBAaHH.H.

3 a B /1. a H H SI. 3HaiilJ,H Bi/J, 90. p 0 3 B'.H 3 8 H HSI: 90: 5 = 18. Bi /1. II o Bi /1. h: BiP. 9011.opiBmoe 18.

! BilJ. 720. PoaB'.Haann.H aalIHIIIH. 644 . .l{oa:nmna ! ruy1(aHoro ai11.pia1•a 3 3mlli:11.u . . . . 2) 3Haii:11.n

CM.

IJ.OBJKH-

...,

ny myKanoro n111ip1aKa 1 HaKpecJIH Horo B aoIIIHTL

645. ,ll:JI.H lIIKOJIM npHA68JIH 240 KBHTKiB y IJ.HPK Ta 420 KBHTKiB y TeaTp. l.JeTBepTy 1.IaCTHHY I<BHTKiB y IJ.HPK . . 1 llIOC'ry qacTHHY KBMTKlB y TeaTp Bl/Ji,ZJ;8JIH yqHSIM no"tJaTKonux KJiacin. CKiJILKH Bchoro KBHTKiB ni,n;,n;anu yqH.HM no-c1aTKOBHX KJiacie?

646. 3Haii,n;H 3Hat.ieHHH no,n;aHHX BHpaaiB, 989:a - 20

1000 - 774:a

.HK~O

a = 43.

17·a - 567

647°. B yHieepMaai 6yJio 280 minoqux i 150 qonoeiqHx KOCTIOMiB. Ili,n; t.1ac poarrpo,n;a.my aa ,n;eHh rrpo,n;aJIH qeTnepTy qacTHHY .miHO'tJHX i TPCTIO qaCTHHY TIOJIOBi 1 1HX KOCTIOMiB. HKHX KOCTIOMiB rrpo,n;aJIH 6iJihllle i Ha CKiJihKH?

648°. 3a ,ZJ;8HHM11 MHJIIOHKa 3H8H,ZJ;H' Ha CKiJibKH KiJIOMeTpiB ni,n;cTaHh KM MeHrua Billi rronoBHHH Bi'"'cTaHi KO.

100 KM

Kt:

• 320

649. Ha MaJIIDHKY (c.100) 7 o,n;naKOBHX upHMOKYTHHKiB. Ileprnnli - DJJIHH, 11ipyruii - no,n;iJICHHM Ha 2 piBHi qaCTHHM, TpeTiii - Ha 3 piBHi •1acTHHH, qeTBepTHH - Ha 4, t*

n'.HTHii -

piBHMX qacTHH.

IIIOCTMii -

8 i

CbOMlfll -

~iJIOMY rrp.HMOKYTH Ky MiCTHTbC.ff

ABi IlOJIOBHHH, TpH rrpeTix l.£8CTHHM, "lJOTHPH t.IeTBepTHX, n'-HTh n'.HTnx, siciM BOChMHX a6o AeC.HTh AeC.HTHX 1 1acTMH. CKiJihKM t.IeTnepT11x qacT11u y noJIOBHHi? KopncTyIO't.IHCh MaJIIOHKaMn, nopiBH.HH qacTHHH:

1.1 1.1 1.1 1.1 - 1. -1-· - 1-. 2 8 ' 8 10 , 3 2 ' 4 5

-1-.

:: ~ ]

1 4 1

-1 1

1 8

5 1 8

1 10

I 10 I lo I

650. (Y CHO.) 1 JI CORY p03JIHJIH y Cl'~JIHHKH y CKiJibKH TaH:Hx CKJIJIHOK HBJIHJIM ciK? 651. 4

JI MOJIOKa p03JIHJIH y

1 4

I I I 11~ I lo I -- I lo I to I 1

1 3

1 2

-1

1 10

I I I I I I

MiCTKiCTIO _!_JI. r.:

nisJiiTposi 6aHKH. C1<:iJibKH

noTpi6Ho 6yJio TaKHX 6auoK?

,. 1 652 • 3 H8HAH: 5

653. y

Bl)];

1 Kr, -1 Bl,ll; . 2 1 XB, -

caJIOHi IIITOp 6yJio

450

BIJJ;

1 ro.n;.

M TK8HHH11. Ilep111oro )J;IUI

npo,n;aJUI rr'SITY 1 18CTHHY TKaHHHH, a JJ;pyroro 11aCTl1HY

TpeTIO

Toro, ll\O 38JIHlllHJIOC.H. CKiJibKH MeTpiB TK8HH-

HH npoAaJIH Apyroro AH.H?

654. 100

KniTHHK np.HMOKYTHOi c\>OpMH Mae ,n;onmHny

i IIIHPMHY 20 M.

nJio~i KBiTHMKa 3aii,rv1a10Tb rBoa,n;H-

KH, a peIIITY nJio~i ,n;meHo TIOJibITaHaMH?

TIOJibnaHH. HKy rrJioru;y 3aca-

655°. CKBep Mae npHMOKYTHY c}>opMy. Moro ,n;oB:>K11Ha .n;opiBHIOe 50 M, a lIIHpnna 20 M. ! CKBepy aaiiMae irpOBHH ... . .5 . . . MaII.zi;aHqHK, a peIIITY ITJIOIJJ;l BtABe.zi;eHO Ill)l; ,n;epeBa 1 Kyn\l. 3HaH~lf HJIOU~Y' Bi,n;Be,u;eHy rri,n; ,n;epeBa i Ky~i.

656°. 756: 3 966: 21

100 000 - 7245. 4 + 9754 100 000 + 82 056 : 4 - 7109

3·3027 3027: 3

657. 3anHIIIH y 30IIIHTi "CJ8CT11HH B nop.H,u;Ky 3pOCTaHHH. 1

6 ' 2'

10 '

8 '

l 12 '

3' 5 4 . 9

658. I-Ia CKiJibKH piBHMX l:IaCTMH no.zi;iJieHo KO)KHMM KBa,n;paT? HK HaanBae'rhCH KO.W:Ha Heaacl1ap60Bana qacTMHa KBMpaTa? CKiJihKM i HKHX qacTMH y ItBa,n;paTi aacpap6oBatto?

•

659. IloJiil:JH' Ha CKiJihKH piBHHX qacTMll rro.zi;iJieHO KO:>KHHH Kpyr. CKiJihKH TaKHX qacTHH aac}1ap60BaHo?

qHCJia BH,n;y

! ' ~' ! ' 2

_!_ ' ~ H83HBRIOTh iJpo60lJUMU 6

- .n;pi6, 5 - 1tllC€Jlblillli ,n;po6y, a 6 - 3/tll~teJtHUK .zi;po6y. 3HaMeHIIHK - 'tlHCJIO ni,n; pncKOIO ,n;po6y IIOKa3ye, Ha CKiJibKH piBIIHX qaC'fHH no,niJieHO I\iJie. lln:ceJibHHK - q11cJIO H~ pHCKOIO ,n;po6y - noKa3ye, CKiJI~Kll B3.HTO piBHHX t.{3CTHH ~iJioro. 1tuCJtll.Mll.

lf HCJIO

101

660. 3anHIIlH ~po6oM, HKY qacTHHY KOmHoro np.HMOKYTHHKa aacpap6oBaHo.

661 . 3HaH~H (ycHO

qJi

Il''tCbMOBO)

.!. Bi~ KOmHoro qHCJia 8

320, 1600, 10 128, 2 KM, 2 ro~, 4 IJ.. 662. Y MaraaHH npHBeaJIH 2 T 4 u Kpynin. Tp'"THHY KpyrriB a6o BeJIHl:IHHH:

npH~6aB pecTopaH, a pellITY -

poaqlacyBBJIM B rraKeTH, no 4 Kry KO.mHHH. CKiJihKH BHHIIIJIO naKeTiB a KpynaMH?

663 *. Bi,n;cTaHb Bi,n; _n;oMy ~o WKOJIH 1 KM 300 M.

Yqem. npoihIIOB .no lllKOJIH 1 KM aa

ro,n. Ha peIIITY IllJisrxy B Hhoro aaJIIIlliHJIOC.H 3 XB. l.JH BCTHrHe yqeHh CBOe'l!aCHO npHHTH _n;o lllKOJIH, .HKIIJ;O 6y.n;e HTH a ·riero caMoro IIIBHJJ;KiCTIO?

664 °. HaKpecJIH Bi_n;piaoK aaB_n;oB.mKH 8 CM i noKamH Koro

~ 4

~ym

D;bOrO Bi_n;piaKa.

665°. y 840 Kr rOTOBOl Hri~HOl KapaMeJii _!_ Beier MaCH CTa-

1 7 c . HOBJI.HTb .HrO~H, - - MOJIOKO, a pellITY - ~yKop. KlJib• . 4 KH KlJiorpaMlB UYKPY BHKOpHcTaJIH JJ;JI.H npHroTyBaHHSI KapaMeJii?

666. IlpoqHTaii _n;po6H i noSICHH, .HK 1x yTBopeHo.

,, 2 7

EfE EfEE 4

-6

~....._...., 1

3 8

_______., 2

667. 3anHIIIH IJ.Hc}>p8MH _n;po6H: n'amb CbO.MUX, 11omupu w.oc1nux, ci.M 60CbJ.WX, OBi ae8'Rmux, w.icmb aeB'.Rmux, oiJHa aecRma. 102

668. PoarJIHHb MaJIIOHOK i poaB' H3aHHH aa.zi;f.lqi Ha aHaxo.n;meHHH .zi;po6y Bi.zi; l.JllCJia. 3 a ii; a q a . .D:oBmHHa Bi.zi;piaKaAB 3 n;Loro Biii;piaKa?

10 CM. qOMY .zi;opiBHIOe

10 CM

A~t~-----~------------------------____.~iB

A-l4__2_c_M__~i-------·-------·--------·-------·B 1

5 3 5

0 3

B'H

1) CKiJihKH caHTHMeTpiB B

H H .H

Bi.n;piaKa AB?

;)

2) qoMy .n;opiBHIOe

10: 5=2 (CM) Bi.n;piaKa AB? 2 · 3 = 6 (CM)

Bi .n; no Bi .n; b: ,noBmHHa

ei.n;piaKaAB .n;opiBHIOe 6 cM.

669. 3Haff,n:H : Bi,n: 64 260. 64 260 : 9. 5 = 35 700 - 64260 lJ!__ x7140 63 I 7140 5 12 35700 9

36 36

670. 3Hali.n;n

.! 7

Bi.zi;

28;

Bi.n;

3864;

Biii;

1575.

671 °. Ha o.n;Hiil JiicoBiti .n;iJIHHD;i noca.n;HJIH 12 650 .n;epen, a Ha .n;pyriil - y 5 paa MeHme. IIIocTy qacTHHY Bcix .n;epeB cTaHoBHJIH .n;y611, a peIIITY - iHIIIi .n;epeBa. CKiJILKH .n;y6ie noca.n;HJIH Ha o6ox ii;iJIHHKax?

'103

672°. 3a 7 .n;uiB 8 6ypyH)J.yKiB nepeHeCJIH

HipI<:H 1960 ropixis, nopis Hy KO»<HHH. CKiJILI<H rop ·• · iB nepeHece B nipH:y 0)1.HH 6ypyH.AYK aa 21 )J.eHh? B

~~s~

673. (Ycno.) 3aaiiAH

! . : . !.

3 10 BiA

1 XB.

674. ,U,o TIHC.na 72 060 AO,ll,aii : Horo. 675. HaKpecJIH Bi.n;piaoK AB = 10 CM. IIoTiM HaKpecJIH u~e )I.Ba ai.n;piaKH: Bi.Apiao1<: MK, 11.\0 CTaHOBHTh ~ Bi.n;piaKa AB, i Bi.ApiaoK OE, ~o cTaHOBHTb ~ Bi.n,piaK~ AB.

4 676. 06"CJHCJIH (b • 7 - b: 34) · 3, HK~O b = 884.

677. Ila nTaxocpepMi 6yJio 8420 nTaxiB: KYPH CTanOBHJIII : , ryc11 -

ycix nTaxia, a pernTy -

K3"CJKH. CKi.TinKH ·

Ha nTaxocpepMi 6yJio oKpeMo Kypeli, ryceii i Ka'l!oK?

678. IlJio~a napKy CT8HOBHTh 86 000

1-IacTHHY ~horo napKy y BHrJIH.Ai npHMOKYTHOl .n;iJI.HHI\.H ai CTOpoHaMH 3 320 Mi 100 M ai.n;se.n;eHO ni~ irpoBHM M8M.lJ.8lllllfK. pelliTH napKy 38HM810Th KyIQi i )J.epeBa . .HKy IlJIO~~ aaHM810Tb Ky~i i .n.epeBa?

679. (Ycao.) 780 - 180 : 2 · 6 (800 : 8 - 20) : 4

M2•

(780 - 180): 2·6 800: 8 - 20: 4

680°. 7·(14057-27054:6) 20T35Kr:5 20M35cM:5 681 °. Y MaraaMH aaBeaJIH 1750 KaJieH,n;apiB y naqKax. IlepeKll,D;Hi KaJieH.n,api 6yJIH y 6 J]ftl.JK8X, no 50 y :KOjKHiH. 104

9 pemTH cTaHOBHJJH siJJ.pHBHi KanettJJ.api. CKiJJhKn 10 Bi,ApHBHHX KaJieH,n;apiB aaae3JIH B MaraaHH?

682. 11o6y.n;yli np.HMOKYTHHK ai CTOpouaMH 10 CM i 2 CM. TT • 1 7 ·? '"'l.OMY )J;OplBHIOe 3 11oro nepHMeTpa 1 10 1'10110 IlJIO~l o

•

683. (YcHo.) 3uali.n;11 -3 , -3 , -1 , -5 , - 5 , - 1 ai.n; 1 ro.n;. 684. 3Haii)l.H

Bi,ll. CYMH •rnceJJ 20 454 i 8406.

685. IlapKOBa 30Ha MiCTa CTaHOBHJia 3400 ra. IliCJIH poaIllHpeHHH IlJIO~a napKOBOl 30HM a6iJihlllHJiaCH Ha .!_ • 8 fl Ka IlJIO~a rrapKOBOl 30Hll MiCTa? 686. AoBmuua ca.n;11611 lOO M, a lllHpHna - Ha 60 M MeHrna.

a nJio~i ca.n;H6n aar aroTh 6y.n;ia;Ii, .n;Bip i ca.n;, a pewT8y - ropo~ • .HKy rrJioI..Qy aaliMae ropo.n;? 687. Y xnon•rn:Ka 6yno 11 rpH. 70 K. Ha ~ ycix rpomeH BiH Kyn11a 3 KHHmKH 3a o.n;t1aKono10 ~iHoro. CKiJihKH KOlllTye O,ZI.Ha KHR.>KKa?

688. IlpoqHTaH IlO.HCHeHHn,

aa.n;a~1y

i po3rJISIHb 11 po3B'H-

38HH.H.

II o H c H e H H H. Api6 Mom Ha poarJI.H)J;aTH He TiJihKH HK cyMy o,n;HaKoanx qacTHH, a li HK qacTKY .n;aox qMcen.

5:8=~

8 3 a 11. a q a. 4 XJIOillJUKM ai6paJIH 3 Kr 0jl{l1HH i no.n;iJIHJIH 11 rropiaHy. CKiJILKH om:nHM o.n;epmaa KO:>KHHH xJiorrtIHK? 105

0 3 B' .fl 3 a H II .fl:

3 : 4 =~ (Kr) = 7 50 ( r) 4

1 Kr= 1000 r, 1000 : 4 · 3 = 750,

(Kr)=

750 (r).

689. 1) 06~111cJIH 'ABOMa cnoco6aM11: 3 · (5 · 4), (2 · 8) · 4. 2) Q6qHcJIH apyqHHM cnoco6oM: 34 · (5 · 2), 25 · ( 4 · 8).

60 825 : 3 + 10 850 : 5 (60825:3+10 850): 5

690. 7544 + 23. (81 - 75) (78 + 65)·(13 - 8)

691 °. Y Tphox uexax o.n;Horo aaBo,n;y HMKiB.

npa~roe

ycix po6iTHHKiB npan;roe

2940 po6i T-

a nepII.IoMy uexy, .

a pemTa - y .n;pyroMy 1 TpeTbOMY' noplBHY B KO:>KHOMY. CKiJihKH po6iTHMKiB npauroe a TpeT1>0My n;exy?

692°. Bi.n; npMcTaHi o.n;HoqacHo y npoT11JiemH11x aanpHMKax Bi,ZJ;iMWJIH .n;Ba MOTOPHllX qoBHli. llepea 6 ro,n; Bi,ZJ;cTaHh Mi:>K HllMM 6yJia 378 KM. 3HaM.n;ll IIIBll,ZJ;KiCTb ,n;pyroro • qoaaa, HK~o mBM.n;KiCTb rrepmoro 35 KM/ro,n;.

q11cEJI, 3AKIHqYIQThCH HYJIHMH MHOmEHH.H

693. Bi.n; JlyraacbKa ,n;o JibBOBa JieTiJIH JiiTaK i BepToJii T. CrroqaTKY JiiTaK 6yn noaa.n;y nepTOJibOTa aa 400 KM. llIBH,ZJ;KiCTh JiiTaKa 12 KM/XB, a BepTOJihOTa - 2 KM/XB. HK a si,n;cTaHh 6y.n;e Mim HHMH qepea 20 xa? Kon11 JiiT&K rropiBHHeThCH 3 nepTOJibOTOM? .HKa Bi,ZJ;CTRHh 6y,n;e Mi:>K HHMH qepea 1 ro.n;?

JlbBiB

106

12 KM/XB

,...__ 2 KM/XB

I~-1----~--~~~-40_0~KM__~------~---J JlyraHCbK

694. 1) ,Il;JISI 3Haxo,n;meHH.H q11cJIOBHX 3Haqe11b BHpaaiB yqeHh BHKOpHCT8B nepecTaBHHH i cn<Jt.tyqHHii 38KOHH MHomeHHSI. Ilo.HCHH ,n;il y't!H.H.

8. 7. 5 = (8. 5). 7 = 40. 7 280 2. 3. 25. 3 = (25. 2). (3. 3) = 50. 9 = 450 2) Ilo.HCHH piaHi cnoco611 o6qncJieHH.H.

15 x 42

15. (7. 6) 15. 42 = 630 15. (7. 6) = (15. 6). 7 = 90. 7 = 630

+ 30 60 630

3)06'tJHCJIH: 8·(5·3), 5·7·2·9, (49·25)·4, (53·2)·5.

695. (Yetto.) 2·10

53·100 6·10

15·100

18·1000 15·1000

8·10 000 2·100

696. 1) PaarJI.HHh aanHcH i no.HcH11, HK MO:>KHa KpyrJie tIHCJIO 38Ill1C8TH y BllrJIHAi ,n;o6yTKY ABOX q11ceJI, O,D;HMM . . 13 MHO:>KHHKlB .HKOro e "lJHCJIO, 38IlHCaHe O,D;HHHIJ..HMH 3 HYJI.HMH. 8· 100 = 800 800=8·100

3·10=30 30=3·10

27 • 100 = 2700 2700 = 27. 100

2) 3anHWH y BHrJI.H~i ,n;o6yTKy: 500, 50, 6800, 40 000.

697. Y'lleHb npO'tlliTRB 40 CTopiHOK KHR:>KKH, ~o CTRHOBHJIO _!_ Bciel KHR:>KKH. CKiJihKH CTOpiHOK y KHH:>KI.JJ? 10 698. PoarJIHHh aa.n;aqy i rro.HCHH 11 poaB '.H3aHH.H. 3 a A a q a. Ha noJI11BaHH.H oripKiB XJIOWIHK BMTpaTHB 25 JI BO,D;H, ~o CTaHOBHJIO qeTBepTy qacTHHY BO,D;H, .HKa 6yJia B 6oqn;i. IloTiM 30 JI BO,D;M BiH BHTpaTMB Ha Il0JIHB8HH.H .H6JiyHh. CKiJihKH JiiTpiB BO,D;H aaJIHIIIHJIOC.H B 6oqu.i? PoaB'.HaaHH.H 1) 25. 4 = 100 (JI) 2) 25 + 30 = 55 (JI) 3) 100 - 55 = 45 (JI)

~n oB

1>: y 6oqui aaJIHIIIHJiocH 45 JI Bo~H. 107

699°. y rreKapHi .D;JIH rrpHrOTyBaHHH BaTpymoK Bl1'rpaTHJilJ 24 Kr c11py. Ha ~e nimJia .!.. Bcboro CH , u~o 6yn y neKapHi. Ha rrpJiroTyBaHH.H ~acoK BlITpaTHJilI ~e 36 Kr cIIpy. CKiJibKlI KiJiorpaMiB c11py 3aJIMillM.noc.H ~ neKa pHi?

700°. CyMy qnceJI 123 456 i 789 3MeHllI Ha TpeTHHY rreprnoro tIHCJia.

701 . Po3B' HmH npMKJia.n;n, n HKMX ocTaHHhOIO e .n;i.H Bi.n;HiMaHH.H.

(46 - 3). 2 460 - 30· 2

10·1000 - 1 1000 - 82·10

20·20-10·10 23· 3 - 40 + 50

702. PoarJUIHb 3anncn i rroncHn, HK aHaiimJIJI .n;o6yTKM.

23. 40 = 23. ( 4·10) = (23. 4). 10 = 92. 10 = 920 4200. 20 = ( 42. 100). (2·10) = ( 42. 2). (100. 10) = = 84 . 1000 = 84 000 703. 13·50

22·30

1500·20 80·400

3200·300 60·40

160. 40 + 1000 500. 400 - 100 000

704. Y Mara3HHi 6yJio 720 Kr pncy. Ilepmoro .n;n.H npo,n;aJIH

~, a 'Apyroro ~ ycboro p11cy. CKiJibKM KiJiorpaMiB pncy

9 5 npo.n;aJIH aa ,n;ea .n;Hi?

705. TypncTy Tpe6a 6yno npoliTH 180 . ... BlH rrpOMillOB

3a rrepIIIHH .n;eHb 4 BChOrO IllJISIXY' a 3a .n;pyrnM 5 Toro ICM.

IIIJIHXY, m;o rrpoiilllOB aa nepIIIHH .n;eHh. CKiJihKH KinoMeTpiB npoiiUIOB TypncT aa .n;na AHi?

706. B11K0Hai1 .n;il i apo6u rrepeBipKy o6epHettoro .n;ie10. 28 784 : 7 37 054 • 5 2707 - 987 19 M 4 CM : 8 707. Ao o6i.n;y rocno,u;apKa ai6paJia 3 .n;iJI.HHKH 4 o.n;HaKoBnx .HIIV1KII IIOMi.n;opiB, a niCJI.H o6i.n;y 2 TaKHX C8MJ1X .HIJ\HKM. Bchoro BOHa ai6pa.Tia 60 Kr rroMi,u;opiB. CKiJihK11 KiJiorpaMiB TIOMi.n;opiB BMi~ye OAHH .H~HR?

708°. 210·300 108

900·40

60·60

150. 20 - 2000

709°. K111,DKKa MiCTHTh 120 cTopittoK. 3a rrepllIHH ,n:eHh .

,AlB1.llIHK8 npOt.IHTaJia

.n;eHh

. ..

..,

BClEl I<HHmKif, a 38 ,n:pyr1111

Toro, I..1\0 aa rrepIIIHH ,n;eHb.

cKIJILKH .

CTOplHOK

- KHH:>KI<:H ,n;iB'CJMHKa npOl.JHTaJia 38 ,n;pyr11i1 .n;eHL?

71 O. PoarJI.HHh, .HK attaxo,n:HTH aHat.JeHH.H ,n:o6yTKY 24 · 300 YCHO

. IlllCbMOBO.

Y CH o: 24 • 300 = 24 • (3 · 100) = (24·3)·100 = = 72. 100 = 7200. ITH c b M 0 Bo: 24 x 300 7200 711. flepeBip p03B'.H38HlUI npHKJia,n:iB.

5784. 50 = 289 200 741·400 - 28 200 = 268 200 5784 741 296400 x x 400 28200 - - 50 289200 296400 268200 71 2. Poan' .nn<H a noSicneHIUIM: 4 78 · 600. 506. 50 - 1500 345·600 20 000 - 173.80 87·400 4107·90 714. x: 500 = 25 x - 500 = 25 x + 25 = 500 715. Tpoe nopoc.HT ai6pann paaoM 300 Kr moJiy,n:iB. HicJ.>Hic]1 i HacI>-Hac}> ai6pa.TJM no 1 MilllKY moJiy,n:ie, a Hyc}>Hyc}> - 3 MilllKH. CKiJlhKH KiJiorpaMiB .moJiy,n:ie B o,n;Ho-

713. 28·60

MY MillJKy?

f!h) .. •

109

716.

cI>yT60JibHMH M' Hq KOIIITye

y Mara3HHi CKJia.n;ae

__!_

Bi.A

100

rpH. He,AiJihHa 3HMmKa

~iHH TOBap~

3HaM,AH n:iny

M 51qa IIICJI.H 3HHmKH.

717°.

KpiJih aa .n;eHh a'l.n;ae

CTaIIOBHTb

718°. 873·30 873·300

24·400 48: 3

720. 97·800 16·70 721.

7 10 ' a 3epHO -

paaoM TpaBH

719. 0

500

r I<opMiB, a HHX TpaBa

7 100

yc1x KOpMlB.

25 700 - 92. 60 92. 600 - 25 700 96: 2 9600: 100

800·900 8000·100

16·500 4000:1000 8000 - 4000 4 . 6 1000 - 25·40 1000 - 25·10

8286·50 9700: 10 56 KM

i ttlllOB Bech "l!8C 3 O,AH8KOBOIO

IIIBH.n;KicTro. Ao ayn11HKH BiH irnon

3 ro.n;.

cltlJihKH .

aepna a '1.n;ae itpiJih aa ~eHh?

JIHmHHK npoi1IllOB

K11

4 ro,A,

a nicJIH aynHH-

CKiJihRH KiJioMeTpiB rrpoi1IIIOB JIHmHHK rricJI.H

3YIIHHKl1'?

722.

lJ:ea CTOJI.HpH O.AepmaJIH

BRB

,Alli, a ,Apyr11:H -

189 rpH. 0.n;HH 3 HHX rrpa~ro 5. CKiJihKH rpomeli aapo6MB

KO)KHHM CTOJI.Hp, .HKIIJ;O fIO.AeHHa OIIJiaTa 6yna o.n;HaKOBa?

723. 3aKiH"llH p03B'.H3yBaHH.H 41·20 = 41·(10.2) =

IIpHKJia.n;iB.

41·12 = 41 · (10

+ 2) =

724. 3HaH.AH qacTKH i BHKOHaii nepenipKy MnomeHH.HM. 836 : 4 928 : 32 972 : 36 7 41 : 3 725°. Ha

l}>a6pi-i~i 6yno 2826

M TKaHHHH. :

~iei

BHTpaTHJIH Ha noIIIHTT.H miHoqMx I\.OCTIOMiB.

TKaHHHH

qono-

Bi4i KOCTIOMH BHTpaTHJIH _!Bi,[( KiJihKOCTi TKaHHHH, IIiIIIJia Ha miHoqi

KOCTIOM~.

CKiJihKH TK3HMHH IIiIIIJIO

Ha IlOIIIMT'l'.H 'l!OJIOBi"llHX KOCTIOMiB?

726°. 12. 56 727.

903: 21

3248: 16

Poar JI.HHh 3Haxo,AmeHH.H .n;o6yTKY ycHHM i nHChMOBHM

crroco6aMH.

110·

15·400

Y CH o: 2400 • 30 = (24 · 100) •(3 · 10) =(24 • 3) •(100·10)= = 72. 1000 = 72 000. IT H c b M 0 B o: 2400 x 30 72000 728. IIepeBip npaBHJihHiCTh BHKOHaHHSI MHomeHHSI.

x 17800 40 712000 729. 380. 600 73 000. 4

x320 x 7540 300 50 96000 377000 5400. 50 230. 40 - 6800 3040. 5 20. 30. 40 + 80 000 730. BpaT KYIIHB k n;yKepoK, a cecTpn c TaKHx ~yKepoK. PaaoM BOHH aarrJiaTHJin a rpH. CKiJihKH KOllITye o,n;Ha ~yKepKa? CKJia,n;H BHpaa i SIKI.QO k = 6, C = 9, a = 3.

o6qHcJIH iioro aHaqeHH.ff,

731 . Ha rrpHqirr rroKJiaJIH 4 MiIIIKM :>KHTa i 3 MiIIIKII rrmeHH~i, B KO:>KHOMY MiIIIKY aepHa nopiBHY. Bchoro

560 Kr

aepHa. CKiJihKH KiJiorpaMiB :>KHTa rroKJiaJIM Ha npHqin'?

732 . Ha 6aay aaBe3JIH 2 naroHH rricKy i 4 BaroHH I.Qe6ea10, y KO:>KHOMY BaroHi 6y,n;iBeJihHHX MaTepia.rriB rropiBHY. Bc&oro 96 T 6y,n;iseJihHIIX MaTepiaJiiB. CKiJI&KH aaaeaJIH rricKy i CKiJibKH I.Qe6eHIO?

733. Q6qucJIM TiJihKH Ti 'llaCTKH, .ffKi e ,n;ao~Hcl1poBHMII.

882: 21 336 : 42 580 : 4 510: 6 858: 33 734 *. 1 ra COCHOBoro Jiicy aa piK BH,ZJ;iJI.ffe CTiJILKH KHCHIO, CKiJihKH IIOTpi6Ho ,ll;JISI aa6earreqeHHSI )KHTTe,n;i.RJibHOCTi 2500 JI10,n;e:M:. CKiJihKOM JIIO,ll;SIM BIIcTaqHTb KHCHIO a 400 ra cocHoBoro nicy?

735°. IIepIIIoro ,ll;H.ff KpaBllHH.ff nolIIHJia 2 o,n;HaKoBi crri,n;HH~i, a ,n;pyroro -

3. Bchoro soHa BttTpaTHJia 10 M TKaHH-

HH. CKiJihKH MeTpia TKaHHHH BHTpaTHJia Kpaa·cn1H.H rrepllloro ,n;a.R?

736°. 620. 600

870·90

70 070- 9000

570·60: 5

4900·20

49 544: 8 111

737. 72 JI racy poa.nw.1111 rropinHy y 4 KanicTpH. CKiJihI<H no·rpi6no TaKHX KanicTp, ~06 po3JIHTH

54 JI racy?

738. Bettann 6yB y 5 KatticTpax, y Komuiii nopinHy. Y rrepanT0Mo6i.11L 3arrpanHJIH 54 JI 6enaHHY, a n APYrHii CKiJibKH KanicTp 6euauny 6yno 3arrpan11c110 n nepu111ii 8BTOMo6iJib i CKiJihKH B .n;pyr11ii?

111uf1 36 JI.

739. CKJia,u;n aa.n;a11y 3a KopoTKIIM aanucoM i poan'fDKH iI. KiJihKiCTb Sl~HKiB

Maraann

Ilepwni% ,l(pyru~i

740. x: 20 = 240

X•

Mac a 60 1<r 36 Kl'

20 = 200

741. Ilpn .HKHX 3Hat.JeHH.HX 6yKB cnpaBJJ;»CYIOTbCH no.n;aHi HepiBHOCTi?

5 · x < 20

20 - a < 15

7 42. Poan '.HmH rrpHKJia.n;n i nopiBHHM ai.n;noBIAI 1comttol napH.

54 : (2. 9) 54: 2 : 9

32 : (4 4) 32 : 4 : 4

96: (12·4) 96 : 4 : 12

743. 0611ncJin apy1n-1HM cnoco6oM.

4·320·5

15·2·240

180·5·20

50·128·2

744°. X.norrCJHK KynwB o.n;nnn:oni aou1u1·u .n;JI.H MaJI1onaHHsi: 2 l(JI.H ce6e i 3 .n;.nn CBOlX .n;pyaiB. 3a nci 30I11HTII Hill 3anJiaTnB 4 rpu. CKiJihKn rporneii Ma10Th nonepHyTH XJIOill.JHKOBi )J.pyai?

7 45°. Ani 6pnra,n;M ai6paJIH 7 o.n;HaKoBHX .Kop3MH MopKBH. Ileprna 6pHra.n;a 3i6paJia 36 Kr, a .n;pyra 48 Kr MOPKBM. CKiJihKH KopaHH MOPKBM 3i6paJia Kamna 6pHra.n;a? ~IJIEHH.H 1fl1CEJI,

3AKIHqYIOTbC.H HYJI.HMM

746 . Po3rJI.HHh poan' .H38HH.H npHKJia.n;y pi3HHMH cnoco6aMM. Ilo.HCHM rrpaBHJIO ,uiJieHIUI qHcJia Ha ,uo6yTOK.

112

108 : (18. 2) =

108: 36 = 3 (108 : 18) : 2 = 6 : 2 - 3 (108 : 2) : 18 = 54 : 18 = 3

747. Y"(1eHh poaB'.H3aB npHKJH\'AH. lloncHH apy'lIHiCTh cnoco6y. 540:(2·5)=540: 10=54 540: (6·18)=(540: 6): 18= 90: 18= 5 5600: (14·100) = (5600 : 100) : 14 = 56 : 14 = 4 748. 3ttaH:p;tt 3H3t:IeHHH BHpaaiB apyt:IHHM cnoco6oM. 36 000 : (25. 4) 720 : (8. 3) 960 : (24 : 2) 749. PoarJIHHh npuKna,u;u i rroHCHH aacTocyBaHH.H npaaHJta ,niJieHHR t111cna Ha A06yTOK AJIH ycuoro ,u;iJieH1ui Ha )J;BOu;1-1Cppone Ta p03pHp;He ~HCJIO.

168: 28= 168: (4·7)= 168: 4: 7=6 56 000 : 800 = 56 000: (100·8) = 56 000: 100: 8 = = 560: 8 = 70 750. 3600: 60

360: 12

7200: 600

270: 45

751. ,Il;BoMa aaToMo6iJISIMH nepeae3JIH 60 T KapTonJii. IIeplllHM nepeBe3JIH 20 T' a ,u;pyruM - pellITY K8pTOilJii. Ba11Tam1-1icTh aBTOMo6iJiefr o,u;uaKona. 3araJihHa KiJihKiCTh peticiB 12. CKiJihKH peliciB apo611a Komen aBToMo6iJih?

752. BiACTaHh Mim p;noMa nyHRT8MH 1456 KM. Ia u.11x IIYHKTiB OAHOt.IaCHO Ha3yCTpi l.{ OAHH O)J;HOMY BHIXUJIH )J;Ba an-ro6yc11. HKa Bi~cTaHh 6y,u;e Mim an1 06ycaMH Ha TOH qac, KOJIH neplllni1 npo1p;e ~ , a JJ;pyrHii - ~ BcieI . .? 8 7 Bl)J;CT8Hl. 1

753. B11K0Hai1 AiJieHHH a ocTat:1ero. 23 : 4 30 : 7 48 : 9

51 : 7

754°. 25: 3

56: 6

755°. 240 : 30 240: 120

60: 8

27: 4

6300: 900 6300: 300

756. (Ycno.) 1) 46 000: 100

300. 70 + 420 000 100 000 - 600. 20 46 000: 1000

8340: 10 113

2) 24: 8

26: 8

30: 5 33: 5

18: 6 21: 6

72: 9 80. 9

757. PoarJIHHb .n;iJieHHH a ocTa'llero Ha ,n;Bop.ncppoBe 'l!HCJIO.

53 : 16 = 3 (OCT. 5)

II o .H c H e H H .H. Bnnpo6oByBaHHHM 3Hali,n;eMo t.IHCJIO, HKe MeHille Bi,n; 53 i ,n;iJIHThCH Ha 16. ~e 'lHCJIO 48. 16 noMHOmHTH Ha 3, 6y.n;e 48. y ~1acT~i 3. 3Haii,zi;eMO OCTa'tly: 53 - 48 5. B ocTaqi 5. Bi ,n; no Bi .n; h: 53 no,zi;iJIHTH Ha 16, 6y,zi;e 3 i B ocTat1i 5.

758. 3HaH,n;H 'll8CTKY i OCTa'tly.

60: 16 52 : 24

40: 15 75 : 21

80 : 35 420 : 70

560: 80 6400: 800

300: 50 400: 80

759. Maca ,n;Box o,n;HaKOBHX cHiroBHX 6apciB 80 Kr. HKa Maca qoTHphOX O,D;HaKOBHX JieBiB, .HK~O JieB y 5 paa Bam'tlHH aa CHiroBoro 6apca?

CHiroBHH 6apc

JleB

760. 3a 10 ro.n; po60TH )J;BHryHa BHTpaTHJIH 90 JI naJihHOro,

54 JI lJ..O nepepBH, a pernTy nicJIH nepepBH. CKiJihKH rO)J;HH ,D;BHryH npa~IOB8B ,n;o nepepBH i CKiJihKH niCJIH nepepBH, HK~O BHTpaTa naJibHOrO aa ro,n;HHY 6yJia o,n;HaKOBa?

761. 3Haii,zi;H 3HaqeHHH BHpaay 250. b - b. 5,

.HK~O

b = 200.

762째. 3a ,n;o6y 3 6epean i 2 eBKaJiinTH paaoM norJIHHalOTh

760 JI BO,n;H. 0.n;Ha 6epeaa norJIHHae 40 JI Bo,n;n. CKiJihKH Jii TpiB BO)J;H norJIHHae O,ll;HH eBKaJiinT aa .n;o6y?

763째. 32: 5

70: 8 114

40: 12 72: 30

630: 90 630: 30

5400: 60 3200: 80

764.

Po3rJIHHh, HK ycno i nHChMOBO 3HaiilllJIH qacTKY i ocTa-

294 i 40. 294: 40 = 294: (10 • 4) = 294: 10: 4 = 7 (OCT. 14).

qy Bi,n; ,n;iJieHHH llHCeJI

Y CH o: IT

o .H c H e n 11 .H. 3uaxo,n;11THMeMo l:fac·rKy 11ocJii,n;oBHMM

.n;iJieHHHM Ha

10 i 4. y

xo.n;i BMKOH8HH.H OKpeMHX ,n;ili

OCTaqy He Tpe6a 3H8XO,ZJ;HT11, aJie CJii,n; IIaM'.HTaTM, ~o BO-

294 no,n;iJIHTH Ha 10, 6y;:i;e 29. 29 110,n;iJIHTM Ha 4, 6y,n;e 7. qaCTK8 7. ,Ui3Ha€MOCH, CKiJibKH IIOJJ;iJIHJIU. 40 IIOMHOlliMTH ua 7' 6y,n;e 280. 3Haii;:i;eMo OCTat:1y: 294 - 280 = 14. ITH ch M 0 Bo: ~06 IIOJJ;iJIHTH 294 Ha 40, Tpe6a crroqaT294, 40 KY no,u;iJIHTH ~e •mcJio Ha 10, 6y,u;e 29. IloTiM - 280 7 no,n;iJIHTM 29 Ha 4, MO)KH8 B3.HTlf no 7. 14 ,D;iauaeMOCH, .HKe qucJIO no_nJJIMJIH. IloMHO)KMMO 40 Ha 7' 6y;:i;e 280 . .D;i3Ha€MOCH, CKiJibKH 3aJII1Illl1JIOC.H: 294 - 280 = 14. qaCTK8 7, OCT8"CI8 14. Ha Mae 6yTH MeHIIIa BiJJ; JJ;iJihHHK8.

765.

PoarJIHHh 3anuc11 i rro.HCHH po3B' .H3yBaHH.H.

- 3851 70 350 5 35 766 .

- 608180 560 7 48

3HaHJJ;H qacTKy

523 : 60

356 : 60

767. x : 20 = 680 768.

OCTffCJY IIHCbMOBO.

X•

710 : 80

433 : 50

248 : 80

x - 20 = 680

20 = 680

IlpoTHrOM )J;BOX THmHiB MOTOI.J;:HKJiiCT 6yB y

;:i;opoai

60 ro,n;. IlepIIIoro THmHH BiH rrpoixaB 960 KM, a ,n;pyroro 1440 KM. CKiJihKl1 roJJ;HH 6yB y ;:i;opo3i MOTOI.\IIKJiicT KO.iKHOro TM.iKH.H?

769.

KiHb-BaroB03 nepeBia

5 a;

BaHTa.my.

CKiJibKH

peiiciB M8€ apo6HTM 8BTOM06iJib, B8HTamHiCTh HKoro

2T 5

~' m;o6 rrepeBe3TH TaKy caMy Macy BaHTa.my?

5074 - 4902: 6 + 100 277: 90 5074 - (4902: 6 + 100) IT e p e B i p c e 6 e: 3 (ocT. 7); 3 (ocT. 16); 8 (ocT. 10); 8 (OCT. 10); 4357; 4157.

770°. 136 : 40

650: 80 410: 50

115

771 *. 3a 20 c KiHb npo6ir 400 M. AHTHJiona aa 12 c npo6irJia 300 M. CKiJihKH?

Y Koro 3 TBapnn IllBMJV<iCTb 6iJihIIIa? Ha

KiHh

AHTIIJiona

772°. B OB0 1 1ecxoB1n:1~i 6yJIO 39 T 600 Kr KapTonni. Ileprnoro ,ll;H.H 3

OBO"tJeCXOBH~a

9 . .. . . BlIBe3JIM 100 I.J.1€1 KlJibKOC'l'l, ,l(py-

roro ,n;H.H _!_ peIIITH. CKiJibRM RinorpaMiB KapTonJii rn19 ,, Be3JIM ,n;pyroro ,D,H.H •

773. 3ttaii,n;n 1 18CTKY i1 OCTa 11y. 554 : 60 112 : 40 610 : 70 774. 371000.20

+ 630: 70

(57 500 - 9855). 20

125 : 50

3 70 : 80

(810: 90 + 640: 80). 300 (960 - 240): 30

775. Po3B' .H.mH i nopiBH.HM 3a,n;a11i. 3 a ,zi; a lJ a 1. IlepIIIoro lliH.H 111BatJn:a nollIM.na 8 <l>apTyxia, a ,n;pyroro - 6 ap·ryxiB. Ha nOIIIHTTSI Bcix c}1apTyxiB niIIIJIO 28 M TK8HMHH. CKiJihKH MeTpiB TKannHH IIIBUl!Ra BHTpa11aJia KO.iKHOro ,lJ;H.H? 3 a 11. a~ a 2. 3a ,n;ea ,n;Hi IIIBfllIK8 TIOllIHJia 14 <)>apTyxiB. Ileprnoro ,ll,H.H BOHa BHTpaTHJia 16 M TK8HHHl1, a ,n;pyroro - 12 M. C1tiJibKH c}1apTyxie IIIHJia I11Ba11Ra RomHoro ,ll;H.H?

776. x - 40 = 280

x: 40 = 280

x·40 = 280

777. 3 KYCKa ,n;poTy aae,n;oB.mKH 16 M Tpe6a airnyTH T8KH11 np.HMOKYTHHK, 11\06 nJio~a :Haro 6yna Haii6iJihlllOIO. B11auaq poaMipM cTopiH np.HMOKYTHMKa.

116

778*.

Ha AiarpaMi

ao6pameHo

AOB:>KMHY AllOX

:>KHTHix

KOJIOCKiB. IleplliMM KOJIOCOK BHpic Ha A06pe b6po6JUOBaHOMY r'pynTi,

a ,upyr11if -

na r'pyHTi, ot'.tpo6JieHOMY

HCA6a.110. 3HaM,ZU-I i nopiBH.HH AOBmHHY KOJIOCKiB, .ff KIJ~O

1 CM Ha

779掳.

MaJilOHKY Bi,D.IIOBi,D.ae

5 CM.

3a IIOARHHM IlJiaHOM AiJISIHKlf

3Hai1,rv1,

BiABe,D.CHO OKpeMO AJI.ff orip1<iB, fIOMi,uopin

.HKY II.TIO~Y caJiaTy.

20M

OripKH

10M

780掳. 966 : 42

40 928: 8 10 032: 6

252: 42 781.

3HaH,T.J;H l.J8CTKY

782. 3

161 : 30 275: 40

23路43 30路 25

ii OC'l'aqy: 457 : 60, 378 : 60.

ABOX HaceJleHlfX nyHKTiB O,T.J;HQ'C.{8CHO B npOTHJiemHMX

Harrp.HMK8X BHIX8JIH KOJiiCHHH i ryceHH'-IHHH TpaKTOpH. lIIBH,AKiCTb H'.OJiiCHOro TpaKTOpa

Horo -

KM/ ro,A MeHrua.

Bi~CT8Hb Mim 'l'paKTOp8MII

30 KM / ro,A, a ryceHMl.Jqepe3 CKiJibKM rO)\HH

oy,ne 120 KM? 117

783.

flpO'llHTaM, .HK 3H3XO,ZJ;HJIH 'IJ8CTKY t.IH-

ceJI

45 780 i 60.

f l 0 .H C H e H H .H. Ilepme HeITOBHe AiJieHe

_ 45780160 420 763 378 360 180 180 0

457 COTeHh. y "ll3CT~i 6yAe 3 ~McpplI. IloAiJIMMO 457 COTeHh Ha 60. ,ll;JISI ~horo IlOAiJIHMO 45 Ha 6, 6yAe 7 (coTeHh). MH0.m11Mo 60 Ha 7, 6yAe 420. B OCT8"lJi 37 COTeHh. ,lJ;pyre HenoBHe AiJJeHe 378 AeC.HTKiB. 378 AeCHTKiB noAiJIHTH Ha 60, 6y,n;e 6 AeC.HTKiB. MHomMMO 60 Ha 6, 6yAe 360 (,n;ec.aTKiB). B ocTfflJi 18 Aec.aTKiB. TpeTe HerroBHe AiJieHe 180 OAHHHIJ.h. 180 noAiJIHTH Ha 60, 6yAe 3. OcTa'lli HeMae. "tJ:acTKa 763. IlpM .l\iJieHHi MM 33MiHHJIH ,n;iJieHe apy'lIHHMM .n;o,n;aHI(a-

MH I KOpHCTyBaJIHC.H npaBHJIOM AlJieHH.H CYMH Ha 1 IHCJIO.

45 780: 60 = (42 000 + 3600 + 180): 60 = = 42 000 : 60 + 3600: 60 + 180: 60 = = 700 + 60 + 3 = 763 784.

299 600 i 700. 299 600 : 700 = (280 000 + 14 000 + + 5600) : 700= 280 000 : 700 + + 14 000: 700 + 5600: 700 = = 400 + 20 + 8 = 428

IlOHCHH, .HK 3HaXOA11JIH T.I3CTKY 'llHCeJI

- 299600 1700 2800 428 1960 1400 5600 5600 0

785. 1) 3HaHAH l.!8CTKY

11 480 : 40 3 IIO.HCHeHH.HM. 2) 3H8MAH qacTKY "llJ1CeJI 26 880 : 70 i nepeBip ,n;iero MHOq11ceJI

.meHH.H.

786.

ABTOMo6iJih IIpolxaB

480

KM 33

ro,ZJ;.

rOAHH IIOAOJiae ~IO BiACTaHh MOTO~HKJI, IIIBH,ZJ;KiCTb CTaHOBHTh

CKiJihKH

.HKm;o noro

lliBliAKOCTi 8BTOM06iJIH?

787*.

XJionqJIK MaB npo1xaTH

aBTo6ycoM

KM.

niBAOP031 BIH aacHyB, a KOJIH npOKHHYBC.H, TO Ai3H8BC.H, ~o

38JIHIIIIIJl0Ch 1X8TII CTIJihKH

I<lJIOMeTplB, CKlJihKII

Bin npoixaB, KOJIH cnaB. CKiJihKH KiJioMeTpiB npo1xaB XJionqHK, KOJIH cnaB?

118

788°. ,ll;Ju1 o6KJierosaHHH o,n;Hiei: KiMHaTH KynHJIH 10 pyJIOHiB mnaJiep, a ,lJ;Jifl ,zi;pyro1 15. YcLoro 6yJio 250' M wnanep. CKiJibKH MeTpiB IIIII8Jiep niruJIO Ha KO»<HY KiMHaTy?

789°. 11 520: 30

192 400: 400

870: 5 935: 85

680: 8 527: 17

1860: 60 5760: 80

790. 3anOBHH nponycK i o6qHCJili 'CJ8CTKY.

6300 : 700 = 6300 : 100 : ... 791.

= ...

2100 900----30 90

: 30

100 40 r - - - - - - . 1

180

·40

2 4 0 - - -....... 140 6000

120----360 3000

792. 1) Poar JiflHb aarrHCH i noHCHH poaB' .H3yBaHH.H.

- 28210 L1Q_ 280 I 403 210 210

- 32400 LfilL 300 I 540 240 240

2) 3HaH.n;H qacTKH i nepeeip .n;iero MHO:>KeHHfl.

27 600 : 60

32 560 : 80

793. PoaB'.HmH a no.HcHeHH.HM: 5760: 60, 20 160: 70. 794. x. 90 =36 810

x: 90 = 990

795. Ilepworo ,llHfl Me6Jiee:u:H MaraaHH npo,zi;ae 18 CTiJILD;iB, IIO 50 rpH. KO:>KHHH, .n;pyroro JJ;H.H npo,n;aJIH 30 TaKHX cTiJIL~iB. Ha cKiJILKH 6iJILWe rpome:H BTopryBaB Mara3HH aa cTiJIL~i .n;pyroro .D;H.H, aim nepmoro?

796. Ilepme t.IHCJIO b, .n;pyre - y k paa MeHme. 3aaii.n;H cyMy ~HX t.IHCeJI. 3a YMOBOIO aa.n;atti CKJia.n;H BHpaa. 3Haii,zi;H :Horo 3Hat.IeHHfl, .HK~o b = 9870, k 30.

797*. y t.IHCJii 375 38KpeCJIHJIH ~Hcppy 5. HKi .n;ii Tpe6a BHKOHaTH a t.IHCJIOM 375, ~06 ,zi;icTaTH TOH caMHH peayJILTaT?

119

798°. 14 500 : 50 12 040: 40

307 200: 800 6270·300

(5045 - 985): 5 280Q - 800 : 4 + 600

799°. ,n:oBmHHa BYJIHUi 800 M, a lllHpnHa 15 M. By.1111QIO n0Kp11.1111 acc}>aJibTOM. Ha KO>KHi 100 M 2 noTpi6Ho 3 T accpaJihTY. CKiJihKH BChoro TOHH acc}>aJihTY BHTpaTHJIH HR IlOKpHTTH BYJIHJ..d?

800. (Ycao.)

200 • 90 250·50

5430: 100 700·700

1200 : 400 1700. 3

801. PoaB'.Hmn a rroHcHeHHHM: 20 400 : 50, 268 800: 700. 802. 14 rpH. 80 .K.: 40 14 rpH. 80 K. : 40 I<:.

803. 7200 - 200. 8 - 600

5 T 60 Kr. 50 9 M 64 MM. 20

30 M 80 CM: 40 12 T 720 .Kr: 80

(8208 - 1944) : 6

804. 3 OAHie1 AiJIHHKH ai6paJIH 30 MimKiB KapTonJii, a a APYro1 - 32 TBKHX MirnKH, npHt.IOMY a APYroi AiJIHHKH ai6paJIH Ha 100 Kr KapTonJii 6iJibrne, Him a nepwoL HKa Maca OAHOro MilIIK8 KapTOilJii?

805. Y CHAY ai6paJIH 3200 Kr H6JiyK. l.JacTHHY u;nx .H6JiyK IlOKJl8JIH D 90 Hlll;HKiB, nopiBHY y KO)KHHM. IlicJI.H I..J;hOro aaJIHIIIHJIOCH ~e 1400 Kr n6JiyK. CKiJihKH KiJiorpaMiB H6JiyK KJIRJIH y KO.iKHHH Hlll;HK?

806. HaaBH qncJia, HKi piBHi Mim co6oro. llOT 20Q2Kr 6500cM 32 M 8 CM 65 M 2002 Kr

2600 r 2 Kr 600 r 110 000 Kr

2600 M 3208 CM 2 RM 600 M

807*. Tpn MaBrrn IJIH 6aHaHH. Ilepma MaBna a'iJia 5 6aHaHiB, TpeTH 3. Ileprna i Apyra M8Blll1 pa30M 3'lJIH y 3 pa3H 6i.11bwe 6aHaHiB, Him TpeTH. CKiJlbKH 6anaHiB a'iJia 'APYra MaBrra?

808°. x: 40 = 6840

728 100:

x = 900

809°. Ha AepeBoo6po6HHH KOM6iHaT aaBe3JIH 10 OAHaKoBnx earoHiB i 20 caMOCKH,n;ia ,n;epeBHHH. Maca AepeBHHH Ha OAHOMY CRMOCKHAi 40 u; 60 Kr, a B O,lVIOMY BaroHi y 4 paa11 6iJihrna. HKa Maca aciei .nepeBHHH?

120

I AlnEHHS1 B~X

cno

MHOJKEHHH HA ABO~Hct>POBE l.JMCJIO 810. Ila MoJioKoaaBo,n; aaBe3JIH 36 6i,n;oHiB MOJioKa, no 32 JI y KO:»<HoMy. CKiJibKH nchoro JiiTpia MOJIOKa aaBeaJin?

811. Ilpoq11Taii rroSicHeHHH rrpo ycHHH i rr:ncbMOBHH crroco6u 3Haxo,n;meHHH ,n;o6yTKY '-IHCeJI

32 i 36.

Y CH o: 32 ·36 = 32 •(30 + 6) = 32 ·30 + 32 •6 = = 960 + 192 = 1152. Ia U.boro 3anlicy BH,n;Ho, ~o ,D;JIH aHaxo.n;meHHH peayJibTaTy MHO:>KeHHH Ha ,l{BOIJ.Mc}>poae ~UiCJIO Tpe6a neplllHH ... MHO)KHHK IIOMHO»tHTH OKpeMO Ha .n;eCHTKM ll O.ZJ;HHHU.l, a peayJibT8TH )J;O,l(8TH. Ha ocHoBi nepecTanHo1 BJiacTMBOCTi .n;i1 MHomeHHH MO>KHa cnoqaTKY IIOMHO:>KHTH qncJIO H8 OAHHHIJ.i, a rroTiM - Ha ,n;ecnTKH. TaK po6JISITb npH nHCbMOBOMy MHO>KeHHi. II H c h M o B o: MHomHHKH poaMiI.QYIOTb TaK, x32 ~06 O)J;IUUUJ.i 6yJIH 38IIHC8Hi rri.n; 0.D;HHHl1-HMH. 36 :rv1HomeHHSI poarroqHHaIOTb 3 O)J;HHH~b. IlpM +192 MHOmenHi Ha .n;eC.HTKl1 u.11cI1p11 IIOl.JliH810Tb 96 aarrncyBaTH ni,n; ,n;ecHTKaMH. B ocTaHHiii .n;i1 1152 3HaXO,lJ;SITb cyMy 3Haii,n;eHHX HeIIOBHHX ,n;o6y'l'. KlB.

812. Ilepeaip poaB' H3aHHH. Ilpo~urrai1 01<peMo rrepmuii i .n;pyrHii HeIIOBHi .n;o6yTKH. Ilo.HCHH xi,n; o6"CJHCJieIIH.H.

x67

84 + 268 536

5628 121

813. 82·67

55·74

78·39

75.34

814. Poas'HmH aa,n;at.ii.

3 a ,n; a q a 1. IloKyneu.b KYI1HB 2 M TK8HHHJI i aanJiaTHB 18 rpH. CKiJibKH KOIIITye 1 M TKaHHHI1? 3 a ,n; a q a 2. IleplllMH noKynen:b KYI1HB 5 M TKaHHHH, a ,n;pyrnti - 3 M TaKOl caMOl TK8HHHH. IleplllHH noKyneu.b aanJiaTHB Ha 18 rpH. 6iJibllle, Him ,n;pyrnli. CKiJlbKH KOlllTye 1 M TKaHMHH?

3 a ,n; a

a 3. IleplllIIR noKyneu;b KYilHB 5 M TKaHHHH, a ,n;pyrnli - 3M TRKOl caMOl TKaHHHH. IlepllIHH IlOJ{yneu.b aanJiaTHB Ha 18 rpH. 6iJibllle, Him ,n;pyrnli. CKiJihKH rpollleH aanJiaTHB ,n;pyr11i1: IlOKyneu.b? q

815. Maca

~ KaByH~?

816°. Maca

KaByHa cTaHOBHTb 2 Kr 600 r. HKa Maca

~ rap6yaa cTaHOBHTh 4 Kr 500 r. flKa Maca

IJ.bOro rap6yaa? 817°. (9209 - 7750) ·23

+ 75 ·28

84 • 25 • 7 - 39 • 39

818. 110 MaCH TOpTa CTaHOBl1Tb 78 r. HKa Maca

! I.J;bOro TOpTa?

819. llepeBip p03B' 513aHHH i I1051CHH xi,n; o6t.IllCJieHHH. CKiJibKH BChoro o,n;HHHIJ.b y ,n;pyroMy HellOBHOMY ,n;o6yTKy?

820. 517·84

804·67

345·48

608·25

x428 37 + 2996 1284 15836

821. Maca 30 SI~HKiB net.IHBa TaKa caMa, HK Maca 25 n~nKiB n:yKepoK. HKa Maca o,n;Horo .JIII~HKa net.iHBa, HK~O Maca $III~HKa n:yKepoK 12 Kr? 822. Ilepllloro ,n;HSI rocrro,n;apcTBO Bi,n;rrpaBHJio Ha ceaoHHHH 5IpMapoK 4 Mallll1HH 3 KanycTOIO, a ,n;pyroro - 7 T8KHX M811IHH (MaJIIOHOK Ha c.123). }l;pyroro ,D;H5I Bi,n;npaBJieHO Ha 9 T KanyCTH 6iJibllle, Him rrepllioro. CKiJibK,H TOHH KanycTH si,n;npasneHo ,n;pyroro ,D;H.H?

122

1-H ):(eHh

2-:ii ):(eHb

823°. 256. 25

308·84

723 ·48 - 940 ·20 578 : (84 - 256 : 16)

1152: 6 975: 65

824°. Maca 25 TeJI.RT TaKa caMa, HK i Maca 8 KopiB. HKa Maca O.D;Hi€i KOpOBH, .HKID;O Maca o.n;noro TeJI.RTM C1'aHOBMTb 80 Kr? 825. 0.n;HH BepTOJiiT npoJieTiB 480 KM, a .n;pyruii 800 KM. IlepmHM BepTOJii T 6yB y IlOJlbOTi Ha 2 ro.n; MeHIIIe. CKiJihKH ro.n;HH 6yB y noJibOTi KO:>KHHH BepToJiiT, .RK~o ix lllBH.D;KiCTb O.D;HaKOBa? lliBH):(KiCTb 0'AH8KOB8

l.J:ac

Bi.ncTaHb

? , Ha 2 ro.n MeHwe

480KM 800KM

826. PoarJUIHh aarrncn i no.HcH11 poaB' nayBaHH.H.

4076 x 67 + 28532 24456 273092 827. 14 580 ·54

5480 x 38 + 4384 1644 208240 4208·27

8410·85

3701. 39

828. CKJia,n;H piBH.RHH.R aa 110.n;aHHMH yM0BaM11 i.poas'.RmH ix.

1) HeBi.n;oMe q11cJio aMeHIIIHJIH y 23 paaH i .n;icTaJIH 828. 3HaM.ZJ;H HeBi.D;OMe qHCJIO.

123

2) qlICJIO 957 3MeHIIIHJil:I Ha HeBi,D;OMe q11cJIO i .n;icTaJIH 33. 3ttaii.n;n HeBi.n;oMe qncno. 829. 3anHIIIH BHpaaH, aHaii.n;H Ix aHa'1eHH.H. 1) Bi.n; ~111cJia 270 051 Bi.n;ttjlTH .n;o6yToK 1 1nceJI 348 i 89. 2) ,ll;o t(HCTKH 1 1nceJI 12 960 i 60 .n;o.n;aTH ix cyMy.

830°. Ao MJI1n1a npuBeann 58 MiII1KiB nmeH111.JJ i1 38 MiIIIKin mHTa. IlrueHHIJJ np11Be3JIH Ha 16 "'6iJihIIIe, Him iltHTa. CKiJihKH oKpeMo 1tiJiorpaMiB mHTa i nIIIeHHIJ.i aaBeaeHo, HKil.\O nci MilIIKH ia aepHOM M8JIH O,l(H8KOBY Macy?

831 °. 5405. 96

4850. 44 832. (Ycuo.)

50 rpH. 80 K. : 40 5 rpH. 42 K •• 50 1 T : 20 1 U. : 20

3 rpu. 50 K. • 4 2 rpH. : 20 K.

1 T - 20 Kr 1 :a; - 20 Kr

2 Kr 500 r . 2 3 M 50 CM • 4

833. BattTam.HiCTh o,n;Hiei MarnnHH 42 IJ. 65 Kr. 3ttail.n;:n BfiHTamuiCTh 28 T8KHX MaIIIHH.

x4265 28 ll11u M1£0:J1Cenni CKllafJeni iJJieno6aKi 1£UClla +34120 8530 3aMin10101nb npoc1nu.1tut. Y BiiJnoaiiJi npocnie 119420 iMeno6ane itUCllO 3ltMin10ro1nb CKllaiJeHUM. 42 :u; 65 Kr ·28 = 1194 ~ 20 Kr

834. 9 M 76 CM •48 5 M 25 CM ·24 83~.

7 l~ 8 Kr •45 24 1tr 800 r ·35

11CM5 MM ·66

5 M 42

·50

PoaB'nmn aa.n;a~1i Ta nopiBHHH Ix.

3 a ,n; a q a 1. 0.n;HH moq1ep nepeaia caMocK11,n;oM 560 II. IJ.CMCHTY, a ,npyr:uii 490 :u;. I1eplll11H llIOC}lep apo6nn Ha 2 peiicH 6iJihme, Him .n;pyrnil. CKiJihKH peliciB apo6HB ItO:>ItHHii rnoc11ep, HKI.IJ:O naHTam.HiCTb caMOCKH.n;iB 6yJia o.n;HaKOBa? 3 a .n; a 1 1 a 2. Ana moc}1epu nepeB03HJIH caMOCKH.n;aMH :u;eMeHT. 0.n;HH apo6nB 16 peliciB, a .n;pyrnii 14. IlepmHli moc}1ep nepeBia Ha 70 u. 6inhme, uim ,ApyrHli. CKiJihKH 1~eHTnepis a;eMeHTY nepeni3 KOm.HHil moc}1ep? 1 836. Maca 3 TopTa cTaHOBHTh 170 r. HKa Maca 25 TaKHX TOpTiB?

837. ~oB:>KHHa cTopoHH KBa,n;paTa a cM. CKJiaAH BHpaaH AJISI 3H8XOA:>KeHH.H nepHMeTpa i IlJIOI.Qi KB8AP8Ta. 3naii~H 3HfflJeHHH BHpaaiB, HK~O a = 36. 838°. Ilepworo AHH MiKpoaBTo6ycoM 6yno aaee3eno y KHHrapHIO 627 nat.IOK a KnnraM11, a .n;pyroro - 285 rrat.IOK. Ilepruoro J~HSI 6yno apo6JieHo Ha 6 pe:HciB 6iJihllie, Him 11.pyroro. CKiJILKH peliciB 6yno apo6JieHo nepmoro ti;HH i cKiJihKH - 11.pyroro? 839°. 4 M 8 CM ·25 9 Kr 40 r ·95

14 ~ 25Kr·18 5 /1.M 8 CM • 2 5

240 • 35 : 50 - 27 30 800 - 28 400 : 40 • 3

840. B11KopHCTOBYIO'-IH MaJIIOHKH, CKJ18AH piBHHHH.H ii poaB'HmH lX.

841 . M a T e M a T H

H H ii /1. H K T a II T. 1) 3MCHlllyBane 540, BiA'eMHHK BHpamenuii .n;o6yTKOM '-IMCeJI 20 i 15. 2) IleprnHii 11.0,n;aHoK 880, APYrHii - qacTKa 'lfHCeJI 2400 i 60. 3) Ileplllllll MHO)KHHK 650, ,n;pyrH:t'I - t.JaCTKa llUCeJI 200 i 4. q

842. PoarJIHHh 3anrrc i rro.Hcuu nop.H/J.OI( BHKOHaHHH Aili. 427. 58 - 604 • (816 : 24) = 4230

- 816124

x604

x 427

58 + 3416 2135 24766

96 96

*1812 2416

20536

843. (984: 24

+ 1270) ·43

(4080 ·67 - 20 445): 5

844. 3a c}1ap6yBaHH.H BiKOHHHX paM 75 rpH., a ,npyruii 45 rptt.

24766 20536 4230

O/~HH MaJIHP

~pyr1-1i1

o,n;epjJ(HB po6iTHUK npaa;10BaB

125

n:a 2 AHi Me11rne, Him nepm11ii. CKiJibKH 'AHiB npaI\JOBaB KO)KHHH, SIKI.QO no,n;eHHa OIIJiaTa 6yna OJI.H8KOna?

845 . Maca KO:iKHoro a Tpbox iH,n;HKiB 16 Kr 450 r, a 1tomnoro a ,n;BOX iHIIIHX - 12Kr150 r. Ila cKiJILKM 3aruJibHa Maca BCiX iH,n;HKiB MeHill8 Bi~ 100 Kr? 846 . I1ep11MeTp np.HMOKyTHOl ,n;iJISIHKH 296 M. ,ll;OB:>KHHa ,n;iJI.HHKH 96 M. 3HaH,n;H IlJIOIIJ;y ,n;iJIHHKM. 847°. 4038. 97 - 24 600: 60. 32 6912 ·(3. 27) - 94 508 848°. y ,ll;HT.HqoMy caHaTopii «Cotte"lJKO» Ha IlOJiy,n;eHb BII,n;aJIH 420 nepc11KiB, a B cauaTopil «3ipoq1<a>.> - 375. y caHaTopii «COHe"lJKO» 6yJIO Ha 15 ,n;iTe:H 6iJihIIIe, Him y «3ipo"ln_\i». CKiJihKH ,n;iTe:li 6yno y KO.)KHOMY cattaTopii, HKIQO BCiM BH,ll;8JIH nepcHKiB rropiauy·!

849. IlopiBH.HH 38IlHCH MIIOmeHH.H Ha ,ll;BOI.\HcppoBe i TpHIJ.HC}>pone qncna.

4184 x 37 + 29288 12552 154808 850. 284·366

568·475

•

x4184 237 29288 +12552 8368 991608 2488·249 2081·353

851 . ~o6yTOK queen 13 7 i 239 36iJihlll Ha 24 7 500. 852. Bi,n;cTaHl> Mim MicTaMHA i B 900 KM. 3 MicTaA B MicTo B BHPYillHB BaHTa»tHHH aBTOMo6iJih, i OAHo-i:1acHo HaaycTpi q iioMy 3 MicTa B BHpymnn JierKonHi1 aBTOMo6iJih. y CIO Bi,n;CT8Hb B8HTU:>KHHH aBTOM06iJih npoiiIIIOB 38 15 ro,n;, a JierKOBHH - aa 10 ro~. qepe3 cKiJII>KH ro,n;HH nicJI.H BHla~y aBTOMo6iJii aycTpiJIHC.H?

853. CKJia,L\H aa,n:aqy Ha aycrpi1flllli:i pyx aa no~aIDIM anpaaoM.

540 : (42 + 48) 854. Haae11 nop.H,n;oK ,n;ili y BHpaaax i 3Haii,n;H 1x aHaqeHHH. 100 - (16 ·6 + 4): 25 400 - 480: 6 + 180 (120 + 80): (100: 10) ·5 2800: (40: 2) - 70 ·2 126

855°. 1240. 24

1240·324 856°. y

907 ·28 -18 000: 2 (907 ·28 -18 000): 2

~BOX O,D;HaKOBHX MilllKax aepHa Ha

938: 67 714: 7

4 :a; 20 Kr MeHme,

Him y ceM.H TaKMX caMHX MimKax. CKiJihKH ec1>oro aepHa y IJ;HX MillIK8X?

200 : 200 60·0·1

857. (YCHO.)

858. PoarJI.HHh aanHc ,n;o6yTKiB

200: 1 500: 5

500. 2: 4 500: 100

0: 500 2800:40

aHaxo~meHH.H "tJHCJIOBHX aHaqeH1>

1578 •43 i 1578 •403. 1578 1578 x 43 x 403 + 4734 + 4734 6312 6312 67854 635934

859. 1243·207

4054·104

2517·305

420·607

860. JliTaKy DOTpi6Ho ,6yJio npoJieTiTH 4500 KM. Ilepwi

3 ro,n; BiH JieTiB ai IIIBH,D;KiCTIO 695 KM/ro~, a HacTynHi 2 ro~ - ai IIIBH.D;KiCTJO 642 KM/ ro,n;. CKiJI1>KH KiJioMeTpiB iioMy aaJIHlllHJIOC.f.I npoJieTiTH?

861.

~OB:>KHH8 Ilp.f.IMOKYTHOI ,n;iJI.HHKH

120 M, IIIMpHHR

46 M. 3HaR,D;H lllHpHHY ,n;pyroi np.f.IMOKYTHOI ,n;iJISIHKH 3 T3K010 caMOIO IlJIO~elO, ,D;OBmHHa .f.IKOI 80 M. 862. Be11ocHne,n;HCT aa 3 ro,n; npoixaB 36 KM. Ha aBopoTHOMY IIIJISIXY lioro lllBH.D;KiCTb 6yJia Ha 3 KM/ ro,n; MeHIIIa. CKiJI1>KH qacy aaTpaTHB Benoc11ne~11cT Ha anopoTHHH lllJISIX?

863°. IlepHMeTp TPHKYTHHKa 186 MM. ,D;onmHHa O,D;Hiei CTOpOHH 42 MM, ,n;pyra CTOpoHa y ,D;Ba paaH 6iJibllI8 Bi,D; Hei. qOMY ,n;opiBHJOe TpeT.ff CTOpOHa TpHKYTHHKa?

864°. 1084 . 34

1084·304

7235·77 485. 604

2400 : (300 - 260) 1000 - 50. 6 + 700 127

AIJIEHHH I-IA ABOIJJ1:Cl>POBE qMCJIO

865. (Ycno.)

240: 60 60·7

3600: 40 90·7

84: 12 220·3

96: 24 140·3

866. I1po'llliT8H IIO.HCHeHHH .n;iJieHHH na .ABOUHCppoBe qncJIO 6ea ocTat.Ii i a ocTaqero.

182 , 26 -182 7

.n; i JI e II H SI

6 e 3 0 c T a 'I i. ,D;iJICHe 182, .AiJibHHK 26. y qacTuJ 6yAe O):\Ha II_H<I1pa.

Ha:H6JIH}l<.t1e MCHllle Bi.A .AiJibHHKa poapH,ru1e t111cJio 20. AinHMO 18 Ha 2, 6y.Ae 9. IlepeBipHMO IJ.H<}1py 9. 20 IIOMHO)l{HTH Ha 9, 6y.Ae 180, Ta "-'e 6 IlOMHO>KHTH Ha 9 (T06To 54), y peayJihTaTi 6y,n;e lJHCJIO, 6iJihllle Bi,n; 182. I(ncI1pa 9 ne nip;XO.ZJ;HTb. BiahMeMo u.11c}1py 8. 20 noMHO»<HTH Ha 8, 6y.Ae 160, Ta ~e 6 IlOMHO)KHTli Ha 8 (T06TO 48), peayJibT8T 6y.n;e 6iJib1I1H11 Bi.A 182. U:11c}>pa 8 ue rri.n;xo.AHTb. Bi3hMeMo UHC}>py 7. 20 IlOMHO)KlfTH Ha 7' 6y,n;e 140 Ta ~e 42, 6yp;e 182. Un<}>pa 7 ni.l(XOJJ;l1Th. 3ani-nneMo 11 B qacTu.i.

65 21 86 A i JI e n H SI 3 o c T a 'l e ro. ,D;iJieHe 652, - 602 7 ,n;iJibllHK 86. Y qacTu_i 6y.n;e o.n;ua n_uc}1pa. ITo50 .n;iJIHMO 65 na 8, 6y,n;e 8. IIepeBipMMO IJ.IH.}>py 8. 80 IlOMHOmHTH Ha 8, 6yp;e 640, Ta ~e 6 IlOMHOmHTH H8 8, pa30M 6yp;e 688. 688 6iJihllle, Him 652. ~ucppa 8 He ui,n;xo.n;HTh. BiahMeMo u.11c}>PY 7. 80 IlOMHOmIITH Ha 7, 6y.Ae 560, Ta ~e 6 IlOMHO)l{HTH Ha 7, pa30M 6y,zi;e 602. 602 Menllle, Him 652. I(H<iJpa 7 ni.Axo.n;HTb. 3Haiip;eMO OCT8tiy. 652 Bi.AH.HTU 602, 6y,zi;e 50. OcTat1a 50. 1-JacTKa 7. 867. 3H8HAH qacTKY Ta OCT8l.Jy: 453 : 62, 505: 74. 868. 0,n;HH B8HTamHHM Il0l3.D; 1xaB ai lllBH.AI<.iCTIO 78 KM/rOlJ. i npottllIOB 468 KM, a ,n;pyrHH rroia.A IxaB ai IllBM.AKiCTIO 67 KM/ro.n; i npoiillloB 603 KM. Ha cKiJibKH ro.n;HH 6iJibllle 6yB y p;opoai .APYrHii no!ap;, ni.m neprn11i1?

869. Ilpo"(nrrau aa,zi;aqy. PoarJI.HHh poaB'HaaHHH

aa~aqi Ta

IlO.HCHeHIUI. 3 a ,n; a q a. TecJIHP poanHJISIB .AOllIKY Ha .ABi qacT1u1u. AoniKHHa op;Hici" 11acTHHH 2 M 30 CM, a .Apyroi -

128

2 M 60 CM. 51KOIO aae,noBmKH 6yJia 6 KO»<:Ha qacTHHa, HK6H )l;OIIIKY poanHJI.HJIH Ha 'ABi piBHi qaCTM~H? Poas'.HaaHH.H

1) 2 M 30 CM+ 2 M 60 CM= 4 2) 4 M 90 CM : 2 = 2 M 45 CM.

rr 0

90 CM;

c H e H H H. AoB>KHHa 2 M 45 CM - ~e cepe'AH.H )l;OB)KHHa 'AJIH .n;ow;oK aaB)l;OB:>KKH 2 M 30 CM i 2 M 60 CM. H

870. PoarJIHHh aa.zi;aqy i aaKiHqn poae'HayeaHH.H.

3 a 'A a q a. YqeHh TpHqi BHMiproeae ei.n;cTaHh Bi'A .n;oMy .n;o IIIKOJIH. IIepIIIoro paay eiH HaJii"lIHB 207 KpoKiB, ,zi;pyroro 195 i TpeThoro - 204 KpOKH. CKiJihKH B cepe,nHbOMY KpOKiB .n;o IIIKOJIH? Poae'.RaaHH.H

1) 207 + 195 + 204 = 606 (KpOKiB); 2) 606: 3 = 1

871. 3 3 ra JIHnoBHX Haca.n;meHh o.n;epmaJIH 220 Kr Me'AY. CKiJihKH KiJiorpaMiB Me.n;y O'AepmaTh a .! ra JIHilOBHX HaCa'AmeHh? 4 872*. Ilepeeip, w;o .n;o6yTKH .n;eJIKHX )l;BOX qHceJI MO»tYTh no3HaqaTHCH THMH caMHMH ~H<}>paMH, ~o :H MHO)KHHKH.

27. 81 = 2187 873 . 402: 67

°.

305: 43 529: 85

1435

2 KM: 400 M

5 T - 5 Kr

3 ~ - 3 Kr BpHra.n;a aa HopMoIO MaJia peMOHTYBRTM a MaIIIHH aa

511:73 87

35 ·41

BM 4 )l;M. 5

,zi;eHh. A.Jr.e BOHa peMOHTyBaJia Ha k M8IIIHH 6iJILWe. CKiJibKH MaIIIHH 6pHra.n;a ei.ii;peMoHTyBaJia aa 5 .n;HiB? CKJia.n;H BHpaa.

875. PoarJIHHL aanHc .n;ii .n;iJieHH.H i npoqHTali noJicHeHH.H.

- 452, 14 II o JI c He H HSI. AineHe 452, .n;iJILHHK 14. 42 32 Y qacTn;i 6y.n;e 2 ~McppH. IIo.n;iJIHMO 45 Ha 14, 6y'Ae 3. 14 IlOMHO)KHTH Ha 3, 6y.zi;e 42, 32 3aJIHIIIHJIOCH 3 .n;eC.HTKH. 28 Apyre HenoBHe AiJieHe 32 OJJ;HHH~i. 32 no4 .n;iJIHTH Ha 14, 6y.n;e 2. OcTaqa 4. 5.

MllTOM8TKKB.

4 KJI,

129

876. 3Haii,n;H 'tJaCTKH ii ocTatii a rro.HcHeHH.HM. 785 : 23 438: 12 877. Maca 8 o,n;naKOBHX 6iJiyr TaKa caMa, .HK Maca 12 oceTpie. Maca O'AHie! 6iJiyrH 1 ~ 23 Kr. HKa Maca o,n;noro oceTpa?

Bi.rryra

878. Ha 222 rpH. KYTIHJIH TKaHHHY uJtto10 37 rpn. aa 1

CKiJibKH cyKOHh Momtta noI11HTH a ~ie! TK8HHHM, .HKI.l\O Ha o,n;ny cyKHIO ii,n;e 3 M? Poae' H.mH aa,n;aqy ,n;BoMa cIIoco6aMM aa no,n;aHHMH IIJI8H8MH.

1-ii c no c i 6 IlJiaH poaa'nayaaHHSI 1) CKiJihKH MeTpin TK8HHHH KYIIHJIH Ha 222 rpH.? 2) CKiJihKM Mo.mna rrolllHTH cyKOHh? 2-ii c 11 0 c i 6 IlJiaH p03B'H3YB8HH.H 1) CKiJibKH KOlllTye TKaHHHa Ha OAHY cyKHIO? 2) CKiJihKH Mo.mHa nolllHTH cyKotth?

879. PoarJIHHh poae'.aaaHHSI

aa,n;a~Ii

Ha anaxo,n;.meHHH

cepe,n;Hhoro a pHc}lMeTHqHoro. 3 a ,n; a q a. BenocHne,n;HcT 1 ro,n; ixaa ai mBH,llKiCTIO 15 KM/ro11., 2 ro,n; - ai lllBH,ZJ;KiCTIO 13 KM/ro,n; i ~e 1 ro.n; - ai IIIBH,ZJ;KiCTIO 11 KM/ro,n;. 3 HKOIO cepe,n;HhOIO lllBH,ZJ;KiCTIO 1xan BeJIOCHrre,n;HcT? Poan'.aaaHH.H 1) CKiJihKH Bchoro ro,n;HH ixaB seJIOCHneAHCT? 1 + 2 + 1 = 4 (ro.n;) 130

2) CKiJihKH BCboro KiJioMeTpiB npo1xaB eJioc11rre_n;11cT? 15·1 + 13 • 2 + 11 · 1 = 52 ( M) 3) HKa cepeAH.H lllBHAKiCTh pyxy aeJioc11rre,l\HCTa?

52 : 4

13 (KM/ro_n;)

PoaB' .HmeMo aa_n;aqy, CKJJaBIIIH q11cJioB11ii BIIpaa.

(15·1+13·2+11 ·1): (1+2+1) = 13 (KM/ro_n;) lll,06 3nau1nu cepeiJne apuljJMemu11,ne Ki.nbKOX 11,ucea, 1npe6a "ix cy MY noiJi.numu na KiabKic1nb ~ux 11,ucea.

880. Ma ca o_n;Horo KPOJI.H 2 Kr 200 r, a _n;pyroro 1 Kr 600 r. 3HaHti;H cepe'AHIO Macy ll;HX KpOJiiB.

881 . 3HaH):\H 3Hat:IeHH.H BHpaay a : 6 + 60 aa A8HHMH Ta6-

JIHIJ.l.

I o I 6 I 54 I 72 I 360 I 600 I 960 I

882°. Ha CKJI8A 3aBe3JIH 6 u; 60 Kr OBOliiB: 10 MillIKiB u;n6yJii, IIO 36 Kr y KO»<HOMY' i KiJibK8 MilllKiB MOPKBH, IIO y KO:>KHOMY. CKiJihKM aaBeaJIH MiIIIKiB MOpKBH?

60 Kr

883°. 3HaMti;lf qaCTKY i1 OCTaqy: 630 : 24, 995 : 31, 950 : 35. 88 . (YcHo.) (102 + 98): 100 · 25: 10 (12 · 10 + 180): 3 · 6 180 : 18. 23 - 230 + 50 (16. 3 + 2) : 5. 10 885. 1) PoaB '.H»<H a KOMeHTyBaHH.HM: 900 : 36. 2) IlepIIIe t:IHCJIO 806, a 'APYre - y 31 paa MeHme. 3Haiiti;H cyMy a;Hx 'CJHCeJI.

886. x. 25

900

966: x = 21

887. KoJieco, .n;oB:>KHHa 060,l\y .HKoro 1 M 2 ,zi;M, Ha AeSIKiii BiACTaHi o6epHyJIOC.H 48 paa. CKiJibKH paaiB o6epHeTbC.H Ha Tiff CaMiH Biti;cTaHi KOJieco, AOB)KHHa o6o_n;y SIKoro Ha 6 ti;M 6iJihma Bi,zi; AOB»<HHH 060,zi;y rrepmoro KoJieca?

888. 3 20 ra ai6paJIH rro 13 T KapTOIIJii a reKTapa, a a 5 ra no 18 T a reKTapa. 3HaRAH cepe,zi;Hro Bpo.maiiuicTh KapTOIIJii Ha UHX ABOX .n;iJI.HHKax. 1~1

PoaB'.HaaHH.H

- 350125 25 14 1) 13 · 20 = 260 (T) - ai6paJJH a 20 ra; 100 2) 18 · 5 = 90 (T) - ai6paJJH a 5 ra; 3) 260 +. 90 = 350 (T) - BChOro ai6paJ1H 100 0

Ka pTOIIJil;

4) 20 + 5 = 25 (ra) - BChoro reKTapiB aeMJJi; 5) 350: 25 = 14 (T). B i .n rr o B i .n h: cepe,nHH BpomaiiHiCTh KapTorrJii Ha D;HX ,nBOX ,niJJHHKax 14 T 3 1 ra.

889. 3 12 ra ai6paJJH 108 a; rpeqKH, a a 6 ra -

72 a;. 3Hai1,n11

cepe,nHIO BpomaiiHiCTh rpeqKH Ha U.HX ,niJJHHKax.

890°. CKJJa,nH aa,naqy aa KopoTKHM aarrHCOM. PoaB'.HaaHH.H

aa,naq1 aarrHUIH.

12 aBTo6yciB no? nae. 4 aBTo6ycH no 41 nae. 891 °. 910: 35

•

624 : 48

} 536 nacamHpiB

42 . 49 + 40. 50

100: 25. 4

892. IlpoqHTaii 110.HCHeHH.H, .HK BHKOH8HO ,niJieHH.H. IIepUie HerroBHe ,niJJene 305 coTeHh. y qacTu;i 6y,ne 3 l\HC}lpH. lliyKaTHMeMO rreprny u;Hcppy qacTKH. IIo,niJJHMo 30 na 5, 6y,ne 6. IIepeBipHMo. 50 rroMnomHTH Ha 6, 6y,ne 300, Ta ~e 7 IIOMHOlliHTH Ha 6, peayJJhTaT 6y,ne 6iJJbIIIHii aa 305. BiahMeMo II,Hcppy 5. IIepeBipHMO. 5 7 0 noMHomHTH Ha 5, 6y,ne 285. Bi.nniMeMo 285 Bi,n 305, 6y,ne 20. 1(1uppy 5 ,ni6paHO rrpaBHJ1hHO. ,IJ;pyre HeIIOBHe ,niJJeHe 205 .nec.HTKiB. Ilo,niJIHMO 20 Ha 5, 6y,ne 4. IIepeBipHMO. 57 rroMHomHTH Ha 4, peayJJhTaT 6y,ne 6iJJhIIIHH Bi,n 205. BiahMeMo l\Hcppy 3. 57 rroMHOmHTH Ha 3' 6y.ne 1 71. 1(H<l>PY 3 ,ni6paHO rrpaBHJ1hHO. Bi,nHiMeMo 171 Bi,n 205, 6y,ne 34. TpeTe HerroBHe ,niJJeHe 34 2. IIo,niJJHMo 34 Ha 5, 6y.ne 6. 57 IIOMHO}RHTM Ha 6, 6y,ne 342. 1(Hc}lpy 6 ,ni6pano rrpaBHJ1hHO. y ci o,nHHHI.\i rro,niJ1HJ1HC.H. qaCTKa 536.

_30552157 285 1536 205 171 342 342

132

893. 1) 3uaii,n;H t{8CTKY 2) 3612: 84

IlO.HCHeHH.HM: 12 168 : 52. 13 902: 42 3772: 82 14 147: 43 3

894 ByJio 1932 T w;e6eHro. Moro nepeseaJIH 7 caMoCKH,n;iB BaHTR.mHiCTIO 12 T KO:>K.HHH. CKiJibKH BCbOro peiiciB apo6HJIH caMOCKH'AII, .HK~O KiJibKiCTb peliciB KO:>K.HOro o,n;HaKoBa? (Poas'.HmH aa,n;aqy ,n;BoMa cnoco6aMH.)

895. 3 25 ra ai6paJIH no 24 n mHTa a reKTapa, a a 15 ra -

no 32 u; 3 reKTapa. 3HaH.D;H cepe,n;HIO BpomaiiHiCTb :>K.HTa Ha I..J;HX ,n;iJI.HHKax.

896. HKe Haii6iJILIIIe aHatieHH.H MomHa Ha,n;aTH 6yKBi x, w;o6 HepiBHiCTb 200 -

x > 42 6yJia npaBHJlbHOIO?

89T. 3 O.D;Hiei .D;iJI.HHKH ai6paJIH 42 MiIIIKH un6yJii, a

,n;pyrol - 29. 3 ,n;pyroi .n;iJI.HHKH ai6paJIH Ha 715 Kr a;H6yJii MeHIIIe, aim a neprnoi. CKiJihKH KiJiorpaMiB u;H6yJii ai6paJIH 3 KO.)KHOl .n;iJIHHKH?

898°. 4505 : 85

162 • 67 407 • 89

5418: 43

899. (Ycao.)

3M : 25 CM 2 T: 25 Kr

48: (48: 4 + 4) 48 : ( 48 : 8)

900. 1) 3HaH,ZJ;II lIRCTKY 31 872: 83

36 • 20 25 • 60

10 T - 10 Kr 10 M - 10 CM 640: 80: 2 640: (80: 2)

IIO.HCHeHH.HM. 2) 3aaii,n;n t.1acTKH 27 931 : 53, 15 912 : 34 i nepeeip . peayJibTaTM )::\1€10 MHomeHHH. 3

901. HKe t{lfCJIO Tpe6a noMHOJKHTH Ha 26, w;o6 ,n;icTaTM 10 296?

902. 3HaH.D;H cepe,n;He ap11q1MeTHtIHe lIHCeJI 28, 30, 32 i 26. PoaB'.HaaHHH 1) 28 + 30 + 32 2) 116: 4 = 29.

+ 26 = 116;

Ilo.HCHH, npo w;o .n;iaHaJIHCSI KO)KHOIO ,n;iero.

903. 3 3 a ,n;iJISIHKM ai6paJIH no 30 Kr nllleHHI..J;i apa, a a 2 a . nrneHHI..J;I.

KOmHoro no 50 Kr. 3Hali,n;11 cepe,n;Hro BpomaiiHiCTh 3

133

904. Po3rJI.HHh MaJIIOHOK i ,n;ali Bi,n;noBi,n;i Ha aannTaHH.H • .HKi qHcJia 6y,n;yTb Ha CTOBni, BiM8JICHOMY pi.n 3o6pameHoro B 6iK XapKoBa Ha 34 KM? .HKy BJiaCTHBlCTh cyMH MH TYT cnocTepiraeMo?

KHIB

306

144

~ XapKiB

905°. 3a neprny ro,n;HHY no13,zi; npoifllIOB 68 KM, a aa ,zi;pyry -

84 KM. 3HaH,ZJ;H cepe,zi;HIO llIBH,ZJ;KiCTh Il0l3,D;8 38 u.eii qac. 906°. Ha cKiJihKH qacTKa qnceJI 20 988 i 53 6iJihllla Bi,zi; qacTKH qnceJI 12 420 i 46? 907 . .HK HaMilIBH'Allie 3H8HTH ,n;o6yTKH: 24. 25. 4; 20. 13. 5;

5 . 2 7 5 • 2; 2 • 2 5 • 90? 908. 3Haif,zi;H 3H81.IeHH.H BHpa3iB: 46 057 : a, .HKID;O a = 53; b : 64, .HK~O b = 49 536. 909. IlpoqHTaH IlO.HCHeHH.H. TI o .H c H e H H .H. Ilpn ,n;iJieHHi 6araTou.ncppoBHX qnceJI Ha qncJia ,zi;pyroro 'AeC.HTKa, a TaKom y Bnna,zi;Ky ,zi;sou.ncppoBoro HenonHoro ,zi;iJieHoro ~Hc}>py qacTKH Kpa~e wyKaTH cnoco6oM ,zi;o6opy.

_ 1376 , 16 128 86 96 96 0

91 0. 7176 : 2 3 134

,D;ineHe 1376, ,n;iJihHHK 16. Ileprne HenonHe ,n;iJieHe 137 ,zi;ec.HTKiB. Y qacTnJ 6y,zi;e ,ll;Bi ~H<l>pH. IloAiJIHMO 137 Ha 16, 6y,n;e 8. IlOMHO)KHMO 16 Ha 8, 6y,n;e 128. Bi,zi; 137 si,n;H.HTH 128, 6y,zi;e 9 (,zi;ec.HTKis). .IJ:pyre HCilOBHe ,n;iJieHe 96. 96 no.n;iJIHTH Ha 16, 6y.n;e 6. "t.JacTKa 86.

1122: 17

9889: 31

6059: 73

911 * . Ha MaIIIMHY HaBaHTamMJIH o,n;naKoBi 6o'l!KM i3 coJioHHMH oripKaMH 3araJibHOIO M8COIO 4 T 840 Kr. y KO:>KHiii 6ot.Iu.i 70 Kr oripKiB, a Maca 6o"l!KM 3 po3COJIOM 18 Kr. CKiJibKH 6yJio BCboro KiJiorpaMiB oripKiB?

912. 3 nepmoY AiJUIHKH nJio~ero 6 a ai6paJIH no 45 Kr .ff1:IMeH10 3 1a,a3 'APYrOi AiJI.HHKM IIJIO~ero 2 a - no 41 Kr. 3Ha1'1,n;ll .... . . cepe,zv-110 Bpoma11H1CTh .ffqMeHro Ha u.11x AIJUIHKax.

913째. B111\:0Haii ,n;iJieHH.H i apo611 rrepesipKy ,u;iero MHomettn.H. 17 061: 33

35 856: 83

7475: 13

3462: 6

914째. Ilepmoro AH.ff aBTo6yc ixan ai IIIB11:.Z:J;KiCTIO 70 KM / f'OA,

a Apyroro -

82 KM/rOA. 3HaH,ll;H cepe.zi;HIO llIHHAKiCTh pyxy aaTo6yca aa ABa ,n;Hi.

915. 3HaH,D;M 'lJaCTKlf i nepeBip ,n;ieIO MHOllieHH.H. 6832 : 16

28 567 : 53

916. PoarJI.HHh 3arrHc ycHoro ,zi;iJieHH.H i aaepHM yaary, n~o

. .

a t.1acTu.1 ,u;1cTaJIH HYJih ,u;ec.HTKIB. 4284 : 21 = (4200 + 84) : 21= 4200 : 21 = 200 + 4 = 204

+ 84

: 21 =

917. PoarJUIHb apaaoK ,n;iJieHH.H, KOJIH q:acTKa MicTHTb HYJih. _ 44165 I 73 . II o .a c H e H H .H. flepwe HerroaHe 438 '605 ,n;iJieHe 441 COTHH. y 'l!aCTU.i 6y,n;e TPH 365 U.Hc}lpH. Ilo,n;iJIHMO 441 Ha 73, 6yAe 6. 73 365 IlOMHOlliHTH Ha 6, 6y,u;e 438. 441 MiHyc 0 438, 6yAe 3 ( COTHi). ,[(pyre uenontte AiJieHe 36 .zi;ec.HTKiB. 36 .zi;ec.HTKiB He MomHa rro,zi;iJIHTH Ha 73, ~06 AicTaTH AeC.HTKM. Ha Mic1.1.i ,n;ec.HTKiB y 'tiaCTU.i rr:nrneMo HYJih. TpeTe HerroaHe AiJieHe 365. IloAiJIMMO iioro HS 73, 6y,n;e 5. 73 IlOMHOlliHTH Ha 5, 6yAe 365. OcTa'tli HeMae. 'l.JacTKa 605.

918. 1) 3ttaii,u;M qacTKY 19 026: 63 3 TIO.HCHeHH.HM. 2)32 238: 81

44 918: 74

919. y TpaKTOPHY 6pnra.zi;y 3aBe3JIH 36 OAHaKOBHX 6oqoK rraJihttoro aaraJihHOIO MiCTKicTro 7308 JI. CKiJibKM JJiTpiB rraJibHOro OKpeMO B 5 i 13 TaKHX 601rKax?

135

920. Ba 6aHKax k JiiTpiB coKy. CKiJibKH coKy B 12 TaKHX 6aHKax? CKJia,n;tt s11pa3 ,n;;u1 poaB' .H3Y'8-HH.H aa,n;a'l!i. no 36 u.. 3HaHJJ;H cepe,n;HIO npomaiiHiCTb nmeHH~i Ha ~HX ,n;1JI.HHKax.

921 째. 3 32 ra 3i6paJIH no 27

u. nmeHHU.i, a a 4 ra -

922째. 8772 : 43

34 974: 87

24 583: 61

923. IlepeBip npaBHJlbHiCTb o6qHcJieHH.H. Ilo.HCHH, qoMy B ,n;pyroMy poap.H.n;i 'CJaCTKM ,n;icTaJIH HYJib .n;ec.HTKiB.

321 600: 800 211110 62 186 3405 251 248 310 310 0

924. PoaB'.HmH a nepeBipKoro: 17 136: 51, 106 236: 52. 925. IlepeBip p03B'.H38HH.H i npoqHTaH nOSICHeHH.H. fl 0 .H c H e H H SI. y UbOMY npHKJia,n;i 285360 82 OCTaHHe (qeTBepTe) HenoBHe .D;iJieHe HY Jib. Hy Jib no,n;iJIHTH Ha 82, 6y.n;e HYJib. Ha MicuJ o,n;ttHHl.J.b y '-IaCTI.J.i aan11cyeMo HYJib.

246 393 328 656 656

3480

926. 272 640 : 71

202 950: 45

927. 3a 5 ro,l( onepaTop Ha6paB Ha KoMn'roTepi a cTopiHoK TeKCTy. 3a CKiJibKH ro,n;HH BiH Ha6epe k CTopiHOK? CKJia,n;H BHpaa ,ZJ;JI.H poae' .HayeaHH.H 3a,n;a,qi.

928. Ha nomTi npHHHHJIH 8 nocHJIOK no 4 Kr 500 r i 1 7 TIOCHJIOK no 4 Kr. 3Haii,n;H cepe,n;HIO Macy o,n;Hie1 noCHJIKH.

929째. 323 640: 62

44 474 : 74

30 600: 51

305. 28

930째. ,Il;Ba n0Ia,n;11 BMHIIIJIH o,n;HoqacHo HaaycTpit.1 o,n;HH o,n;HoMY. Ileprnuii no1a,n; pyxaBC.H ai IllBH,n;KiCTIO 72 KM / ro,n;, 68 KM/ ro,n;. ~pyrttii no1a,n; ,n;o aycTpit.Ii a .n;pyrnli rrpoiiIIIoB 408 KM. HKy Bi,n;cTaHb ,n;o aycTpiqi npoiilllOB nepllIHH noia,n;?

136

931. 8 6HqKiB 6y;n1 MaCOIO no 298 Kr KOiKHHH 5 6Ht.JKiB - no 510 Kr i 1 611t.JoK - 316 Kr. 3eali.n;H cepe,nHIO Macy O.D;HOro 6Ht.JKa.

932 .. PoarJI.HHh poaB'.HaaHHH npHKJIMY i npoq11Taii no.HcHeHH.H.

23227154_ - 216 l43c) _162 162 7

23 227: 54 = 430 (OCT. 7) I10 .H CH e H H H. Y :a;boMy npHKJIMi TpeTe HeilOBHe .n;iJieHe qHCJIO 7 (o.n;HHIUJ;b). 7 He .n;iJIHTbC.H Ha 54. 0TiKe, B qacT:a;i 6y.n;e HYJib O.D;HHHIJ;b. ':laCTKa 430, OCT8l!8 7.

933. 3HaH,ZJ;H qacTKY ii OCTaqy: 19 691 : 82, 34 568 : 64. 93 • KomHe a qHceJI 3650, 4599, 6424 aMeHm y 73 paaH.

935. y IJ.HCTepHi 6yJio 4800 JI BO.D;ll. 0,n;HH Hacoc MO:>Ke BHKaqaTH BCIO no.n;y aa 24 XB, a }.J.pyrHH - aa 40 XB. 3a CKiJihKH XBHJIHH MO)KHR BHK8'l18TH BCIO BO.D;Y, SIK~O .nOCT8BHTH Bi.n;paay ,ZJ;Ba HaCOCH?

936. Bi.n; KOmHoi KopoBH cpepMep o.n;epman aa piK y cepe.n;HhOMY no 54 :a; MOJIOKa. 3 O,ZJ;Horo :a;eHTHepa MOJIOKa MO:>KHa nnroToBuTn 4 Kr MacJia. CKiJibKH MacJia MO:>KHa BHrOTOBHTH 3 MOJIOKa, o.n;epmaHoro ni.n; 8 Kopin?

937°. 3HaH'AH 11acTKY :H ocTaqy: 21 324 : 37, 216 724 : 42.

939•. CKJia,n;H aa,naqy aa TaKHM poan'SiaaHH.HM: 1) 792 : 36 = 22; 2) 22. 8 = 176. 939. IlepeBip poan'.HaaHH.H aa,n;a11. 3nepHH yBary Ha Te, .HK .n;iJIHJIH iMeHoBaHi 'lJHCJia. 3 a .n; a q a 1. ,lI;JI.H ni.n;npanKH Ha 6aaap poaKJiaJIH 1 T 2 :a; rpyw y .H~HKH, no 16 Kr y KomHHH. CKiJILKH Il0Tpi6Ho 6yJIO HID;HKin?

1 T 2 Di : 16 Kr = 75 _ 1200116 112 175 80 80 0

(.H~HKiB)

137

a 2. 3a 16 peiicie aeToMo6iJib nepeBia 207 ~ 36 Kr ciHa. CKiJibKH ciHa rrepeB 3HB aBTOMo6iJib 38 O.ll;MH peflc? 3 a /1. a

'II

207 ~ 36 Kr: 16 = 12 _ 20736116 16 11296 47 32 153 144 96 96 0 940. 280 KM 896 M : 44 235 T 924 Kr : 52 941 *. IT p a

K T 11 q H

96 Kr

256 rpH. 5 K. : 15 K. 10 rpH. - 5 rpH. 5 K.

a p o 6 o T a.

1) Bi.zi;pim ~ cMymKM, .zi;oam11Ha SIKoi 22 CM 5 MM. 7 2) MaMa Bi11.pi3aJia /J.JI.H Oni 10 M cTpit:IKH, a 11.JIH Jleci 4 M. y Koro 3 .zi;iet:IaTOK KOpOTllla CTpit.J.Ka i Ha CKiJibKH gaHTHMeTpiB? IIepeBip poaa'.HaaHHH 3Mat:Ii npaKTHqHo.

942. KiT y qo6oTHX rroJIIOBaB Ha KponiB. Maca 4 KponiB, SIKMX BiH 3JIOBRB, 6yna no 1 K:r 950 r KO)l{HHH, 7 KpoJiiB - no 2 Kr 200 r i OJJ;HH KpiJih Ba.mHB 2 K:r 300 r. H Ka B cepe.z:r;HbOMY Maca o.z:r;Horo KpOJI.H?

138

943. IIpoqHTaii BHpa3H, rro.HCHH nop.H.ZJ;OK s111coHaHH.H .n;iif, u

•

ycHo auau.n;11 aHa"tJeHH.H BHpaa1e.

7. 600 + 20 000: 4 - 700 (420: 42·10 - 280: 4) · 12 1000 - (420 + 180: 6 + 400) 25 ·6 - 250: (50: 10) - 100 944°. 77 M 76 CM: 54 10 KM 512 M : 73

256 T 60 Kr: 62 379 T 440 Kr: 62 Kr

•

945 . rocno,napKa ai6paJia Ha npHC8.ZJ;H6HiH

.n;iJISIH~i

24 Kr

. . 3 . . . IlOMl.ZJ;OplB. ~HX DOMl,z\OplB BOHa 38COJIHJia nopIBHY 4 y 12 6aHKax. CKiJihKH noMi.n;opiB rocno.n;apKa noKJia .. Jia B KOJKHY 6aHKy? 3aIIHilIH Bi,nnoei.n;b y KiJiorpaMax . i rpaMax.

946. (YcHo.)

20 Kr 2 U.: 5 Kr

947. (1247 + 39 096: 54): 73

2 2

- 20 Kr ~ - 5 Kr

300 Kr: 50 3 Kr: 500

(1000- 36 202 : 46) ·82

948. Pa3 Ha 3 pOKH Ha KO)KHHH KBMP8THHH MeTp BHHOrpMHHKY BHOC.HTh 3 Kr .n;o6pHB. CKi.rrhKH KinorpaMiB .n;o6pHB Tpe6a BHeCTH H8 .n;iJI.HHKY BHHorpa.n;HHKY np.HMOKYTHOl c}>opMH ai CTOPOH8MH 15 Mi 50 M?

949 . j}ta6eH.H MOJKe IlOC}>ap6yBaTl1 napKaH 38B,ZJ;OBJKKH 300 M aa 6 ,nHiB, a KiT Mome apo6HTH ~e y .n;ea paaH IIIBll.D;llle. 3a CKiJihKH .D;HiB BOHM noc}lap6yJOTb napKaH, npau.1010qu paaoM?

+ 9850) = 16 000 (1100 + 508): x = 24 951 . 27. (12 003- 294 735: 35) + 511 ·36

950. x - (23 603

139

952° 3MOJIOJIH 3

600 Kr nIIIeH1111J. BopoIIIHO cTaHOBHJIO 5 ycie1 nrneHuuJ, MaHHHX Kpyrrie 6yno ~ 40 paa MeHllle, peIIITa - BHCiBKH. CKiJibKH o.n;ep.maJIH KinorpaMiB MaHHHX KpyniB?

953. 3Haii.zi;H qacTKY .H OCTaqy: 384 276: 83; 579 685: 91. 954. 26 T 496 Kr : 92

28 Kr 32 r : 64 404 M 4 CM : 74

77 M 22 CM : 33

955. {16 205: 35 + 185) .49

(480. 60 - 3636): 18

956. {Ycno.) qHcno 4200 cnoqaTKY a6iJiblIIHJIH y 5 paa, noTiM a.n;o6yTHii peayJihTaT 3MeHIIIHJIH y 3 paa11. HKe q11cJio ,n;icTan:u?

957. 3 23 ra ai6pan11 506 u. rpeqKH. CKiJihKH u.eHTHepiB p11cy ai6panH a 18 ra, .HKI.QO Bpomaf1HiCTb p11cy BHI.Qa, Him rpeqKH?

2 paaH

958. CKJIBJJ;H i poaB'HmH aa.zi;a-qy npo a611paHHH npoca. )]JJI.RHKa

YpomaiiHiCTh

Ileprna JJ;pyra

12 I\ 7 L\

"l.hlCJIO re1<TapiB

3i6paHo npoca

28 ra

} 460

959. IlpM HKHX 3HaqeHHHX a cyMa 500 + a 6y.n;e 6iJihIIIa Bi.zi; 1200? pi3HHIJ..H 500 - a 6y.n;e MeHIIIa Bi)J; 200?

960°. 3a 5 XB 7 IIIBeHHHX MaIIIHH apo611JI11 52 500 CTi6KiB. CKiJihKH cTi6KiB apo6JI.HTh 18 TaKHX Ma11111H aa 1 xB?

961 °. 27 922 : 46

42 372 : 66

+ 358

962. {YcHo.) 110 + 220 - 50 ·5: 10

110 + 220 - 50: (10. 5)

30 744: 42 ·91

1000 - 800·10: 100 {1000 - 800) · 10: 100

963. 30 000 - 37 800 : 84 : 18 + 589 964. 26 Kr 372 r : 76 - 22 Kr 88 r : 88 30 KM 8 M: 88

140

+ 14 KM 600 M ·42

10 Kr: 5 r 10 M: 5 CM

965. CKJIRAH piBH.HHH.H i1 poas'.H.mH lioro • .HKe qHCJIO Tpe6a flO'AiJIHTH Ha 61, ~06 'AlcTRTH 305?

966. <llepMep BHPOCTHB i ai6paB 1445 I.\ KapTODJii. 245 u; BiH

. . 5 aaJIHIIIHB 'AJI.H ro,l\lBJil TBapHH, a 6 peruTH rrpoAaB Ha 6aaapi. CKiJihKH u_eHTHepis KapTorrJii c}JepMep rrpo,n;as?

967. HaaBH qJICJia' nponyll\eHi B Ta6JIHIJ;i. lfHCJia OCTaHHbOl KOJIOHKH cnpo6yli 3HaHTH BHnpo6oByBaHH.HM.

~OB:>KHHa

45M

lliHpRHa

20M

16CM

8'AM

? ?

320 CM 2

Ilno~a

IlepHMCTp

? 24 CM 2

40 'AM

20CM

968 . Q6q11cJIH, aanHcyroq:u yMosy i Bi'ADOBi,n;h. 1) ~o6yTOK tIHCeJI 2684 i 16 3MeHIIIHTH y 8 paa. 2) qaCTKY q:uceJI 784 i 28 a6iJihllIHTH y 14 paa.

969°. 3anHIIIH Il0Tpi6Hi 3HaKH 'Aiii. 27 ••. 9 •.. 3=729 27 .•• 9 .•• 3 = 1 27 ••• 9 ••• 3 = 54

27 ••• 9 ..• 3=240 27 •.• 9 ••• 3 = 9 27 ..• 9 ••• 3 = 12

970. (YcHo.) 800: 400

6400: 800

7400: 100

971. 3Haii,n;H qaCTKY ii OCTa'lly: 613: 300; 5448: 600. 972*. PoarJI.RHh ,l\iJieHH.H Ha TPH~Hc}JpoBe q11cno. IlpoqHTaii IIO.HCHeHH.H npo p03B, .H3yBaHH.H rrepworo npHKJIMY.

- 8521213 852 0

- 20349, 323 1938 63 969 969

0 HSI. ,[(ineae i ~iJihHHK -

c He H TPH~Hc}Jposi q:ucJia, y qacTu_i 6y'Ae o,n;Ho~uc}>poBe qucJio. ~06 ,n;i6paTH ~ucppy qacTKH, no,n;iJIHMO 852 Ha 200, 6y'Ae 4. Ilepesi-

IT o

PHMO

n1i1cppy 4. 213

IIOMHO>KHTH Ha

6y~e

852. Uiup ..

PY 4 ,n;i6paHO npaBHJibHO.

. ..

973. 3HaHAH qacTKY 2268 : 324 3 IlOHCHeHHHM. 974.

CKJI~H i poaa'snKH aa,n;aqy aa no,n;aHHM anpaaoM.

1118: (546: 42) 975. 3 )J;BOX MiCT, Bi,n;cTaHL Mim HKHMH 2775 KM, BHJieTiJIH

OAHOqacHO Ha3yCTpl q O)J;HH O)J;HOMY ,n;aa Jll Ta Kif. IIIan,n;KiCTh nepmoro JiiTaKa 4 7 5 KM/ro11., a APYroro 450 KM/rOA. l.fepe3 CKiJILKH rOAHH JiiTaKH aycTpiHYTLCH?

976°. 1) CyMy q11ceJI 4 752 i 6840 noAiJIH Ha 72.

2) B~ q11cJia 9280 BiAHiMH qacTKY q11ceJI 33 048 i 54. 977°. Hoea 6i6JiioTeKa 0Tp11MaJia 3128 KHHmoK. IlicJIH Toro HK qacTHHY KHHmOK p03CTaBHJIH Ha IlOJIHIJ;i, no 34 Ha KOmHy, aaJIHWHJIOCH poacTaBHTH 680 KHHmoK. CKiJILKH IlOJIHIJ;b aaiiHHJIH KHHmKaMH?

978*. PoarJIHHh aan11cn i noHCHH, HK 3HaxOJJ;HJIH qacTKH.

·_ 149929, 247 1482 607 1729 1729 0

_1927801306 1836 630 918 918 0

Ilepeaip npaBHJILHiCTL poas'saaHHH Aiero MHomeHHH.

979. 36 ·28: 24

(36

+ 28) ·24

6048: 72: 12 6048 : (72 : 12)

4085 + 32 ·85 (4085 + 32) ·85

980.. BeJioc11rre,n;ncT ixaa 3 ro11. 3 011.HaKOBOIO mBHAKiCTIO. HKII.\O aiH npoiAe II.\e 6 KM, iioro mJIHX AOPiBHIOBaTHMe 45 KM. 3 SIKOIO lliBHAKiCTIO lxaB BeJIOCHileAHCT?

981. Ao6ep11 q11cJia i CKJia11.11 aap;aqy npo a611paHHH orip-

I<IB.

3i6paJIH

OKr

142

BmnpaBHJIH

0Kr II - ? , y 5 paa 6inLwe I-

3aJIHIIIHJIOCH

982. Ha a rpH. KynHJIH b o.n;HaKOBHX aaraJihHHX aoIIIHTiB. CKiJihKH TaKHx aowHTiB MO)KHa KYilHTH Ha 9 rpH.?

983. YpoK TpHaae

ro.n;, nepepBa

roA. CKiJihKH XBHJIHH

3 6 Tp11aal0Th paaoM TpH ypoKH i ABi TaKi nepepaH?

984°. 3 OAHiel AiJISIHKH ai6paJIH 5428 n; CTOJIOBHX 6ypSIKiB, a a Apyroi - y 7 paa 6iJibllle. 'leTaepTy qacTHHY acix 6ypSIKia noKJiaJIH a 0Boqecxoa11~e. CKiJihKH n;eHTHepiB 6ypSIKiB IlOKJiaJIH B OBoqecXOBH~e?

985°. PoaMipH cnopTHBHoro KoMnJieKcy,

~o Mae cpopMy 950 M 2 aaiiMae

npSIMOKyTHHKa, 125 M i 350 M. 14 KaTOK, a ~ pemTH IlJIO~i - cnopTHBHi M8HA8HqHKH. 3Han.n;H IlJIO~Y cnopTHBHHX Maii'AaHqHKiB.

MIPH l!ACY. IIOBTOPEHHH 3A.IJ;AqHoro MATEPIAJIY 986. Ilpoq11Ta:H noSicHeHH.fl npo o.n;HHHI.ti BHMip10BaHHsr 'llacy. 0AHHHD;i BHMipIOB8HH.ff qacy noa'SI3aHi 3 pyxoM HamoY nJiaHeTH 3eMJii HaBKOJio Coan;sr, pyxoM MicSID;SI HaBKOJIO 3eMJii, o6epTaHHHM 3eMJii H8BKOJIO BJiaCHOl oci. 3eMJISI po611Th noBHHii o6epT HaBKOJIO CoHn;H npH6JIH3HO 38 365 .n;i6 i 6 rOA. ~e - O'AHH piK. ,lJ;JISI apyqHocTi Jiiq611 a 'A8BHix qacia npHiiHHTo, ~o TPH poKH HaJiiqyIOTb no 365 AHiB y KO)KHOMy, a qeTBepTMH BUCOICOCHUU 366 AHiB. IlpoMimoK qacy B 100 poKiB Mae Haaey cmoJLimma. PiK noAiJIHIOTh Ha 12 npoMimKia Mic.an;iB. IlpoMimoK qacy o6epTaHHSI 3eMJii H8BKOJIO CBO€l oci .n;o6a. ,Il;o6a IlO'AinHeThCSI Ha 24 piBHi qacTHHlI rO,D;HHH. 1 rOA -

~e _!_ ,n;o611.

ro.n;HHa IlO.D;iJUleThC.H Ha 24 60 piBHHX qaCTHH-XBHJIHH, a XBHJIHHa-Ha 60 CeKyH.n;,

1 C - n;e

XBHJIHHH. 60 987. PoarJI.HHb OCHOBHi O,D;HHHD;i BHMip10BaHHSI qacy (c. 144) i aanaM'srTaii ix.

143

CToJiiTT.H .n;opiBHIO€ 100 poKaM. PiK .n;opiBHIO€ 12 Mic.Hn;SIM. y 3BHqaifHOMY pon;i 365 .n;i6, y BHCOKOCHOMy-366. y MiC.HIJJ 30 a6o 31 .n;eHb (y JIIOTOMY 28 a6o 29 AHiB). ,lI;o6a .n;opiBHIO€ 24 rO,D;HHaM. rop;HHR ,ZJ;OpiBHIO€ 60 XBHJIHH8M. XBHJIHHa .n;opiBHroe 60 ceKya.n;aM.

988 1) IlepeBip,

MOmHa aa 10 c HR3BaTH 10 .ZJ;BOIJ;Hc}>poBHX qHceJI, npOHTH 10 M. 2) IlepeBip aa Ta6eJieM-KaJiea.n;apeM, qH e MicHn;i, .HKi MalOTb 30 ,ZJ;HiB, ~cyci,n;aMH)) TpaBHSI a6o moBTH.H. qg

989. 1) Y 1982 p. CB.HTKYBRJIH 1500-piqq,R CTOJIHn;i YKpaiHH - MicTa KHeea. CKiJI&KH cToJiiT& icHye KHie? 2) 3a no.n;aHHMH B .n;ymKax .n;aTaMH mHTTSI BHJJ;RTHHX ,n;iSJqis YKpaiHH cKamH, B SIKOMY CTOJiiTTi BOHH m.HJIH i npan;roeaJIH: Bor.n;aH XMeJI&HHIJ;bKHH (1595-1657), Tapac IIIeeqeaKo (1814-1861), Jlecx YKpaiHKa (1871-1913).

• 3 TpbOX CTpayCOBHX .H€[(h MOmHa 3p06HTH OMJieT .D;JI.H 72 oci6. AJia cKiJI&Kox oci6 MomHa apo6HTH OMJieT a .nBOX T8KHX aen;L?

1 .. Maca .n;eox o,n;HaKOBHX 6apaHiB 156 Kr. HKa Maca

OJ(HaKOBHX nopOCHT, HKJ:qO Maca OJJ;HOro nopoc.HTH y 3 pa3H MeHIIIa Bip; MRCH 6apaHa?

.. TpH B' H3H aa 6 Micnuie norJIHHa·IOTb 3 noeiTp.R 360 r mKiAJIHBHX raaie. CKiJI&KH rpaMiB IIIK~JIHBHX raaie nornHaae o,n;HH e'.Ha 38 8 MicaaJB?

144

993°. 3a 3 ro.n; po60TH 6 MaiicTpliHh BHrOTOBHJIM 36 rJiellHKiB, nopiBHY KOmHa. CKiJihKH rJiet:IHKiB apo6HTh op;Ha M8HCTPHHSI aa 8 ro.n; po60TH?

99 •. 3a 4 ro.n; ~eHL BMrOTOBMB 128 .n;eTaJieii. MaiicTep aa 1 ro.n; BHrOTOBJIHe Ha 9 .n;eTaJieii 6iJILme, Him yt.JeHL. 3a CKiJihKH ro.n;HH MaHCTep Bl1rOTOBHTb 246 AeTaJieii?

995. B11Kop11cT0By10q11 Ta6eJIL-KaJieHAap noTOt:IHoro poKy, ,.

AaH BlAilOBIAl Ha aanHTaHHH. 1) Ha .HKHH AeHh THmHH B IJ;LOMY pon;i npHnap;a€ 24 cepnHH-,ll;eHh HeaaJiemHocTi YKpa1HH? 2) Ha HKHH AeHh THmHH np11na,n;a€ .n;eHh TBoro HapoAmeHHH?

99 • 1) f aaHyci MHHYJIO 10 poKiB i 2 MicHu;i. CKiJihKH n;e MiCHUiB? 2) MaTepi 34 poKH 8 Mic11n;is, a ~O'llUi 9 poKiB 9 MicHn;is. Ha CKiJihKH poKiB i MiCHUiB AO'llKa MOJIOAIIIa Bi.n; MaTepi?

99 • 3oJIOTi BopoTa B KHesi -

roJIOBHY 6paMy MicTa qaciB KH1BCLKo1 Pyci - cnopyAmeHo B 1037 p. B HKOMY CTOJii TTi Bi.n;6yJiaCSI ll,SI no.n;iH?

99 " (YcHo.) TaTOBi 40 poKiB, CHH Ha 30 poKiB MOJIOAWHH siA HLoro, a 6a6ycH cTapIIIa sip; oHyKa y 6 paa. CKiJILKH poKiB 6a6yci?

145

999. ~JI.ff IlIKOJIH-iHTepHaTy KYIIHJIH 3 XOJIO)J;HJibHHKH i 2 rrpaJihHi M8llJHHH. QiHa XOJIO,ZJ;HJlhl!HKa a rpH., a rrpaJihH01 MalllHHH b rpH. CKiJihKH KomTye noKyrrKa? CKJI8)1;M BHpaa.

1000. An.fl crropTHBHoro KJiy6y rrp11)1;6aJI11 8 TpeHamepiB i 3 rnTaHrH. 3a BCIO noKynKy aanJiaTHJIH a rpH. CKiJihKH KOllITye TpeHamep, SIKIIl;O Bi)J;OMO, m;o llITaHra KOIIITye b rpH.? CKJia)J;H BHpaa.

1001°. 3a 8 3MiH 6 TpaKTopiB MomyTh BHOp8TH 768 ra. CKiJihKH reKTapiB Mome snopaTH O)J;MH TaKHH TpaKTop aa 5 3MiH?

1002°. Ha aaniaHHt.IHY nnaTcpopMy HaBaHTamHJIH 3 O)J;HaKoBHX JierKOBHX aBTOM06iJii i 4 MOTOIJ;HKJIH. 3araJihHa Maca aBTOMo6iniB i MOTOIJ;HKJiiB 3 T 690 Kr. Maca MOTOIJ;HKJia 330 Kr. HKa Maca nerKoBoro aBTOMo6inSI?

1003. PoarJISIHb apaaKH aaMiHH 6iJihlllHX O)J;HHHIJ;h BHMiproBRHH.H qacy MeHll1HMH TaTH. 5 p. = 60 Mic. 3 )1;0611 = 72 ro)J; 10 ro)J; = 600 XB 2 XB = 120 C

•

IlOSICHH, SIK 3H8HlllJIH peayJib-

2 p. 4 Mic. = 28 Mic. 1 )1;o6a 8 ro)J; = 32 ro)J; 5ro)J;10 XB = 310 XB 3 XB 20 C = 200 C

1004. PoarJISIHb, HK aaMiHHJIH MeHllli o.n;11ttnn;i BMMiproBaHH.H

qacy 6iJihlllUMH i IIO.HCHH, .HK 3H8MlllJIH peayJibTaTH.

120 c = 2 XB 200 c = 3 XB 20 c 50 ro)J; = 2 )J;06H 2 ro)J;

300 XB = 5 ro)J; 100 XB = 1 ro,ZJ; 40 XB 40 Mic.= 3 p. 4 Mic.

1005. 3aMiHH aa apaaKOM 6iJihllli

O~HHHIJ;i

BHMiproeaHH.H

MeHIIIHMlI (IIHChMOBO). 3 p a a o K. 23 )J;06M 7 ro~ = 559 ro)J; x 24 21 ro)J; 15 XB 23 4 7 )1;i6 8 rO)J; + 72 17xB47c 48 15 rO)J; 29 XB 552 552 + 7 = 559

146

1006. IIeperrHmH, aarroBIIIOIO'tJH rrporrycK11:

13 XB = D c

1200 xe = D ro,n; 210 xe = D ro.n; D xe

ro,n;

3 4 480 c = D XB 72 ro,n; 50 Mic. = D p. D Mic.

= D XB =

D ,n;o6n

1007. Haii,n;oBIIIHH .n;ettb y KH€Bi Tp11aa€ 98 7 XB. 3arrnmH B ro,n;HH8X i XBHJIHHax TpHBaJiiCTb ~Laro ));HSI. 1008 . .D:JIH o6KJieroBaHHSI 50 M2 cTiH noTpi6Ho 7 pyJioHiB wnaJiep. CKiJILKH pyJioHiB IllnaJiep noTpi6Ho ,n;JIH 06KJieroBaHHH 200 M 2 CTiH?

1009°. 3 10 Kr 6opOIIIHa BHXO)J;HTb 14 Kr XJii6a. CKiJibKH IIOTpi6Ho 6opoIIIHa Ha BHilil.JKY 70 Kr XJii6a? 1010°. Y 100 Kr MOpCbKOi BO)J;H MiCTMTbCSI 2500 r COJii. CKiJILKH rpaMiB COJii MiCTHTbCSI y 20 Kr MOpCbKOl BO,n;H?

1011 . Bi,n;cTaHL si,n; MicTa A ,n;o MicTa B noia,n; npoixae aa 5 ro,n; 48 xe, a ei.n; MicTa B ,n;o MicTa C - aa 3 ro,n; 34 xe. CKiJihKH qacy noia,n; 6ye y ,n;opoai? Poae'SiaaHHH 5 ro,n; 48 XB + 3 ro,n; 34 XB 5 ro,n; 48 xe + 3 ro,n; 34 xs 8 ro.n; 82 xe 9 ro,n; 22 xB Ilo.HCHH xi,n; 061.JHCJieHHSI.

= 9 ro.n; 22

1012. Ilepeeip poae'naaHHH. 4 p. 9 Mic. +5 Mic. 17 ,n;HiB + 2 p. 7 Mic. 4 Mic. 8 )J;HiB 6 p. 16 Mic. 9 Mic. 25 ,n;HiB 7 p. 4 Mic.

+17 XB

45 C

24 XB 57 C 41XB102 C 42 XB 42 C

1013. Ilepeeip npaBHJILHiCTb 061.JHCJieHHSI. 1 7 ro,n; 20 XB - 5 ro,n; 45 xs = 11 ro,n;.·35 xa 16 ro,n; 80 xa - 5 ro,n; 45 xa

11 ro,n; 35 xa 147

1014. 15 roA 16 XB + 9 ro,n; 49 XB 7 ro,n; 34 XB - 2 ro,n; 40 XB 10 XB 30 c + 25 XB 45 c

5 Ai6 6 ro,n;

2 ,n;o6H 18 ro,n;

1015. Y cTiiiJioanii nepio,n; o,n;Hiii Kopoai aro.n;oByBaJIH aa .n;eHL 3 7 Kr CHJiocy. CTiiiJIOBHH nepioA TpHBaB a 2 5 m.oBTH.H no 10 TpaBH.H. CKiJILKH KiJiorpaMiB CHJiocy aro,n;yBaJIH 96 KOpOBaM aa TpeTHHY CTiMJIOBOro nepio,n;y?

1016. Ilepma aepHooqHcHa MalIIHHa aa 6 xB O'llIIIl.\ae 90 Kr aepHa, a ,n;pyra aa 4 XB - 80 Kr aeptta. 3a .HKHH "tJac paaoM oq11cT.HTb ~i M8lllHHH 7 T aepHa?

1 017째. ,IJ;ai 6pHra)J;H ai6paJilI 24 KOp3HHlI MOpKBH, BChOro 288 Kr. Ileprna 6pnra,n;a ai6paJia 156 Kr MOPKBH, a APyra - pernTy. CKiJihKH KopanH MOPKBH 3i6paJia Kom.Ha 6pHra.n;a?

1018째. 21ro.n;17 xa - 12 ro.n; 45 XB 11 p. 4 Mic. - 6 p. 6 Mic. 9rOA16 XB + 8 rOA 57 XB

7 .n;i612 ro.n; - 5 .n;i616 rO)J;

1019. 3H8ll)J;H qacTKH 3 IlO.HCHeHH.HM: 15 953: 53; 44 856: 84. 1020. 3Haii.n;H pi3HHI.\i i nepeBip .n;o.n;aBaHH.HM. 14 roA 35 xa - 8 ro.n; 57 XB

16 Ai6 10 ro.n; - 6 ,n;i6 15 ro.n;

1021. Mara3HH BiJJ;KpIIBaeTLC.H o 8 ro)J; paHKy, a aaKpHBaeTbC.H o 9 ro.n; aeqopa. CKiJILKH ro.n;HH rrpal.\IOe MaraaHH, .HK~o o6~H.H nepepaa TpHBae OAHY ro)J;HHy? (PoaB'sDKH aa.n;aqy aa AOIIOMOrOIO rOAHHHHKOBOro I.\Hcpep6JiaTa.)

1022. Po3rJI.HHh poaB'.HaaHHH 3a.n;aq Ha BlI3HaqeHH.H TpH-

... ....

B8JIOCT1 IIO,ZJ;ll,

38KlHqeHHH Ta noqaTKY.

3 a ,n; a q a 1. Ilepepaa poarroqa.rracsr o 10 roA 10 XB i 3aKiHt.IHJiacL o 10 ro)J; 30 XB. CKiJihKH qacy TpHBaJia nepepaa? 10 ro.n; 30 XB - 10 rOA 10 XB = 20 XB 3 a A a q a 2. IIepepBa poarroqanacL o 9 ro)J; 15 XB i TpHBana 10 XB. KoJIH 3aKiH'tJHJiacH nepepaa? 9 ro.n; 15 XB + 10 XB = 9 ro)J; 25 XB 3 a .n; a q a 3. Ilepepaa TpHaana 30 xa i aaKiHqHJIRCh o 10 roA 35 xa. KoJIH poarroqaJiacH nepepBa? 10 ro.n; 35 XB - 30 XB

148

= 10 ro,n; 5 XB

1023. CoHn;e aiiilllJIO o 7 roA 55 XB paHKy, aalilllJIO 0 4 rOA 16 XB Beqopa. BH3Haq TPHBaJiiC AHH. 1024. Mara3HH rrpoAaB AO nepepBH 37 .HII(HKiB .H6JiyK, a niCJI.H nepepBH 23 T8KHX caMHX .H~HKH H6JiyK. IliCJI.H nepepBll npOA8JIH Ha 168 Kr H6JiyK MeHme, Hi:>I( AO nepepBH. CKiJILKH KiJiorpaMiB .H6JiyK npoAaJIH oKpeMo AO nepepBH i nicJI.H nepepBH? 1025. 3 IIJIOII(i 36 ra OAepmaJIH no 30 u oaHMoi nmen11u,i · a reKTapa, a a 4 ra - no 40 u a reKTapa. lJoMy AOpiBHIOe cepeAHiH ypomaii IIllleHHU,i 3 D;HX AiJI.HHOK? 1026*. 3 TpbOX yt1HiB Ha iM'n AHTOH, BorAaH i CepriiI, ,n;Boe BiAMiHHHKR. BHaHa'lJ, XTO BiAMiHHHK, .HK~o B napi AnTOH i BorAaH - OAHH Biti;MiHHHK, o.n;HH Hi, a B napi Borti;aH i Cepriu - Tem OAHH BmMiHHHK, oti;HH - Hi. 1027°. 1) CoHu;e aiifllIJIO o 6 ro,n; 35 xB. Tp11BaJiiCTb ti;H.H 11roti;10 XB. BHaHaq qac aaxOAY Cottu;n. 2) TpHBaJiiCTb AH.H 16 ro,n; 17 xe. CoHu;e aaiillIJIO o 9 roti; 5 xB Beqopa. BHaHaq qac cxo,n;y CoHIJ,H. 1028°. 160 034 : 46 600 280 - 158 430 349·86 30 014 ·20 88 370 + 71 684 441 850: 5 1029. PoaB '.HmH rrpHKJia,n;H, y HKHX ,n;pyroro e ti;i.H ,n;iJieHHH. 480: 6 - 16 60 + 100:4·3

240 - 80: 4 + 100 (500 + 300):2 - 250

60 ·4 : 30 + 100 560:8 - 10· 4

1030. PoarJIHHh poaB'naaHH.H aa,n;aqi Ha BHattaqeHH.H qacy. YqHi Bui:xaJIH Ha eKcKypciro 7 nepecHH o 10 ro,n; paHKy, a n0Bep11y;u1c.H 15 BepecHH o 8 ro,n; seqopa. CKiJihKlf qacy BOHH npo6yJIH Ha eKCKypcii? PoaB'.HaaHH.H EKcKypci.H poanoqaJiacn, KOJIH MHHYJIO 6 ,n;i6 10 ro,n; Bi.n; IIO'lJaTKY BepeCH.ff. EKcKypci.H aaKittt.1nnacn, KOJIH MHHYJIO 14 ,n;i6 20 ro,n; BIA IlO'lJ8TKY BepeCHH. 14 ,n;i6 20 roti; - 6 ,n;i6 10 ro,n; = 8 ti;i6 10 ro,n;

149

1031 • f eThMaH yKpaiHCbKOrO peecTpOBOro K03aI.J.TBa IleTpo Carai1Aat1HJIH rroMep 20 KBiTHSI 1622 p. CKiJihKH MMHYJIO qacy a .D;HSI iioro cMepTi .n;o <!boro.n;ttirnnhoro .D;H.R? 1032. 3 nyHKTY A noia.n; BHHIIIOB 22 TpaBH.H o 6 ro.n; Be'l1opa i npu6ys y nyHKT B 25 TpaBH.H o 9 ro.n; paHKY. CKiJihKH lJacy noiaA 6yB y .n;opoai? 1033. TenJioxi.n; irnos Bi.n; CeBacTorro;u1 .n;o O.n;ec11. KoJin BiH npo6yn y .n;opoai 2 ro.n; 45 xB, iioMy aaJIHIIIHJIOCSI HTH Ha 13 ro.n; 10 XB 6iJibille, Him BiH iIIIOB. 3a HKHH "C.IaC TenJioxi.n; Mae npoiiT11 IIIJI.HX si.n; CeBacTonoJI.H .n;o O.n;ecn? 1034. ~JI.H

npoKJia,n;aHH.H eJieKTponpoBO.D;KH np11.n;6aJI11 1200 M .n;poTy. 12 MOTRiB .n;poTy, no 60 M y KO:>KHOMY . 3 MOTKY, BHTpaTHJIH Ha BHyTp1u1ttro npoBo,n;Ky, ~ pe1nT11

.n;poTy rrillIJIO Ha aosttirnHro nposo.n;Ky. CRiJii?K11 MeTpiB .n;poTy nilllJIO Ha 30BHilllH10 rrposo.n;Ry? 1035. 3 .n;iJIHHRH IIJIOI.QCIO 22 ra ai6paJI11 750 u; aepHa KYKYpy.n;an, a a .n;iJI.HHKH nJio~ero 33 ra - 1230 u;. BnaHaq cepe.n;ttro Bpo.maiiHiCTh RyKypy.n;an. 1036. Ha KO.>KHOMY 3 5 ra IlOJI.H, aaciSIHoro COHSIIIIHIIKOM, 6yJIO o.n;ep)l<aHo no 8 u; HaciHHH, IIPOAaJK .HRoro .n;aB 14 000 rpn. npH6yTRY. flKHll 1:JPH6yTOK .n;aB 1 Kr HaciHH.H? 1037. 3HaRH .HKHX ap1-HpMeT11qHJ1X .n;ii1 nporryll\eHo?

400 ... 60 ... 3 = 220

640 ... 400 ... 2 = 440

1038* . PyxaioqJich op6iT010 HaBKOJio CoHu;.H, 3eMJI.H aa 1 c npoxo.n;nTh 29 KM 800 M. HKy Bi,n;cTanh npoiiAe 3eMJUI aa 10 XB? 1039°. 650. 73

+ 32 457: 93

(930. 60 - 6336) : 9

(5750 + 158 ·38) - 4877 (16 008: 46 + 4804) ·51

1040°. Y KueBi Ha o.n;tty JIIO,ZJ;l1HY np11na.n;ae 72 M2 aeJieHHX Haca,n,meHh, a B ToRio - 12 M2 • Y cKiJihK11 ,paaiB MeHrne np:una.n;ae aeJieHHX naca.n;meHh Ha o.n;noro MernRaHU.H ToRio, Him Ha o.n;Horo RH.HHHHa?

3 MATEMATM"IHO... CKAP6HM~KM

HArfYPAJ"'lbHMH PH,11;. BY,D;OBA HATYPAJibHOfO q11CJIA Y ,D;EC.HTKOBIR CHCTEMI q11CJIEHII.H. ITOPIBHHHH.H t.IHCEJI qH CJI a l , 2 , 3, 4 , 5, 6, 7, 8, 9, 10, 11, 12, ...

Ha3HBaIOThC.H uaTypaJihHMMH 1 yTBopIOIOTh HamypaJtbnuu paa 'lUCeJl. ,D:JI.H 3RIIHCY HaTypaJibHMX lJHCeJI KOpHCTYIOTbC.H aec.RmlC06010 CUClnPMOIO .HKoi Jie.iKaTh JJ;eC.HTh attaKiB -

1lUCJteHH.R,

u_Mcpp.

Ha neprnoMy Mic-

:u;i B HaTypaJihHOMY p.H.n,i CTOITb t.fUCJIO lJHCJIO

J];8Jli

i TaK }1.0

IlicJI.H

B OCHOBi

38 HMM i.n.e

ari.n.Ho 3 npaBHJIOM

10, a aa 10 i}J.e . HaTypaJibHOMY PHJJ.l HeMae OCT3HHbOro l.JJICJia -

.n,eC.HTKOBOro l{MCJieHH.H, ii.n.e l{HCJIO

. 1 y

11, aa

KO>KHMM HaTypaJibHMM l{HCJIOM CTOlTb ~e OAHe HaTypaJihHe l{HCJIO, aa HKHM- ~e O.ZJ.He i T.

A·

BamJIHBY ponh y )J.eC.HTKOBiii cHcTeMi 1111cJieHH.H BiAirpae t.IHCJIO

10.

,D;ec.HTb 0)1.MHHIJ;b H83HBaIOTb .n;ec.HTKOM,

)J;eC.HTb .n;eC.HTKlD -

I.JJ

COTHeIO, .n,ec.HTb COTeHb -

TMC.HtieIO.

Ha3BH BHKOPHCTOBYIOThC.H rri.n; 11ac l.!MT8HH.H HaTy-

paJibHHX tJMCeJI.

.n.ec.HTKOBiii CHCTeMi t.IHCJieHH.H OJ];HH i TOM C8MMH

3H8K (:u;1uppa) Mae pi3Hi 3HaqeHH.H 3aJiemHO Bi.n; Mic:u;.a (noaH:u;ii), .n;e BiH poaMimeHnii. Ilepma u.11c}>pa crrpaBa y J];eC.HTKOBOMY aanucy HaTypaJibHOro 'IMCJia H83MB8€TbC.H :a;Hc}>poro neprnoro poap.H.n;y, .n,pyra ~n<l>pa cnpaBa -

1~Mll1po10 .n;pyroro poap.H.ZJ.Y, 1·peT.H -

.u;ttl}>poro TpeTI>oro

p03PSIAY. 3auHC KOiKHOro ~BO~:Hc}JpOBOro, TPH~Hq>po151

BOro i T. JJ.. 'llHCJia e CKOpO'lleHHM 3aIIHCOM cyMH iioro p03p.HJJ.HHX 'llHCeJI (JJ.O.n;aHKiB). HarrpHKJiaJJ.:

57 801 = 50 000 + 7000 + 800 + 1.

Jli116a .n;ec.HTKaMH, a6o p03p.HJJ.8Mlf, 3MeHIIIye KiJibKiCTb CJiiB, IIOTpi6HHX JJ.JI.H H8HMeHyBaHH.H HaTypaJibHHX qnceJI. AJie JJ.JIH

BeJIHKHx qnceJI IJ.horo HeJJ.O-

cTaTHbO. IloTpe6a B HOBHX CJIOBax pi3KO 3MeHIIIyeTbC.H, .HKIJ..\O Tp11 rrocJiiJJ.OBHHX poap.H,n;:u o6'e.n;HyBaTH a OJJ.HH KJiac. IlepIIIHll KJl8C -

u.e KJI8C O)J.HHI1JJ.b, JJ.pyrHii -

KJiac THC.Ht!. TpeTiii KJI8C Ha3HBaIOTh KJiacoM MiJihtto-

. .. . THCH118 MIJILJIOHIB. HiB, 8 t.IeTsepTHM -

:KJiacoM MiJib.HpJJ.iB.

MiJILJip,n; -

0JJ.HHHIJ.eIO rrepIIIOI'O KJiacy e OJJ.11HHIJ..H, JJ.pyroro TMC.H'll8, TpeTbOro -

MiJihiioH, lieTBepToro -

MiJib.HpJJ..

~06 rrpOtIHT8TH t.IHCJIO, .HKe MiCTHTb JJ.Ba tIH 6iJihllle KJiaciB,

:Horo 38IIHC poa611Bal0Tb Ha KJiaCM,

Ha3HB810Tb t.IHCJIO

KO)KHOI'O

KJiacy

HanpHKJia.n;, 'lIHCJIO

206 923 740 005

1 Ha3BY

IIOTiM KJl8CY.

qnT8eTbCSI T8K:

iJBiCllti LUiCmb .MiJtbJlp8i8 aea'antC011l iJaaih.Ji.R.fflb mpu . . ' .htl.flbllOHU ClMCOln copoK mUCJl'l n Jllnb • ~

.HKIJ..\O

6iJiblIIMM

b -

H8TypaJibHi 1111CJI8, TO

BiJJ. tIMCJia

BB8maeThCSI

SIKIJ..\0 BOHO 3H8XOJl.HTbC.H

HaTypaJihHOMY p.HJJ.i t.IHCeJI crrpaBa Bill. lJHCJia

Alie

H8TypaJibHi 1IHCJI8 JierKO rropiBHIOB8TH aa ix 3aIIHCaMH.

IJ.bOMY paai rropiBHSIHHSI a.n;iifCHIOIOTb 38 KiJihKiCTIO

poap.HJJ.iB 860 aa BeJIHtIHHOIO BHI.Qoro poap.HJJ.Y qnceJI. HaTypaJihHe lJHCJio BHKOpHCTOByeThCSI He TiJihKH JJ.JI.H Jiiqfin rrpe.n;MeTin, a

JJ.JI.H xapaKTepHCTMKH nop.HJl.KY

rrpeJJ.MeTiB. Ilop.HJJ.KOBi Ta I<iJihKiCHi l.U1CJia 3B, SI38Hi Mim co6oro.

HarrpH.KJiaJJ., •

SIKI.QO

• u

JiiqHTH

rrpeJJ.MeT11

nop.HJJ.KY 1 OCTaHHlH 3 HHX BOCbMHH, TO u.e 03Ha11ae, I.QO

BCbOl'O rrpe.n;MeTlB BlClM.

BEJilf1IMHl1. METPMqHA CMCTEMA MIP KomuoMy JJ.OBOJJ.HJIOcsi BM Mi p10B8TH JJ.OBmHHY, rrJio~y, Bi.n;Jii1IYB8TH

1 1ac,

P03B, SI3YB8Tl1 38JJ.aqi Ha IIIBHJJ.KiCTb,

o6t.IHCJllOB8Tli BRpTiCTb TOBapy • .noamHHa, IlJIOIJ..\8, Maca,

IIIBlfJl.KlCTb, lJ8C, BapTlCTb -

152

yce

I~e

BeJIHqliHH.

BeJIJ-P.IHHn MaIOTh neBHi BJiaCTHBOCTi.

y,ll,:h-5.IKi BeJIH-

qHHH O,ll,HOrO po,ll,y a6o piBHi, a6o O,ll,Ha MeHllla aa iHmy. BeJIHl.IlfHH O,ll,HOro po,ll,y MOmHa ,ll,O,ll,aBaTM, i B peayJihTaTi 6y,ll,e BeJIHl.JHHa Toro caMoro po,ll,y. )];JI.f.1 BeJIJPIHH BH3HaqaIOTb TaKom ,ll,il Bi,ll,HiMaHH.f.I, MHOmeHH.f.I i

.n;i-

JieHH.f.I. IlopiBHIOIOl.!H 0,ZJ;HOpi.n;Hi BeJIHl.IHHH, MO.mHa ,n;iaHaTHC.f.I, pi Bui BOHM q11 Hi. 11(06 M3TH 6iJiblll T0 1IHHM peay JlbTaT nopiBH.HHH.H, BeJIHlIHHH Tpe6a BHMip.f.ITH. BHMip10-

B8HH5.I TIOJI.f.lrae B nopIBH.f.IHHl ,ll,8H01 BeJII-PIHHH 3 .n;e.f.IKOIO BeJIMl.!HHOIO

Toro

caMoro

pO,ll,Y,

.HKY

npHMII.HTO ..

OJ];HHH~IO.

6iJiblllOCTi Kpalu CBiTy YTBep,ll,HJiaC.H

cucmeMa Mip. CHCTeMi e

M.empU'lHU

OcHOBHOIO o,n;HHHIJ.eIO ,ll,OBJKHHH B

.1J'lenip -

u;ill:

O,ll,Ha copoKaMiJihHOHHa TiaCTHHa

,ll,OBmllHH aeMHOro MepH;:i;iaHa, .HKHH npOXO,ll,HTb l.Jepe3 Ilapn.m. Ii-uni MipH ,ll,OBmHHH ,n;icTaJIH Ha3BH Bi,ll, JiaTHHChKMX i rpeU.bKHX lJHCJiiBHHKiB. JiaTHHCbKi l.JHCJiiBHHKH

( 8el{U, can mu, ..ltiJLi)

38CTOCOBYIOTbC.H ,ll,Jl.H Il03Hff1IeHH.H

OJ];:HHH~b, MeHIIIHX Bi,ll, OCHOBHOl, a

ze1enio, KiJLO) -

rpe~hKi (8e1ea,

6iJihlllHX Bi,ll, OCHOBHOl.

Poar JIHHh Ta6JIHU.IO JiiHiMHHX MeTpM"llHHX Mip.

Mi pH

MeTp

,lI;en.11MeTp

CaHTMMeTp

MiJJiMeTp

1000

10 000

100 000

1000 000

100

1000

,lI;en.11MeTp

1 -10

100

CaHTHMeTp

1 100

-1

1 100

AOB>KHHH l(iJJoMeTp MeTp

MiJJiMeTp

1000

Ilo.HCHH, HK KOpHCTyBaTHC.H Ta6JIHI~eIO. 3ttall,ll,II 38 Ta6JIHIJ.eIO, CKiJibKH MiJiiMeTpiB B 0,ll,HOMY ,ll,eIJ.HMeTpi.

153

KpiM MeTpa, y MeTpM'lHiil cHcTeMi 6yJin ncTaHOBJieHi

1.Qe 'raKl O,ZUIHHIJ.l:

ap -

IIJIOl.Qa KBa,n;llaTa, ,ll;OBiKRHa

CTOPOHH .fiKOrO ,n;opiBHIOe KiCTb pi,n;RH

Ky6a

Jlimp -

o6'eM

MiCT-

CHIIycIHX peqoBHH, 1.QO ,Z:\OpiBHIOe o6'eMy

CTOpOHOIO (pe6poM) 38B)\0B)KKI1

1 10

zpa.M -

Maca qncToi so,n;H, 1.QO aaiiMae o6'eM Ky6a a pe6poM

,ZJ;OB:>KlfHOlO - - M .

100

CTBopeHHH MeTpnqttoi cHcTeMH Mip e BeJIHKHM ,n;ocsrHeHH.HM. 11o6y,n;oBaHa aa ,Z:\eC.HTKOBHM rrpHHU.MIIOM, BOHa Ha6yJia BeJIHKOro IIOillHpeHH.H.

,IJ;O,ll;ABAHHH I BI,ll;HIMAHHH PoarJIHHeMo TaKy rro,n;iro: 6iJii Ta qepBOHi TpOHH,n;11 o6'e,n;HaJIH y 6yKeT.

IJ;bOMy paai Bi,l.\6yJIOC.H o6'e,n;HaHH.H

,ZJ;BOX MHO)KHH B o,n;Hy HOBY MHO)KHHY, .HKY H83HBaIOTb cyMOIO ,Z:\8HIIX MHOmllH. ~e B ,n;aBHi qacH rrepe,Z:\ JllO,Z:\MHOIO nocTaJia aa,n;a't.la, HK nepe,n;6alJHTH t.inceJihHiCTh CYMH ,Z:\BOX 1 111 KiJibKOX MHOmHH' .HK~O Bi)lOMi 'CJMCeJihHOCTi MHOmllH-,ZJ;O,Z:\aHKiB. Terrep MH 3HaeMo, :ui;o IJ..H aa,n;aqa poaB' .HayeThC.H ,Z:\iero

iJoiJaBa1t1-lR.

,l(i.H ,Z:\O,ZJ;aBaHH.H HaTypaJihHHX "llMCeJI aaBiK,Z:\H MOmJill-

. rr1,n;rrop.H,Z:\KOBaHa .

Ba I

rrepecTaBHOMY Ta CIIOJIY't.JHOMY

38KOHaM.

IlepecTanu11ii aaKon. Cy.Ma ne 3Mi1t10£mbcR eiiJ 3.1rzinu ~iicf.'1b

iJooanKiB.

a+b= b+a

+ 130 = 130 + 23

CnoJiyqu11ii aaKou. Cy.Ma ne 3.JtiH10embCR, RKU{O 6yiJbaKy zpyny iJoiJaHKiB 3a.1tiiHumu "ix cy.M.010.

a + b + c = a + (b + c) 3

rrepecTaBHOrO

apo6HTH BHCHOBOK, ~o

KiB i"x

.Att.OJICHa

RKU.At 'lUftO.M.•

15·i

+ 13 + 4 7 = 5 + (13 + 4 7)

CIIOJiyqttoro

38KOIIiB

MOmHa

npu iJoiJaBaH1ti KiJlbKOX iJoiJau nepecniaeJtamu i 6pamu B iJy:HCKu 6yiJb-

3MiCT Ail BiAHiMaHHH p03KpIIeMO Ha 38A8tti. 3 a A a ti a. Y xnontIHKa 6yno 12 }>JioMacTepis. 3 c}>JIOMacTepR BiH A8B ApyroBi. CKiJihKH q>JioMacTepiB 3aJIHIIIHJIOC.H y XJIQil'lil1Ka? 3a)J;al1a poan'513yeThC.H Aie10 BiAHiMaHH.H: 12 - 3 = 9. Konn APYr noBepIIe xnonl:JHKY cpnoMacTepH, TO ix 3Hoey cTaHe 12. ToMy KamyTh, Il\O iJiR aiiJui.MaHHR

e 06epneno10 iJo iJfi iJoiJaBa1t1tR. BiiJuiMaHHJl.lu. ua3uBa£mbca iJia, 3a iJono.MozoKJ .RKO°i .Ja cy.Jlto10 iJBox iJoiJanKiB i oiJnuAt 3 nux 3HaxoiJamb iJpyzuu iJoiJano1e.

y MHO:>K11Hi HaTypaJihHHX quceJI AiH BiAHiMaHH.fl MO)KJil1Ba TOAi, KOJIH BiA'CMHHK MeHllJHH a6o AOPiBHIOe 3MeHIIIyBaHOMY. BnacTHBOCTi piaHH~i noB '.H3aHi a piaHHMH crroco6aMH o61:Jl1CJieHh T8Kl1X BHpaain:

a - (b + c), (a + b) - c,

a + (b - c), a - (b - c).

IlepmHH crroci6 noJI.Hrae B aacTocyaaHHi npasuna IlOP.H'AKY BIIKOH3HHH ,nili y BHpa3aX 3 AYmKaMH. ,D;pyrHH cnoci6 cpopMy JIIOeThCH y BurJI.H,ni cneu.iaJibHHX npaBHJI. HarrpMKJia)J;, AJI.H rrepmoro s11paay npaBH. . JIO BIAHIM8HHH cyMH BIA tJHCJia TaKe:

m06

eio ttUCJlU BiiJnamu cyJw.y UBOX l/.UCe.!l, aocmamrtho noc1tiiJoeno eiiJnamu KDJICHUil iJoiJanoK OKpeM O.

,ll;o oco6JIHBHX BHilaAKiB ,niii AO,naBaHH.H i BiAHiMaHH.H HaJiemaTh TaKi:

a + O= a a - O= a

O+ a = a a - a=O

0+0=0 o ~ o = o

Bnna,nKH .noAaBaHH.H i ai,nHiMaHHH no)J;iJI.HIOTh Ha Ta6JIHtIHi :H noaaTa6JIH-CIHi. Pe3y JihTaT11 Ta6nn-c1HHX ,ni:H Tpe6a 3H8TH HanaM' HTb. 11oaaTa6JIHtUii o6tIHCJieHHSI (ycni l:IH nnchMOBi) BHKOHYIOTh aa neBHHMH npaB11JiaMH, cn11pa10qHCb Ha aaKOHH Ta BJI8CTHBOCTi ,niii. 0CHOBHHM npHiiOMOM e npHHOM nopo3pH;:i;Horo AOAaBaHH.H 1:!11 . . Bl;:J;HIM8HHH.

155

MHOJKEHHH

3a ,D;OTIOMOroro ,n;ii MHOmeHHSI 3H8XO,D;.H'Jf> ,n;o6yTOK ,D;BOX 'tlHCeJI. IlOHSITTSI ,n;o6yTKY 03Ha'tlal0Th y TaKHH cnoci6.

µ o6ymKOJlf. HamypaJLbHUX 1lUCeJL a i b Hll3{J,Ba10mb iJe.RKe HaniypallbHe 1lUCJto a •b, .RKe .1aiJoBOJlb1t.R€ niaKi BU.M.ozu: l)a.·b=a+a+a+a+ ••• +a; \..

2) .HK~O 3) .HK~O

OT.me,

b ,n;o,n;aHKiB b = 1, TO a · 1 = a; b = 0, TO a ·0 = 0.

noMHOmHTH HaTypaJihHe l!HCJIO

panhHe qHcJio

Ha HaTy-

~ 03Haqae aHaMTH cyMy qoTHphox

7: 7·4=7+7+7+7.

,n;o,n;aHKiB, K0'1<HHM 3 .HKHX 'AOPiBHIO€

IIepeMHomaTH MOmHa 6y,n;h-HKi HaTypaJihHi 'tlHCJia, T06TO

'AiH

MHOmeHHH

aasm,n;H

M0'1<JIMBa.

,ll;JI.H

'Ail

MHOmeHHSI MaIOTh Mic~e nepecTaBHHH, CilOJiyqHJIH

p03IlO,ZJ;iJihHHH 3aKOHH.

IlepecTaBHHH 33I~OH. /1, o6y moK 1-te 3.M.illHJe mbCR Bio 3.MiHU MiCl{b .1ltllO:JIC1lUKiB.

a·b=b·a

3·285=285·3 CnoJIY'IHHH aaKoH. l(o6ymoK ue 3JitiH10embcR., .R.Kiu,o 6yiJb-sucy zpyny MHOJICHUKiB, U{O cmo.Rmb nopR.iJ, 3a.Minumu "ix iJo6ymKOM.

a ·b ·c =a· (b ·c)

4 ·25 ·2 ·50 = (4 ·25) ·(2 ·50)

nepecTaBHOrO

CilOJIY'llHOro

aaKOHiB

MOmHa

apo6HTM BHCHOBOK, ~o

B iJo6ym1Cy 1CiJlbKOX .1lf.1lOJICHUKi6 lX .M.O:JICltll nepecnlll(:JJ/RmU i 6pa1nu B ay:JICKU 6yiJb-JtKUJlt 'lU llO.M..

25·6·15·8·100 = (25 ·8) . (15 ·6) · 100 Poano,a;inLHHii aaKOH. /1,o6ymoK cyM.u 1ciJtbKOX ttucell Ha 6yiJb-RKe 1lUCJlO iJopiBH10€ cy.Mi iJo6ymKiB KOJICllOZO aoiJallKll llU fie 1lUCJlO. (a+ b + c) · k =a ·k + b ·k + c ·k

(300 + 80 + 5)·8

156

300·8 + 80·8 + 5·8

.HK~O a

> b' TO

npaBHJibH8 piBHiCTh c • (a

b) = c . a - c. b,

. .

.HKa BHpa.mae poano,niJibHIIH 38KOH MHOmeHH.H w.o.no Bl'AH1M8HH.H.

27. (5408 - 907)

27 ·5408 - 27 ·907

o,nHO~HcppOBHX qJlceJI YTBOplOIOTh Ta6-

,D;o6yTKll JIH~IO

MHO.iKeHH.H.

06 1 IHCJieHH.H (ycHe i

IlHChMOBe) .no6yTKiB 6araTo-

~Mc}lpOBHX lJHCeJI Ha o,nHO~McppoBe

6araTO~MCllPOBe

qJlCJIO CilHpaeTbC.H Ha Ta6JIH~i MHOmeHHSI Ta 3aKOHH

MHO.iKeHH.H 1 .no,n;aBaHH.H. ,D;IJIEHH.H

HKu,o a i b - HamypaJLbHi 11ucJta a > b ( a6o a= b ), mo JCa:»eymb, U{O a iJiJLUmbc.H. Ha b HaijiJLo, RICU{O icHye HamypaJlbHe 1lUCJlO c, iJo6ymo1C JllCOZO Ha b iJopiBHIO€ a. a= c·b OmJ1Ce, iJiJteHHR e iJie10, aa iJonoJttozo10 RKoi· aa iJo6ymKOM iJeox ..WHOJICHUKiB i oiJHU.!ft i3 l{UX .MHOJICHUKiB 3HaxoiJamb iJpyzuu JJtnoJICHUK • .HK~O X

= 50: 5. HaTypaJibHe qMcJio a

·5

By,n;h-HKe

50,

TO X

)J;iJIHThC.H Ha

i caMe

Ha ce6e.

a: 1 =a

a: a= 1

Ilo,a;iJIHTH ua HYJIL ueMomJIHBO! BamJIMBi TaKi BJiaCTHBOCTi qacTKH.

m06

noiJiJLumu llUCJlO Ha iJo6ymolC OBOX 'lUCeJl, ~tOJICHa noiJiJLumu ilozo Ha ooull i3 MHO:JICHUKiB i anau.iJeHuil pe3yJlbmam noiJiJLUmU HU iJpyzuu MHOJICHUH:.

150: (3 ·5) = 150: 3: 5 = 50: 5 = 10 2) I1( 06 noiJiJtumu cyJtty ttuceJt na iJaHe ttucJLo, iJocumb noiJiJtumu KO:JICHUU iJoiJaHOK HU ije 1lUCJl0 i ymBOpeHi ttacmKu iJoiJamu.

(18

+ 54) : 6 =

18 : 6

+ 54 : 6 = 3 + 9 = 12

3) H Ku,o KOJICHuu. iJooanoK iJiJlumbca na iJeaKe ttucJto, mo i cy.,;~ia iJiJLumbcR Ha qe 1lUCJlo.

24 AiJIHTbCSI Ha 4, 32 (24 + 32) ,n;iJIHTbCH Ha 4.

.n;iJIHThCSI Ha

OTJKe,

cyMa

,ll;iJieHH.H o,u;Horo HaTypaJihHoro lJ.HCJia Ha iHrne 6ea

OCTff'll He 3aBm,ZI;H MO.iKJIHBe' a ,ll;lJieHH.H 3 OCTac.iero MO.iKJlllBe 38B:>l<,l];l1.

50 : 6 = 8 qHCJIO HH

50 Ha

(OCT.

8 H83HBaeThC.H uenOBHOIO 6, a lJ.HCJIO 2 - ocma11.e10.

2) 1l.UCmKOIO

Bi,D; .n;iJieH-

Bnna.zi;Kn .n;ineHHH TaKO.iK no.n;inHIOThCSI Ha Ta6JIHlJ.Hi

no3aTa6JIHlJ.Hi. Ta6JIHIJ..H AiJieHHH CKJia,n;aeThCH Ha ocHoBi Ta6JIHUi MHOmeHHH, aJie

Tpe6a 3HaTM HarraM'HTb.

IIoaaTa6JIHlJ.Hi BHil8)l;KH .n;iJieHHSI BHKOHYIOTb Ha OCHOBi BJI8CTHBOCTeii tJ8CTKH i aaKOHiB iHIIIHX apHC}lMeTH'4Hl1X

. ..,

,u;111.

KYJUI

npuaMa

KOHYC

3pi38HHll KOHyC

apiaaaa rripaMi.lia

O,D;HHHU,I ]lOBJKHHH:

40 089 KM

-=::::::::''--7

1CM = 10 MM 1,UM = 10 CM 1M = 10,nM = 100cM 1 KM = 1000 :\1

O]lHHHIJ;I IIJIOII.1;1: 1 1 1 1 1 1

1Kr = 1000 r 100 Kr= 1 ~ 1000 Kr = 10 ~ = 1 T

ll.

15 ,l.J;M

20 r

100 MM 2 ,ll;l'vl 2 = 100 CM 2 M2 = 100 ,nM 2 a= 100 M2 ra = 10 000 M 2 KM 2 = 1 000 000 =

O]lHHHU,I MACH:

50M

CM 2

0,lllIHHI.1,1 "lJACY:

1 XB = 60 C 1 roJJ. = 60 xs 1 ,11;06a = 24 ro,11; 1 piK = 12 Mic. 1 CT.= 100 p.

18M:

Poar1u1Hb MaJIIOHKH, 3Haii,ZJ;H rrpllKJla)J.H