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TOPH KAAC
1
. J
Ynpa>kHumeAHama mempagka "y.,a ce Da YMHO)l(aBaM H lleJlR "
e ogo6peHa om MUHucmepcmBomo Ha o6pa30BaHuemo, Haykama u
meXHoAoeuume c npomokoA N~ 6 om 02. 12. 1994 e.
Y"B
ce
aB YMHO)f(BBBM H aeJlR
Ha ........ ... ....... .... ........ .. ......... .
om ..... ...................... .. ..... kAac
Y4uAuLUe .............................. .
,
ttK 3..ulIliMllio IltlN
Da, maka e. Ho a3 LUe 6u 3a6ega caMO go 2paguHama Ha 3aMbka. A 6bmpe mpR66a ga npogbA>kume caMU. AHU, 6RPHO AU e, 4e HaO-AecHO LUe ce HaY4UM ga YMHo>ka6aMe U geAuM, ako omugeM 6 3aMbka Ha 36e3g06poe~a?
L
HRkbge, koO 3HaO kbge komeHua >ku8eJ\u g8e. Ho CbC J\anu u onawku c6uJ\u ce 8egHb>k IoHawku. 6e3 o6a4e ga 6poumel Ka>keme kOJ\ko ca ywume?'
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/ / JI " , ~/ I ~.~1~:- l tfJ___ W~J , : " rf::====j'{l I
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2
=
4
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= VMHO)l(CHHC C 2
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-足
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0
At
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--~~---
TOH40, npogbJ\>ku ga 3aka48aw no peg! Ako npa8uJ\Ho 3a'ka4uM kbpnume u pewuM 3aga4ume, owe gHec we mpb2HeM kbM~_ '"'"~ 3aMbka.
= 2
1
I
I I
\
' \
3a ga BAe3eme B apaguHama Ha 3aMbka, Hanuweme kOAko 4epewku e UMaAO Ha Bceku kAOH omgfl~HO. Te ca 6UAU mOAkoBa, kOAkomo Ha kAOHa omMIBo U~~--......
•ge
e.
e Hagnuweme u ma6eA:k~~~~~~~~ Ha uBemfima. """A~~
Iku iawku. le! llume?
I
/1
I ~/ { ~
~ I
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I I
\
I \
,
I
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Vnpil}I(HeHHSI 3a YMHO)f(eHHe c
2
I
3a ga 6Ae3eme
6 3aMbka, 6ceku mpR66a
npa6uAHo ga u36epe 2 3HaMeHa.
BHuMa6aOme! To6a, koemo e
HanucaHO Ha 3HaMemo omAR60, ga
6bge pa6Ho Ha 4UCAomo 6bPXY
3HaMemo omgRcHo. CAeg kamo
npecMemHeme, ou6ememe
3HaMeHama no g600ku .
.QYMama nbTEKA UMa 0 epu4ku. BeRka epu4ka UMa 0 6yk6u. KOAko ea 6yk6ume? 6pORm UM e HanueaH Ha eguH om kAlo406eme. OmkpuOme 20.
.2 = 2 2.2 =4 3.2= 6 4 . 2= 8 5 . 2 = 10
6 . 2 = 12 7 . 2 = 14 8 . 2 = 16
9 . 2= 18 IIJ........
1
.2=
0.2=4 3.0= 6 4.2 = 8 .2= 6.0=
10
12
.2= 16 .0= 18 11---1----' •
VnpCl)KHCHMII 3a OTKpMoaHC Ha HCM38C(''TCH MHO)l(HTCA
0
=
2
3
= 9
7
3
= 2
4
3
=
6
3
YMHO)l(eHllle c
= 3
1
1
E,,,ame HaCaM, HO 2J\egaOme 4UCJ\ama, Kou om HanucaHume npou3足 6egeHus:l ca om ma6J\ullama 3a YMHo>keHue c 3? CaMo me3U cku ca go6pe 3ako6aHu, Cmbn6aOme 6bPXY
5 8
KOJ\ko nog Mocma?
I ' 13 1=
6mopa u I
KHwkkume Henpe6poeHu ca caMo nogpegeHu.
BMecmo mu ga au 6pouw, Mo>kew ga au YMHO>kUW.
.u06pe gowl\u 6 3aMbka Ha 4ucl\amal 3ag ma3U 6u61\uomeka UMa maOHa 6pama. Ho ms:l 1~___-w..41\~e ce om60pu, ako 6egHaa Hanuweme kOl\ko ca kHuaume Ha 6ceku """~IIIl::t,. pacpm.
rn
CbCTE3AHIf1E
C KOCTEHYPKIf1
Ha kOl\ko caHmu足
Mempa egHa om gpyaa
ca nbp6ama u 4em6bp足
mama kocmeHypka,
ako 3Haew, 4e 6CU4ku
me ce g6wkam Ha pa3足 CmOs:lHUe om no 3 CM.?
1 3 '1 . 13 1=
f
3anuwu kak60 e pa3CmOs:lHUemO Me>kgy kocmeHypkume: 6mopa u 4em6bpma nbP6a u 4em6bpma mpema u 4em6bpma
I 'I
1
1
1
1
1
1
B Hagnuca UMa 21
6ykBu, no 3 Ha Bceku kaMbk .
KOAko ca kaMbHume B Hagnuca?
1211
1
I : 13 = I .ll>kyg>kemo lUe u3Bagu om nell.\ma 14 xMI6a . TpR6Ba ga au pa3geAu 3a 2 gHU no paBHo. KOAko xAR6a lUe cepBupa gHec?
3a mopmume UMa 18 4epewu.
C mRX ykpacu 2 mopmu kamo .ll>kyg>kemama ll.\e eAo>kam
au pa3geAuw no paBHo. nOAoBuHama ROua B 6aHuua足
ma , a oemaHaAume ll.\e eBa足 pRm. KOAko ROua ll.\e eBapRm?
I I I I I I
npeg g>kyg>kemo UMa 27 pe3eH4ema I\UMOH. nOMoaHU My ga au pa3g9J\U no paBHo 3a mpume Maeu .
ACI\CHHC C
2H3
I
no kOAko uBemR tUe noemaBu g>kyg>kemo BbB BeRka Ba3a, ako au pa3g9J\U no paBHo? - r - - ,. . - - ,. - - - ,. . . . - - , . . . - - - . ,
""--1
'pu geua HU am Ha aocmu. NIX cma6aMe 15 gywu 3a 06Ag.
EgHO g>l<yg>l<e naAU mpu cBewu. KOAko g>l<yg>l<ema ca 3anaAUAU cBewume B mpane3apuRma?
Wecm g>l<yg>l<ema we nogpe>l<gam Macume. KOAko g>l<yg>l<ema we nogpegRm egHa Maca? Ha egHa om nokpuBkume e u36pogupaH omaoBopbm.
nOAOBuHama g>l<yg>l<ema ca c 4epBeHu wanku. KOAko ca CbC 3eAeHu?
I II I I I
, llBeg>l<yg>l<emawe m16 4UHUU B mpane3apuRma. no kOA ko mpR6Ba ga npeHece BCRko?
I I I I I I I ina U4e cAo>l<a m RQua B 6aHuua ~aAume U4e cBa Qua U4e cBapRm?
ll>l<yg>l<emama U meXHume aocmu we cegHam Ha 3 Macu no paBHo. no kOAko cmOAa mpR6Bam 3a BCRka Maca? Ha egHa om nokpuBkume e u36po gupaH omaoBopbm. Ha kOR?
~6bAkume ca
21 u g>l<yg>l<emo mpR6Ba ga au pa3geAu no paBHo B mpume cppykmuepu. no kOAko R6bAku we CAO>l<U BbB BCRka?
~
3BbH4emama no wan kume Ha g>l<yg>l<emama ca 3AamHU. cpe6bPHu u Om g>l<yg>l<emama CbC 3eAeHU 6POH30Bu no paBeH 6poo. me wanku nOAoBuHama ca C04U npe6poo 3BbH4emama. Aa. KOAko om mRX uMam o4uAa? KOAko ca 3AamHl:.lme?
I I I I
I I
I I I I I I U4e nocmaBu Rka Ba3a, ako au
Aet\eHHe (2 H 3
I
I
I I I
I
I
Om g>l<yg>l<emama c OYU Aa nOAoBuHama ca kbCOaAegu , a gpyaume UMam gaAekoaAegcmBo. KOAko g>l<yg>l<ema uuam gaAekoaAegcmBo?
I I I I I I I I I I I I I
A3 nbk aomBA MHoao nO-AeCHo om g>kyg>kemama. O~ BCU4ko CJ\aaaM no 4 kUJ\oapaMa, HO Hukoaa He 3HaM kOJ\ko AgeHe l.l.\e ce nOJ\y4u. L-1 Bce He YJ\Y4BaM kOA meHg>kepa ga B3eMa. Ule MU nOMoaH9W J\U?
Ha 2 pa<j>ma
leA-e, AyK, 6ofi, 'lyWKU, opU3, Kapm(}g;u
=
2
Ako cna3Baw Aomo Ha 6poel.\a, Hanu ko nbmu l.l.\e IlOHegeAHuk ----足
=
3
IlOHeg8AHUk u
---足
n~g8AHUk,
=
1
=
2
8mopHUk
nOH8g8A 48m8~mbk,
= 4 0
A np83 npOA8mHam8 10 gHU?
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa. no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060?
.-----.--....--r--"1.........---r--,.
6paWHO - 9 nakema Mopko6u - 5 mop6u s:l6bAku - 6 mop6u 3axap - 8 nakema
Peuenma N2 2 Kapmoffjll, fiofi It Opll3
I I I
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom.
KOAko ca kOMnomume?
~~I~I~I
~I~II~I~I~·
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR
KOAko ca 6ypkaHume c mYPwuR?
~II~I~~I~I I~I~I~I~I~I~I _ KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060? I
I
,I
1
I
I
I
1
1
Ako cna36aw npa6u Aomo Ha 36e3go 6poeua, Hanuwu kOA ko nbmu !..Ue Rgew 6:
4 = 4 1 -----------+-+---t---+--+--+---4
nOHegeAHuk
2
noH6geAHuk u 6mopHuk
=
------------+-f---+---+-+--+-........-4
nOHegeAHuk, 6mopHuk u cpRga
-----------+-+---+---+--+--+---4
nOHegeAHuk , 6mopl-luk, cpRga u 4em6~mbk _ _ _ _ _ _ _ -t --t --t --t -+ -+ --4 nn~'.nA"'Huk, 6mopHuk, cpRga, em6~mbk ~e.!!!.bL _ _ _ _ -I --+ --t --+ --+ --+ --4 nOHegeAl-luk, 6mopHuk, cpRga, 4em6~mbk, nembk ~cb6oma _ _ -f----,-+--+--+--+~I__-l nn~'~(]A"'l-Iuk , 6mopHuk, cpRga, L4EIrllBl.pmbk ~mbk,~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR, kORmo e 10 gl-lu? Vnpil)I(HeHHSl 3a YMHO)KeHHC C
4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka. no kOAko oaAegaAa UMa Ha Bceku ema~? BepHURm omaoBop e ckpum HRkbge. HaMepu ao . .
n
AHU MU 6ewe ka3aAa, 4e 6e3 ga 6POUM, Mo~eM ga .......'''路路emHeM kOAko cBe~u naARm g~yg~emama B 3aMbka BCRka Be4ep.
,
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu, nOAY4eHomo YMHo~ume no 3 U npu6aBume 50, ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka.
5
5
6
5
= = = = = =
3
5
= =
=
4
5 2
3
5
j
I
,
7 9 VMHO)l(eH ....e c
5
5
1 1 2
4
.
Ha ma3U kapma 36e3g06poe足 Ubm e Om6el\~3al\ 36e3gume, koumo e Ha61\loga6al\ npe3 Howma c mel\eckona cu. 3an04Hal\ ega au apynupa no 5, 3a ga au npecMemHe nO-I\eCHO. OnumaO u mu.
I I I I
geHuemo Ha 5 u 4 . nbmu, nOl\Y4eHomo 103 u npu6a6ume 50, Ie 6po~ Ha c6ewume
npo
=
5
2
=
1
0
3
=
1
5
5 =
2
0
5
. I
onbAHU CHamume 4UCAa
1
5
5
=
6
5
-
7 5 9 VMHO)l(eHHe c 5
1足
=
3
=
4
0
=
4
5
36e3g06poeUbm He e cnal\ URI\8 HOW. Ho kOl\ko MUHymu e al\eg8l\ npe3 mel\eckona? ~34UCI\U no gHe6Huka My.
II IIIII
OuBemu c >kbAmo me3U 3Be3gu, Ha koumo UMa BepHU omaoBopu. n03Ha AU koe e moBa cb3Be3gue? 3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku. Ho 3a egHa cuaHaAbm e 6UA HeAceH. nOMoaHU My ga omaamHe kak u3aAe>kga AuncBaLUama cpuaypka.
5.3-15
fr. t; .. . .,
")\,27
V
5.4-20
AS ¢ , .
V
A "'-------'
V >kumel\ume l-'136bH3eMHume ca om6eAA3al\U Ha 3eMAma c uuCPpu, koumo
2 7.3_ 1
¢
¢:
' * -¢2.3-8
3. ..
)KumeAume Ha gaAe4Hama nAaHema He npUI\U4am Ha 3eMHume. Te ca 03Ha4UI\U ce6e cu c uucppu, koumo ca npou3BegeHuA om ma6Auuama 3a YMHo>keHue c 5. Ou6emu au.
OnumaO oU.\e npecMemHu. HaO· 4acmHO cbomBen HaO-MaAkama n. nogpegu au no ( om HaO-aOMIMc HaO-MaAkal
nAaHema I YacmHO
I
~
no I
Hen"1rH~~~: ~ =-~
__
IOnumep 150 : 5 = I --------t-Mapc 130 : 5 = I - - - - - - ---i- 3eMR__ I~~: ~ ~ ...j _ _ BeHepa 35: 5 =
Macau
ca npou36egeHuA om ma6Auuama 3a YMHo>keHue c 3. Kou ca me?
5.2-10
-¢'
'.3•••
KOAko. e uHmepecHol Mo>ke nbk, kamo nopacHa, ga cmaHa acmpoHoM!
~
BpeMe e ga cu npunoMHuM, 4e koaamo B egHa 3aga4a UMa ck06u, nbpBo ce u3BbpwBa geQcmBue mo B ck06ume. Ako HAMa ck06u, nbpBo ce
u36bpwBam geocmBuAma YMHo>keHue u geAeHue.
Vnpa)I(HeHHR 3a YMHO>KeHHe c '1, 3, 4, H 5
npaBUAHO AU nogp' npoBepu! Ako peWl >kbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem. 3Haew AU
1. EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5. CBogbm ~ mo u 3Be3gume 6. n Ae"eHHe c 5
~Q
28
8
06SA cuaHaJ\U no m~x me3U HSAbm e 6UA maamHe kak laypka.
, MaHema He ca 03Ha"lUAU Ipou36egeHuR 損keHUe c 5.
OnumaO o~e ceaa. npecMemHu. HaO-MaAkomo 4acmHO cbomBemcmBa Ha HaO-MaAkama nAaHema. nogpegu au no aOAeMUHa om HaO-aOA~Mama go HaO-MaAkama.
n"aHema I 4acmHO
I
Nv no peg
Hen~H-l~~:~ =--1-足 IOnumeE...I.?~: ~ =-~
__
Map~ _I ~~: ~ ~~ _ _ 3eM~ _I~~: ~ =---1- _
Kamo u36bPWUW npeCMRmaHURma, ~e nOAY"lUW "IUCAO. To noka36a 3a kOAko Meceua 3eMRma ...B _e_H_ ep_a_...3_5_:_S_=....I._ _...... 06ukaAR OkOAO CAbHuemo.
)m6eAR3aAU u$pu, koumo ,6Auuama 3a
\f/
~?
- .0-足 / I "
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa?
npo6epu! Ako peLUUUJ 6RPHO kpbcmocAo6uuama, 6
>kbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama 12 nAaHema 6 CAbH4e6ama cucmeMa. Ho 6 3aga4ama me ca
caMO nem. 3HaeLU AU kOAko ca Ha 6poO nAaHemume?
1. EgHa om nocokume Ha c6ema 2. nocokama, 6 kORmo
3aAR36a CAbHuemo 3. EgUH om ce30Hume 4. nUAom Ha
CaMOAem 5. C60gbm Hag Hac, Ha koOmo 6u>kgaMe CAbHue足
mo U36e3gume 6. nmuuama, CMRmaHa 3a uap Ha He6emo.
AeAeHllle c 5
1
3
14 5 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Je"lu
I
M'bHU"4kume 4»eu om 3aM'bka c'b6upam 6uI\ku u au npeHacRm 8 mop6u"4ku no B apaMa.
I
KOAko 6UAku ca cb6pMU mpume cpeu 06LUO?
KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku? CAeg kamo u3cywam 6uAkume, cpeume au HacunBam BaOAeMU kHU>kHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama, Bceku nAuk cb6upa 7 mop6u4ku, KOAko apaMa cb6upa 1 nAuk? nonbAHU nponycHamume 4UCAa
1
6
2
6 4
6
5
= = = = :;::
~
= =
8 9
6
VMHO)l(CtUtc
= c6
, \
1
2
1
8
3
0 1 cyweHume
3 4 4
6
2
8
Cl>eume npoga6am
6uAku.
EgUH apaM cmpy6a 6
cmomuHku, Ako 3a
cympewHuR "480 cu
kynuw 4 apaMa, kOAko
~e mu cmpy6a moO?
I I I I I I I
Vnpa>KHCHMC la YMHO)l(C I
- -- - -- = = =C-=::"II'I
6060 e nonpaB~A BogonpoBoga 3a q>oHmaHa. Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao. nogcka>ku My. ToO e 3a mpb6ume, BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6.
I
~aCAm
6
mop6u~ku
I I I I
I I I I
9MU kHU>kHU
l1J\uko6e
I I I I
HRk oO >K uBee B kYAama Ha aaMbka. LUe HaY4Uw koo e moO, ako npaBuAHo pewuw aaga4ume. nOAY4eHomo 4UCAO we mu noka>Ke kOR no peg 6ykBa om a36ykama ga Hanuwew.
0 7+60:6=0 0 54:6=0 0 48: (30: 5) = ,0 0 9+48:6=0 0 18:6-2= 0 0 ,_-u 36 : 6 + 5=0 0
I
42:6+9=0
I'
TOH40 Mo>ke ga ce ka4u go kYAama, caMo ako npa6uAHo pewu aaga4ume. Lr1Ha4e cmbnaAama we ce cpymAm.
I I
opaH>k
. 36 : 4=
54: 6
=
AUAa6 .9: 3 =
,
.24 : 6 =
6 :6 =
1路 1 1=1 ,I
12: 6 = . ACt\C HIitC C 6
,.1 1=1 I
I+1 I 1= I
1 <l>eume ca nOpb4aAU Ha l\uAu
~----, 2 ga ouBemu gbaama. Ho ~---"""1 3 nbpBo
- -足 --I ------I
__----J
ga mpR6Ba 4 npecMemHe u3pa3ume. ~ nOMoaHu Q. Hanuwu cpell-'Y 7 BCRka UUQ>pa cbomBemHuR uBRm. A nOCAe au ouBemu. 44epBeHo
9
...
6 5
10 Mo>ke ga CS I go kYAama, ) ako npaBUAHo U 3aga4um e. ~e cmbnaAama :e cpymAm.
I I
opaH>k 36 : 4=
I
AUAaB 9 :3 =
I
3SASH 15 : 3=
I
cB. CUH 28 : 4=
I
___- - - , nOM08HU Ha g>kyg>kemama ga npscMemHam ueHume.
::=:::==:::::
A a3 mpR6Ba ga cspBupaM 2 cynu no 5 AsBa, 3 RcmUR no 4 AsBa, 3 4aR no 6 AsBa U 1 cAagoAsg om 9 AsBa.
\ \.\ \=\ \
\ \.\ \=\ \ \
\ \+\ \ \= I I I Vnp(\)I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c
L-I..1.-1. .L.+I .:.....1.I--L-~1+.. .1-\--L-...I_+.1-.1...L-I-~--,
2, 3, 4, 5,
lit
6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku. nycHaA BbB BCRka no 7 AeBa. KO Ako AeBa UMa B gBeme kacu4ku?
KoO AU cmou 3ag 6060? CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U,(e pa36epew. BCRko cAegBaU,(o 4UCAO e CbC 7 noBe4e om npeguwHomo.
49. 56. Q
V1MaA B g>ko6oBeme cu OLUe 28 AB. Cb6paA Bcu4kume napu B egHa kacu4ka. KOAko AeBa ca cmaHaAu?
+~
nonbAHU Hamume 4UCAa
1
7
2
7
3 7
6
7 7
8
7
= = =
G;>
.7 peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo, Koumo ca paBHu Ha omaoBopume.
,.
2
1
3+3.4=
:;
2
8
9-4.2=
= = = =
3
5
=
6
VMHO)l(eHMe ChC 7
4
9
2.6+4= 2.7+3.7足 4.7+5.7足
3
.ll>kyg>kemama ~ MeAHuu.ama n aoguHu. lile Hi kOAko om omaol
3a BCRka peg apu>kam 14 <l>eu <l>eu ce apwkam kowep?
6.7+7.7足 AeAeHMe (bC 7
r---------~------~~----------~~~~~~~~.
ToBa e B~mbPHama MeJ\HU14a Ha aaMbka. npeCMemHU UomkpuO koe om kpuJ\ama mp~66a ga ce nonpa6u. 0146emu eo.
G BCU4kume cu napu 6060 kynuJ\ "-_~ 7 6a<t>J\u . KOJ\ko cmpy6a egHa
6a<t>J\a?
-28
.7 npeCMemHU aume U oepagu MO meau YUcJ\a pxy aHaMemO, mo ca pa6HU Ha maoBopume.
.4
n>kyg>kemama ca nocmpouJ\u MeJ\HU14ama npegu MHoao aoguHu. W.e HaY4uw npegu kOJ\ko om oma060pa Ha 6~PHO peweHama aagaya.
21 : 7 14
+
9 . 7
+ +
23 6
=7 +
=3 +
23
=
31
6 = 18
21 : 7 = 35 : 7 = 5
+
63 : 7 = 63
+
9 = 72
B apaguHama aag MeJ\HU14ama ca kowepume Ha nyeJ\ume. Te ca 06wo 49 U ca 6 7 pegu14u. no kOJ\ko kowepa UMa 6b6 6c~ka pegu14a?
I I I I I I I
足
2=
. 4足 7
足 足
7. 7
..-
3.7 5
49 : 7
3a 6c~ka pegU14a ce apu>kam 14 <t>eu. KOJ\ko <t>eu ce apu>kam 3a eguH kowep?
I I I ACAeHHe CbC
7
CaMO egHa Bpama e omk'''04eHa. ToBa e Bpamama, Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO. Ako R omkpURm, AUAU, T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume. A mu we R om6eAe>kuw AU? Oapagu apewHume omaoBopu.
9.6==54 36: 4 == 9 9.3== 18 3.5==25 nog4epmaO apeWHume omao6opl
60 60 ce e U3xumpUA. 3an04 HaA e ga konae mYHeA nog cmeHama. TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma. 3a eguH geH u3konaBaA 3 Mempa. npecMemHu kOAk o gHU mpR6Ba ga pa60mu 5060?
VnpCl)I(HCHHSI 3a YMHO>KCHHC H AeAcHHc C
2, 3, 4, 5, 6 H
7
2
8
=
1 Ii
6
8
=
6
3
8
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5
8
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2 I 4
8
8
=
7
6
8
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4
4
8
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3
9
8
=
7
2
8
=
1
VMHO>KeHHe C 8
I
mkJ\104eHa. To6a e 3CU4ku 3aga4u ca kpURm, AUJ\u, TOH40 IR3am 6 apaguHama R om6eJ\e>kuw J\U? !o6opu.
'>---.1.
nog4epmaa apeWHume omao6opu
3Haew J\U, 4e koaamo n4eJ\ama "emu 6 kpba, mR cbo6U4a6a, 4e Hekmapbm e 6J\U30. A koaamo onuc6a oCMopka,
36e3go6poeUbm e omxJ\ynuJ\ egUH kowep. KOR om kUJ\uOkume ce pa3J\u4a6a om OCmaHaAUme? Ou6emu R.
2 '
8
=
1
2
6
8
=
6
4
3
8
=
2
4
5
,8
=
4
0
8
8
=
7
2
6
8
=
4
8
4
8
=
3
2
9
8
=
7
2
Ho
2
8
=
1
6
11 101
,
06ukHo6eHo om eguH kowep ce nOJ\y4a6am 121 . 181=
UMa
I I I kUJ\oapaMa Meg. U pekopgHu
go6u6u
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om
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BHUMal11 noaAegHu gBe CBuBaw m03U n noka3Ba koe 4UC Baw no 9, kamo ~ HagRcHo. OmaoBo npbcmume omARB noka3Bam gece"l gRCHO, noka3Ba CBumuRm He ce 6
T03U, koOmo e HapucyBaH B M03aOkama, U4e mu omkpue MaaURma Ha 4UCAomo 9. Ho mpR6Ba ga BHuMaBaw npu ou,BemRBaHemo.
TaM, kbgemo 4UCAomo ce geAu Ha 8, ou,Bemu CbC cBemAo CUHbO. A kbgemo He ce geAu Ha 8, ou,Beniu c kacpRBo.
Kou npou3BegeHufi ca BepHu?
9
9
=
9
1
4
9
=
3
6
2
9
1
9
7
9
= =
6 3
3
9
=
2
7
8
9
7
2
2
9
1
8
15
9
= = =
4
0
9
9
=
8 1
VMHU)I(CHMe c 9
BHUMameAHO
n02AegHu gBeme MU Pbu,e.
CBuBaw m03U npbCm, koOmo
noka3Ba koe 4UCAO w.e YMHo>ka足
Baw no 9, kamo 6pouw omMIBo
HagRcHo. Om20Bopbm e npeg me6.
npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuu,ume, a om足
gRCHO, noka3Bam eguHuu,ume.
CBumuRm npbcm.__.-li~::::'" He ce 6pou.
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume' B CAbH4e6ama cucmeMa? Ako He cu 3HaeA, ce2a 3anOMHU . Te ca 9.
onumaM!
[3U, HapucyBaH lwe mu omkpue UCAomo 9. Ho uMaBaw npu BaHemo.
:I\omo ce geAu Ha 8, CUHbO. A kbgemo oL\Beniu c ka蔵RBo. 1\0
Kou npou36egeHuR ca 6epHu?
=
9
1
9
3
6
2
9
7
9
3
9
8
9
= 1 9 = 6 3 = 2 7 = 7 2
2
9
5
9
= =
9
9
9
9
4
VMHO)l(CHHC C9
1
8
4
0
= 8
1
Ako pewuw' npaBuAHO 3aga4ama, w.e omkpuew Ha kOAko 20gUHU e Becko.
5.9-4.9= npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm, k02amo ce npu6upa B cBoRma kYAa.
3.9+8.9 足
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua, 3a ga cu Hagye 6aAoHa. Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9, 6MoHbm My we nOAemu. Ho ako UMa apewka, we u36yxHe. CnpaBUA AU ce e 6060?
~~
Oapagu BepHUR omaoBop.
BepHU AU CG paBeHcmBam.
30 - 3 = 3 .
70 - 7 = 7 .
4.9=40-足 50 - 41 = 1 . 36-4=4.
63-7=7.
8 .9=9.8 3.8=6.4
. ~~
AB Aa60pamopURma oe14a, 3a ga CU Hagye HanucaHume BbPXY :Aa ce geARm Ha 9, ~e nOAemu. Ho ako ~ a, U4e u36yxHe. pe e 6060?
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a. Ho XBbp4uAama lUe U3AemRm, aka omaoBopume BbPXY rTmX ca BepHu.
~ยงJ
omaoBop.
BepHU AU ca paBeHcmBama?
30 - 3 = 3 . 9 70 - 7 = 7 . 9 4.9=40-4 50 - 41 = 1 . 9 36 - 4 = 4 . 8 63-7 = 7.8 8.9=9.8 3.8=6.4
~~ Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c
8
H
9
.
<beume ca OpaaHU3UpaAU AOmapU R. Bceku 6uAem ne4eAU m03U npegMem, BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama.
npu3pakbm e 3aMbkauce 3aga4ama, U4e U4e ce cb6ygu
5 . 10 - 2 . 10
9
6
1
0
5
1
0
8
1
0
3
1
0
1
1
0
= = 7 = 8 = 3 = 1
5
1
0
2
1
4
=
npegu ga 3acnu, ' , Ha 3aMbka.
0 0 0
=
5
0
0
=
1
0
1
0
=
4
0
HMC
c 10
Hanuwu koO kakBo cne4eAU I\UAU ' Becko------------- TOH40 - - - - - - - - - - -
--- - --- -- - --
6060 - 5060 - - - - - - - - - - - -
ToO mu npUnOMH~ UMa cb6upaHe, U geAeHue U HRMa cl geOcmBuRma YMHC ck06u, nbpBo ce ck06ume. Aei\eHHe c 10
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10, nupaMugama HRMa ga ce cpymu . .llo6pe AU au e u36pal\ TOHYo?
~~ Oapagu BepHuR omaoBop.
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu . Ako pewuw BRPHO 3agayama, we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak.
5 . 10 - 2 . 10
=
npegu ga 3acnu , moO 06ukaAR BcuYku cmau Ha 3aMbka. npecMemHu kOAko ca cmaume.
(12 - 7) . 10 (ak60 cnSYSI\U
=
ToO mu npunoMHR, ye koaamo B egHa 3agaya UMa cb6upaHe , u3Ba>k g aHe, YMHo>keHue u gel\eHus u HRMa cko6u , nbpBo ce u3BbpwBam geOcmBuRma YMHo>keHue u geAeHue. Ako UMa cko6u , nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume.
W:: " Pewu 3aga4ume
5
1
1
1
= =
9
1
=
6
1
5
1
= =
5
TpA66a ga 3anOMHAI ToBa e MHoao Ba>kHO! Koaamo eguHuRm om MHo>kumei\ume e 0, mo u npou3BegeHuemo e O. 5.0=0.5=0 C 4UCAomo 0 He MoJke ga ce geAul 5 : 0 e HeBb3Mo>kHo geOcmBue.
@
7.2 + 3
7.(2+~
VMHO)KeHHe H AeAeHHC C
1
H
0
9
0
8
0
6
0
3
0
4
0
= = = = =
0 0 0
9:3-1=
6+6.0=
0 4
(6 + S) . ( Vnp(\)I(HeHHII 3a
I
Pewu 3aga4ume
5
1
=
1
1
=
9
1
=
6
1
5
1
= =
5
Sue o6ukOAuxme
Ako HRMa cko6u, nbP80 geAuM U YMHo)\(a8aMe, a nOCAe u38a)\(gaMe U cb6upaMe.
(HO! Koaamo 1eAume e 0, mo lemo e O. 5=0 ke g8 ce geAu!
IMO)\(HO
Je.
7.2+ 3 = 7 . (2 + 3) 9
0
=
0
,8 ,6
0
=
0
0
=
0
3
0 =
0
4
0
=
4
9 :3 -1
8.4+5.6=
-
35:5+2=
足
6 + 6.0= (6 + 6) . 0 = Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
= 70 : 10 = 7: 0 =
• 1.3=3 2.3=6 '3.3=9 4.3=12 5.3=15 6.3 = 18 7.3=21 8.3=24 9.3=27 10.3 =30 1.6=6
2.6 = 12 3.6=1 8
4.6=24 5.6=30 .6 .6=36
7.6=42 8.6=48 9.6=54 10.6=60
1.7=7 2.7=14 3.7=21 4.7=28 5.7=35 6.7=42 7.7 = 49 8.7=56 9.7=63 10.7=70
1.4=4 .2.4=8 3.4=12 4.4=16 5.4=20 6.4=24 7.4=28 8.4=32 9 .4=36 10 .4 =40
1.5=5 2.5=10 3.5=15 4 .5=20 5.5=25 6.5=30 7.5=35 8.5=40 9.5=45 10.5=50
1.10=10 2.10=20 3.10=30 4.10=40 5.10=50 6.10=60 7.10=70 8.10=80 9.10=90 0.10=1
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