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UNIT I Lesson 1: Place Value Up to Hundred Thousands In our decimal number system, the value of a digit depends on its place, or position, in the number. Each place has a value of 10 times the place to its right. A number in standard form is separated into groups of three digits using commas. Each of these groups is called a period.
EXPERIENCE A. Read each number. Write the place value and value of the first digit from the left. 1. 872 2. 5,064 3. 27, 234 4. 9, 105 5. 43, 726
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Write the place value and the value of the underlined digit. Example: 5,076 tens 70 6. 2, 708 2. 17, 1368. 31, 450 9. 52, 093 10. 75, 814
B. Write the number in standard form. 1. 3 thousands, 5 hundreds, 6 tens, 2 ones 2. 7 thousands, 0 hundreds, 4 tens, 6 ones 3. 2 ten thousands, 6 thousands, 4 hundreds, 8 tens, 0 ones 4. 6 ten thousands, 0 thousands, 5 hundreds, 0 tens, 0 ones 5. 5 ten thousands, 6 thousands, 0 hundreds, 8 tens, 0 ones Write the correct number for each number word. 6. four thousand, six hundred twelve 7. eight thousand, four hundred five 8. nine thousand, forty 9. seven thousand, six hundred nine 10. ten thousand, five hundred 11. fifteen thousand, four hundred seventy- seven. 12. twenty- nine thousand, one hundred five 13. forty thousand, eighty- one 14. fifty- three thousand, eighty- one 15. sixty- six thousand, nine hundred nine
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Lesson 2: Comparing and Ordering Numbers
When comparing two numbers, using a greater than (>) or less than (<) sign can help to order the numbers.
to always read the number sentence from left to right!
Different Ways to Compare Numbers Way 1 You can use a number line.
4,843 is to the right of 4,456 on the number line. So 4,843 > 4,456 Way 2 You can look at the place value. Begin at the greatest place value. Find where the digits are different.
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Compare the digits that are different, Write > or <.
Examples: 97 > 91
226 < 232
Say: "97 is greater than 91"
Say: "226 is less than 232"
1,116 > 1,108
44 < 72
Say: "1,116 is greater than 1,108"
Say: "44 is less than 72"
Hints : Think of the Less than sign ( < ) as looking like a tipped "L". & Young Ji International School/College
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The "mouth" of either sign always opens towards the GREATER NUMBER. 58
54
13
23
Remember: Always read the two numbers being compared from left to right, and the mouth of the sign always goes towards the larger number.
EXPERIENCE A. Compare each pair numbers. Write the symbol ><in theď&#x201A; .
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B. Circle the greatest number in each pair. 1. 375
357
6. 2, 242
2452
2. 408
480
7. 3, 065
3,506
3. 523
532
8. 4, 113
4,311
4. 616
606
9. 735
753
5. 1643
1, 634
10. 5621
5216
Write the number that will make each number sentence true. 1. 792 > ______
6. _______ < 4,573
2. 678 < ______
7. 8,110 > ______
3. 2, 075 > ______
8. ____ < 10, 653
4. 3, 172 < ______
9. 12, 563 > _______
5. ______ > 2, 452
10. 15, 100 < ______
Lesson 3: Rounding Off Numbers to the Nearest Ten Here are some points to remember in rounding off numbers to the nearest te. 1. If the ones digit is 5 or more, add 1 to the tens digit and change the ones digit to zero. a. 45 ----- 50
c. 156 ---- 160
b. 78 ----- 80 2. If the ones digit is less than 5, retain the tens digit and the change ones digit to zero. a. 53 ---- 50
c. 142 ---- 140
b. 74 --- 70
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EXPERIENCE 1. Use the number lines to help you answer each question. Write your answer on the blnk.
a. Is 42 nearer to 40 or 50? __________________ b. Is 46 nearer to 40 or 50? ___________________ c. Is 44 nearer to 40 or 50? ___________________ d. Is 48 nearer to 40 or 50? _____________________
a. Is 121 nearer to 120 or 130? _______________________ b. Is 123 nearer to 120 or 130? _______________________ c. Is 126 nearer to 120 or 130? _______________________ d. Is 128 nearer to 120 or 130? _______________________ B. Round off each number to the nearest ten. 1. 48
_______
2.72
_______
3. 66
_______
4. 85
_______
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5. 58
_______
6. 146
_______
7. 187
_______
8. 212
_______
9. 275
_______
10. 309
_______
C. Round off each amoun to the nearest ten pesos. Example: P256 ------- 260 1. P185 _________________
6. P465 ___________________
2. P348 _________________
7. P329 ___________________
3. P572 _________________ ______________________
8. P743
4. P291 _________________ ______________________
9. P868
5. P488 _________________ _____________________
10. P699
Lesson 4: Rounding Off Numbers to the Nearest Hundred Rules to remember in rounding off numbers to the nearest hundred. 1. If the tens digit is 5 or more, add 1 to the digit in the hundreds place. Change the order digits to the zero. 162 ------ 200
1,3760 ------- 1,400
2. If the tens digit is less than 5, retain the digit in hundreds place. Change the other digits to zero. 237 ---- 200 Young Ji International School/College
2716 ----- 2700 Page 10
EXPERIENCE A. Ring the number nearer to the number at the middle. 1.
2. 4.
3.
200 223 300
5.
300
400
600
385
478
615
400
500
700
6.
7.
8.
700
1,300
2,200
4,400
723
1285
2, 168
4,471
800
1400
2,300
4,500
9.
10. 3,500
5,100
3,490
5, 184
3,600
5,200
B. Round off each number to the nearest ten and hundred. Example. 748 Number 1. 627 2. 539 3. 808 4. 1,275 5. 1,416 6. 3,381 7. 4,565 8. 6,172 9. 8,246 10. 9,629
750 Nearest Ten
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700 Nearest Hundred
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C. Round off the following numbers to the indicated place value. 1. 527 (hundreds) ____________
6. 3,762 (hundreds) ____________
2. 2, 083 (tens)
7. 1,076 (hundreds) ____________
____________
3. 1,921 (hundreds) ___________
8. 2, 527 (tens) _____________
4. 946 (hundreds) ____________
9. 4, 194 (hundreds) ___________
5. 2, 738 (tens) ______________
10. 5,662 (hundreds) _________
Lesson 5: Ordinal Numbers Ordinal Numbers tell the position or place of a person or thing in a given order of arrangement To write ordinal numbers: Add st to 1 and other numbers ending in 1 after 20.. 21st, 31st, 41st, 51st Add nd to 2 and other numbers ending in 2 after 20. 22nd, 32nd, 42nd, 52nd Add rd to 3 and other numbers ending in 3 after 20. 23rd, 33rd, 43rd, 53rd Add th after the numbers 5, 6, 7 and others. 5th, 6th, 7th, 8th EXPERIENCE A. Circle the object that matches the ordinal number. Start from the upper left. Write the ordinal number for the encircled object. Start counting from the upper left.
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Write st, nd, rd, or th to make the given numbers ordinal. 1. 21 ________
6. 27 ______
2. 34 ________
7. 41 _______
3. 42 ________
8. 52 _______
4. 58 ________
9. 54 ______
5. 63 ________
10. 76 _______
Write each word in symbol. 11. seventeenth __________
16. Fifty- sixth__________
12. twenty- first __________ first__________
17. Seventy-
13. thirty- fourth __________ fourth__________
18. Forty-
14. forty- third__________
19. eighty- fifth__________
15. thirty- second__________
20. Sixty- sixth__________
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C. Write each number as ordinal numbers in two ways. Number Symbol 1. 13 2. 18 3. 22 4. 27 5. 35 6. 38 7. 46 8. 49 9. 52 10. 55 Lesson 6: Odd and Even Numbers
Word
EMPHASIZE ď ? A number is odd if the ones digit is: 1, 3, 5, 7 or 9 It cannot be arranged in pairs or grouped by twos. ď ? A number is even if the ones digit is : 0, 2, 4, 6, or 8 It can be arranged in pairs or grouped by twos. EXPERIENCE A. Complete the table. Number Can be arranged in pairs? 1. 9 NO 2. 12 3. 15 4. 18 5. 21 6. 24 7. 30 8. 35 9. 47 10. 50
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Odd or Even ODD
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B. Write the EVEN or ODD number that comes after or before each number.
Write the odd number that comes between the two numbers. 7. 21, ____, 25 11. 101, ____, 105 8. 33, ____, 37 12. 123, ____, 127 9. 47, ____, 51 13. 205, ____, 209 10. 69, ____, 73 14. 321, ____, 325 C. Answer the questions. 15. What are the even numbers between 127 and 140? ______________________________________________________________ 16. What are the odd numbers between 500 and 50? ________________________________________________________________ 17. What are the od numbers ending in 5 that are greater than 100 but less than 150?
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LESSON 7: ROMAN NUMERALS EMPHASIZE The Roman number System uses letters as symbols numbers. I= 1
X= 10
C= 100
V= 5
L= 50
D= 500
M= 1,000
Add if the letter of lesser value comes after he letter of greater value. XVI= 10 + 5 + 1= 16 DCX= 500 + 100 + 10= 60 Subtract if the letter of lesser value comes before a letter of greater value. LIX= 50 + (10- 1)= 50 + 9= 59 CXL= 100 + (50 â&#x20AC;&#x201C; 10)= 100 + 40= 140 EXPERIENCE A. Write the equivalent of Hindu- Arabic numeral. 1. VII= _____________
6. IV= ________________
2. IX= ______________
7. LV= _______________
3. XXIII= ____________
8. LIX= _______________
4. XXI= ____________
9. DCII= ________________
5. XLII= ____________
10. MCX= ________________
Write the following Hindu- Arabic numerals in Roman numerals. 11. 13= ________________ 16. 45= _________________ 12. 19= ________________ 17. 56= _________________ 13. 25= _______________ 18. 67= ________________ 14. 32= _______________ 19. 108= _______________ 15. 38= _______________ 20. 125= _______________
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B. Write the following in words in Roman Numerals. 1. thirty- five 2. forty- two 3. one hundred ten 4. fifty- five 5. one hundred forty- five 6. two hundred thirty 7. three hundred forty- three 8. four hundred twenty 9. fivehundres twenty- five 10. one thousand, three hundred six ADDING OF WHOLE NUMBERS Lesson 8: Properties of Addition The order in which the numbers are added does not change the sum is called the Commutative property of addition 12 + 23= 35 23 + 12= 35 The way in which the addends are grouped does not change the sum is called Associative property of addition. (10 + 12) +20= 10 + (12 + 20) 22 + 20= 10 + 32 42 + 42 The sum of any number and zero is that number. This is called the Identity property of addition. EXPERIENCE A. Write the property of addition shown in each question. 1. 10 + 30 = 30 + 10 _________________ 2. 0 + 75= 75 _________________ 3. (30 + 12) + 40= 30 + ( 12+ 40) _________________ 4. 60 + 40 = 40 + 60 _________________ Young Ji International School/College
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5. 56 + 0= 56
_________________
Fid the sum mentally 6. 0 + 8= ______________ 7. 12 + 0= _____________ 8. 0 + 18= _____________ 9. 23 + 0= _____________ 10. 0 + 35= ____________
11. 0 + 56= _______________ 12. 80 + 0= _______________ 13. 0 + 125= ______________ 14. 95 + 0= _______________ 15. 0 + 188= _____________
B. Group the addends that give a sum of ten, then add mentally. 1. 7 + 6 + 4= __________ 6. 3 + 6 + 4 + 5= ____________ 2. 9 + 5 + 5= __________ 7. 5 + 7 + 3 + 4= ____________ 3. 3 + 8 + 7= __________ 8. 6 + 2 + 8 + 3= ____________ 4. 8 + 9 + 2= __________ 9. 8 + 6 + 4 + 2= ____________ 5. 2 + 7 + 8= __________ 10. 7 + 5 + 3 + 5= ___________ Find the sum. 1. 23 + 12= _______ 2. 18 + 30= _______ 3. 45 + 20= _______ 4. 52 + 13= _______ 5. 60 + 30= _______
; ; ; ; ;
12 + 23= _______ 30 + 18= _______ 20 + 45= _______ 13 + 52= _______ 30 + 60= _______
Write the missing number. Then find the sum. 6. (21 + 19) + 15= 21 + (19 + _____) _______ 7. 26 + (34 + 42) = (26 + _____) + 42 ______ 8. (10 + 17) + (20 + 5) = (10 + 20) + ( ____ + 5) ______ 9. (30 + 5) + (40 + 5) = (30 + ___) + (5 + 5) _______ 10. (8 + 20) + (2 + 40)= (8+ 2) + ( ___ + 40) _______
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Lesson 9: ADDING THREE- TO FOUR- DIGIT NUMBERS WITH REGROUPING To add three- to four- digit numbers: Write the numbers in column according to their place values. Add from right to left, beginning with the ones digits, then the tens digits and so on. Regroup if needed. EXPERIENCE
A. Add. DO not forget to regroup.
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Mathematics â&#x20AC;&#x153;Sipnayanâ&#x20AC;? Multiplication of Whole Numbers Meaning of Multiplication
Do you enjoy looking of the starfish under the clear water of the ocean? Most starfish have five arms. They look like a star. Suppose six starfish are in the beach and you want to find out the number of arms they have what would you do?
To find out how many arms they have in all you can add.
5
+
5
+
5
+
5
+
5
+
5
= 30
This addition sentence is the same as 6x5=30 So, we can say that multiplication is a repeated addition.
It is easier to multiply that to add the number repeatedly. The, number sentences 6x5=30 is a multiplication sentence. The numbers 6 and 5 are called factors and 30 is the product. here are 6 groups of 5 objects of 6 fives. This shows 6x5=30
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2. Array
ROW C O L U M N
The objects in an array are arranged in ROWS AND COLUMNS. This array has 6 rows of 5 objects.. This shows 6x5=30 Multiplication is a repeated addition. To show multiplication we can use the equal groups, array or number line. The numbers that are multiplied together are called factors and the answer is called product. 6 x 5= 30
Factors
Product
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A. Complete each number sentence. 1.
a. _________ + ___________ + ___________ = b. _________ x ___________ =
2.
a. ______ + _______ + _______ + _______ + _______ =
b. ______ x _______ =
3.
a. _______ + _______ + ________ + ________ =
b. _______ x _______ =
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4.
a. ______ + ______ + _______ + ______ = b. ______ x ______ =
Write an addition sentence and a multiplication sentence for each picture. 5. a. ________________ = b. ________________ =
6.
a. _______________ = b. _______________ =
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7.
a. ______________________ = b. ______________________ =
a. ___________________ = b. ___________________ = B. Look for patterns to help you complete each multiplication table. 6 x 0= 0 6 x 1= 6 6 x 2= 12 6 x 3= _____ 6 x 4 = _____ 6 x 5 = _____ 6 x 6 = _____ 6 x 7 = _____ 6 x 8 = _____ 6 x 9 = _____ 6 x 10 = ____ Young Ji International School/College
8x0=0 8x1=8 8 x 2 = 16 8 x 3 = ____ 8 x 4 = ____ 8 x 5 = ____ 8 x 6 = ____ 8 x 7 = ____ 8 x 8 = ____ 8 x 9 = ____ 8 x 10 = ___ Page 24
7x0=0 7x1=7 7 x 2 = 14 7 x 3 = ____ 7 x 4 = ____ 7 x 5 = ____ 7 x 6 = ____ 7 x 7 = ____ 7 x 8 = ____ 7 x 9 = ____ 7 x 10 = ____
9x0=0 9x1=9 9 x 2 = 18 9 x 3 = ____ 9 x 4 = ____ 9 x 5 = ____ 9 x 6 = ____ 9 x 7 = ____ 9 x 8 = ____ 9 x 9 = ____ 9 x 10 = ___
C. Draw and write the multiplication sentence.
1. 5 groups of 8 ___ x ____ =____
2. 4 groups of 9 ____ x ____ = ____
3. 6 groups of 7 ____ x ____ = _____
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Read each problem. Draw a picture, then write the multiplication sentence. 4. There are 8 rows of tables. Each row has 4 tables. How many tables are there in all?
________________________________ 5. Nine rows of cars are parked. Each row has six cars. How many cars are there?
________________________________ 6. There are 6 rows of chairs. Each row has 7 chairs. How many chairs are there in all?
________________________________
Complete the table. Look for patterns to help you remember the multiplication facts. X 5 6 7 8 9
5 25
6
7
8
9
36
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49 64 81
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PROPERTIES OF MULTIPLICATION 1. The product of 1 and any number is that number. This is the Identity Property of multiplication. 1 x 8 = 8, 12 x 1 = 12, 20 x 1 = 20
3 sets with no elements in each, 3 x 0 = 0 2. The product of zero (0) and any number is zero. This is the Zero Propertyof multiplication. 8 x 0 = 0, 10 x 0 = 0, 0 x 11 = 0
Let’s try these Find the property of multiplication shown in each equation. 1. 0 x 8 = 0
_____________________________
2. 8 x 10 = 10 x 8
___________________________
3. 4x (4 x 3) = (5 x 4) x3
___________________________
4. 25 x 1 = 25
____________________________
5. x (3x + 2)= (4 x 30) + (4 x 2)
____________________________
The commutative property of multiplication states that the order of the factors does not change the product. 4x8=8x4 The Associative Property of multiplication states that grouping of the factors does not change the product. (4 x 6) x 2 = 4 x (6 x 2)
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The distributive property of multiplication over addition states that one of the factors can be renamed or expressed as a sum of two numbers to find the product = 6 x 32 = 6 x (30+2) = (6x30) + (6 x 2) The Identity Property of multiplication states that the product that the product of one (1) and any number is that number. 1 x 10 = 10, 23 x 1 = 23 The Zero Property of multiplication states that the product of zero (0) and any number is zero. 0 x 12 = 0, 18 x 0 = 0
A. Name the property of multiplication that can help you finds the product. 1. 0 x 17 = 0
_____________________________
2. 8 x (2x5) = (8 x 5) x 2
_____________________________
3. 9 x 6 = 6 x 9
_____________________________
4. 26 x 1 = 26
_____________________________
5. 4 x 27 = 4 x (20 + 7)
____________________________
B. Write an example for each of the following properties. 1. Zero Property
________________________
2. Identity Property
________________________
3. Associative Property
_______________________
4. Commutative Property
_______________________
5. Distributive Property
________________________
C. Use the Distributive Property to find the product of the following. 1. 4 x 42
__________________________
2. 3 x 32
__________________________
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3. 5 x 38
__________________________
4. 25 x 6
__________________________
5. 62 x 5
__________________________
Read the value that states for each letter in the box. Replace the letters with the given values, then solve. A=5 1. b x c = c x b
B=6
2. 1 x d = ______
C=4
D=8
5. a x (b + c)
3. b x 0 = ______ 4. (a x c) x d = a x (c x d) MULTIPLYING TWO-to-THREE-DIGIT NUMBERS by ONE-DIGIT NUMBERS WITHOUT REGROUPING Mother bought 3 boxes of doughnuts. Each box has 12 doughnuts. How many pieces of doughnuts did Mother buy? What operation will you use to solve the problem? We can use multiplication to solve the above problem. The numbers we shall multiply are: 12 ------ number of doughnuts in each box x3 ------ number of boxes
a. 34 ------ Multiply 2 and 4. (2x4=8) x2------- Multiply 2 and 3. (2x3=6) 68 ------ (2x34=68) The basic multiplication facts and mental math can help you find the product easily. ď&#x201A;ˇ To multiply one-digit numbers by two-to three-digit numbers without regrouping, multiply the ones, then the tens and finally the hundreds. Young Ji International School/College
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ď&#x201A;ˇ The basic multiplication facts can help you find the product easily.
A. Complete the product of each multiplication sentence. C. Write a number sentence for each. Then find the product. 1. 3 times 42 the product.
3.multiply 72 and 3. And 10 to
2. multiply 54 and 2. sum by 4.
4. Add 32 and 40. Multiply the
EXCELENCE: Write a number sentence for each problem. Show your solution and label your answer. 1. Rina bought 4 bottles of orange juice. Each bottle costs P20. How much did she pay?
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2. There are 3 boxes. Each box contains 21 tennis balls. How many tennis balls in all?
“MULTIPLYING TWO-TO TREE-DIGIT NUMBERS BY ONE-DIGIT NUMBERS WITH REGROUPING” EXPOSE: Josh has 3 times as many marbles as bonn . If bonn has 25 marbles, how many marbles does josh have? What will you do to solve the problem? EXPOSE: We can solve the above problem by thinking of 3 groups of 25. 0000000000
0000000000
00000
3 groups of 25.
0000000000
0000000000
00000
or
0000000000
0000000000
00000
3 x 25= n
Regroup the 15 ones as 1 ten and 5 ones. Now, we have 7 tens and 5 ones or 75. So, 3 groups of 25 is 75 or 3 x 25=75 Study the following examples done in the short method.
STUDY OTHER EXAMPLES: A-Multiply the ones. (6 x 4 ones = 24 ones). X
34
2
-Regroup 2 tens.White 4 in the ones place of the product.
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6-Multiply the tens.(6 x 3 tens = 18 tens).Add 18 tens and the regrouped number of tens. 204
(18 + 2 = 20)
-The product os 204. B.
12
145 X
- Multiply the ones. 4 x 5 ones = 20 ones. 4-Regroup 2 tens,write 0 in the ones place of the product.
560 -Multiply the tens. 4 x 4 = 16 tens. Regroup 1 hundred. Write 6 on the tens place of the product. Finally, multiply the hundreds. 4 x 1 hundred = 4 hundreds. Add the Regrouped number of hundreds and 4 hundreds. 4 +1=5 the product is 560;
EMPHASIZE: To multiply two-to three-digit numbers by one digit numbers: multiply the ones, regroup if needed. multiply the tens, regroup if needed. multiply the hundreds, add the regrouped number of hundreds if there is any.
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EXPERIENCE A. Complete each product. 1. 27 6. 206 x3 x3 ___________ __________ ____ 1 __ __0
2.
34
3. 53
4. 42
5. 345
x6
x5
x6
x4
__________
_________
2 ___ ___ __ __ __
7. 163 x6 _________ ___ ___ 8
___ ___ 5
__________
___ ___ 2
__
8.
432 x 5 _________ __ __ __ 0
B. Write YES in the box if the product is correct. If NO, write the correct answer in the box. 1. 56
2. 47
x3_
x4
3.60 x5
4. 73 x4
158
188
300
282
5. 85
6. 78
7.234
8. 305
x3
x4
350
702
x6
x5
510
1,220
9. 305 __x3 1,254 Find each product. Regroup if needed. 10. 49
11. 56
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12. 63
13 74 Page 33
x5
x7
x9
x8
14. 234 _x5
15. 321 x7
16.406
17. 519
x6x6
C. Write a multiplication sentence for each problem. 1. 7 times 123 4.
2. Multiply 8 and 305. Multiply
4. Add 34 and 56. Multiply the sum by
5. Subtract 127 from 392. the difference by 5.
3. Find the product of 6 and 543. the product.
6. Multiply 8 and 205. Add 100 to
7. Edwin has six 200-peso bills. How much money does he have?
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8. Robin has four 500-peso bills. James has eight 100-peso bills. How much money do they have in all?
9. A class in grade 3 will donate 8 boxes of canned milk to the orphanage. Each box contains 120 cans. How many cans of milk will they donate
10. Donna bought 3 ballpens at P18 each and 4 pads of paper at P37 each. How much did she spend In all?
EXCEL:
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P P98
P125 P178
P108
Answer each question. Write the multiplication sentence, and then solve. 1.How much is the cost of 4 story books?
2.How much do the two toy trucks and a robot cost?
3.With your P300, can you buy two teddy bears and a story book?_________
4.How much will you pay for 2 robots and 3 toy trucks?
MULTIPLY TWO-DIGIT NUMBERS BY TWO-DIGIT NUMBERS WITHOUT REGROUPING: EXPOSE: There are 14 boxes of chocolate. Each boxes has 12 peaces of chocolates. How many chocolates are in the boxes? What operations tells you the total number of chocolates?
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EXPLORER: We can use multiplication to solve the given problem. Study these steps. MULTIPLY 12 AND 14: STEP 1multiply 14 by 2 ones. 2 x 14=28
STEP 2multiply 14 by 1 tens. 10 x 14=140
14
STEP 3 Add the partial products. 28 + 140=168
14 _X12_ 28
_X12_ 28
14 _X12_ 28 _X140_
X140_ 168
THERE ARE 168 CHOCOLATES IN ALL. We can also use the short method to answer the same multiplication problem: 14
STEP 1. Multiply 2 by 4, then multiply 2 by 1. (2 x 14 =
28) ___x12 STEP 2.Multiply 1by4. Write the product below 2. then multiply 1by1 28 STEP 3.Add the partial products. +14__ 168 ANOTHER EXAMPLE: Young Ji International School/College
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32
- Multiply 32 by 3. (3 x 2=6 ; 3 x 3=9)
X23- Write 96 in the ones and tens places of the product. 96
- Multiply 32 by 2. ( 2 x 2=4)
__+64_ - Write 4 below 9, then multiply 2 by 3. ( 2 x 3=6) 736- Add the partial products.
EMPHASIZE: to multiply two-digit numbers by two-digit numbers without regrouping. - Multiply the number by the ones digits. -Multiply the number by the tens digits. -Add the partial products.
EXPERIENCE:
A. Find each product. 23 X12
1.
34 X21
2.
43 X32
5. 32 X23
3.
20 X23
6. 42 X32
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53 X21
4.
7. 8. 40 X32
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B. Write the numbers in column, then find the product. 1. 43 x 21
3. 42 x 23
5. 72 x 31
2. 33 x 12
4. 34 x 12
6. 53 x 21
EXCEL: How many different products without regrouping can you make? Use the digits 1,2,3 and 4 only once in each place.
X _______________________
MULTIPLYING TWO-DIGIT NUMBERS BY TWO-DIGIT NUMBERS WITH REGROUPING EXPOSE: There are 18 boxes of chocolates in a candy store. each box contains 15 chocolates bar. How many bars of chocolates are in the boxes? EXPLORE: We can solve this problem by multiplying 18 and 15 18x15=n
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Let us study the different ways to multiply the given numbers Step 1. Multiply 15 by 8 ones
8x15=120
4 15 x18 _____________ 120 Step 2. Multiply 15 by 1 tens 10x15=150 18 x18 ____________ 120 150 ___________ Step 3. Add the partial products. 15 x18 __________ 120
partial products
+150 ______________
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EMPHASIZE To multiply two-digit numbers by two-digit numbers: Multiply the number by ones digit. Regroup if needed. Multiply the number by the tens digit. Regroup if needed. Add the partial products EXPERIENCE A. Find the products. 1.
75
2.
x32
67
3.
x23
59
4.73
x32
x27
_________
_________
_________ ___________
5.
6.
7.
37 x43 x35
__________ 9.
84
49 x24
__________ 10.
x33
95 x25
52
8.
68
x37 ____________
____________
11.
12.
79
98
x 43
x
42 ___________
____________
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______________
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B. Write the numbers in column. Then find the product. 24 x 53= 2
68 x 23=n
54 x 35= n
72 x 26= n
42 x 58= n
67 x 34= n
Complete the table. 7.
9.
x 28 42
x 27 36
47 53
83 65
8.
10.
x 42 34
26 38
X 40 60
75 85
C. Write a multiplication sentence for each, then solve. 1. Thirty-eight times forty six. _________________________________________ 2. Multiply 76 and 34. ___________________________________________ 3. Find the product of 80 and 45. _________________________________________
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4. Multiply 56 and 42. Add 75 to the product. ___________________________________________ 5. Find the sum of 40, 32 and 15. Multiply the sum by 53. ____________________________________________ 6. Mr. Calis spends P75 for a newspaper each day. How mush does he spend for 30 days? ______________________________________ 7. A petshop has 56 goldfish for sale at P25 each. How much will the owner get if he sold tem all? _________________________________ 8. There are 15 boxes in a store room. Each box contaoins 24 cans of sardines. How many canned sardines ate there all? ______________________________________________ EXCEL DO WHAT IS ASKED a. Find the difference between the products of the two number sentences. Show your solution 1.
48
75
x 36
x 43
------------------------2.
92
x 52
x64
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=
----------------------
84
______________
--
---=
_____________ Page 43
B. Find the sums of each pair of multiplication sentence. 3.
4.
68
59
_________ + ________
x52
x64
= ____________
_____________
____________
68
59
_________ + __________
X 52
X64
= ______________
_______________
___________
MULTIPLYING BY MULTIPLES OF 10, 100, AND 1,000 EXPOSE If each
= 10 then
If each
= 100, then
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=?
=?
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EXPLORE Study the following examples and find the pattern in getting the answer. 1. Lexy bought 5 boxes of colored pencils. each box contained 10 pencils. How many pencils did he buy?
5 x 10 = 50 2. An office clerk bought 5 boxes of paper clips. each box contained 100 paper clips. How many paper clips did she buy? 5 x 100 = 500 3. A carpenter bought 5 boxes of concrete nails. Each box contained 1,000 nails. How many nails did he buy? 5 x 1,000 = 5,000 Did you notice the number of zeros in the factors? It is easy to multiply any whole number by multiplies of 10, 100 and 1,000. Simply multiply nonzero digits. then count the number of zeros in the factors and add the corresponding zeros to the producr. 8 x 20= 160 There is only one zero in factors Write the product of 8 and 2 Then add one zero to the product 20 x 30= 600 There are two zeros in the factors. Write the product of 2 and 3 Then add two zeros to the product 40 x 600= 24,000 There are three zeros in the factors Multiply 4 and 6 Then add three zeros to the product Young Ji International School/College
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EMPHASIZE To multiply a number by multiples of 10, 100, and 1,000, multiply the nonzero digits first, then as many zeros as there are in the factors. EXPERIENCE A. Write the product as fast as you can. 1. a. 4x 10= ______ b. 4 x 100 = _______ c. 4 x 1,000 = ______ 2. a. 30 x 10 = _______ b. 30 x 100 = ________ c. 30 x 1,000 = _______ 3.a. 5 x 60 = ________ b. 5 x 600 = ________ c. 5 x 6,000 = _______ 4. a. 20 x 30 = _______ b. 20 x 300 = _______ c. 20 x 6,000 = _______ B. Give the products 1. 7 x 100 = ___________
6. 10 x 200 = ________
2. 6 x 1,000 = _________
7. 100 x 40 = ______
3. 12 x 10 = _______
8. 1,000 x 25 = ______
4. 15 x 100 = _______
9. 10 x 300 = ______
5. 19 x 100 = ______
10. 100 x 70 = _____
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Use Mental Math to find the products 11.
15.
100
12.
1,000
13.
100
14.
100
x27
x28
x39
x600
______
________
_______
_____
1,000
16.
100
x500 _________
17.
100
x30 _________
18.
5,000
x500
x300
_________
_______
C. Write the correct number on the blank. 1. 55 x 100= ______
6. 30 x 600 = _____
2. 100 x 72 = ______
7. 200 x _____ = 8,000
3. 82 x _____ = 8, 200
8. ____ x 500 = 10,000
4. 76 x ______ = 7, 600
9. ______ x 40 = 20,000
5. ____ x 65 = 6,500
10. 700 x ______ = 35,000
Use mental math to find the products. 11. 400 x 600 = ________
16. 100 x 600 = _______
12. 800 x 300 = ________
17. 5,000 x 60 = ______
13. 80 x 300 = _________
18. 700 x 60 = ________
14. 600 x 600 = ________
19. 400 x 800 = ________
15. 90 x 800 = _________
20. 80 x 3,000 = _______
Solve each problem 1. Mr. Tan sells oranges by boxes. each box contains 400 oranges. How many oranges are there in: a. 8 boxes? _____________ b. 20 boxes? ____________ Young Ji International School/College
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c. 50 boxes? ____________ 2. A bus can carry 40 passengers per trip. How many passengers can carry in 20 days if it makes 10 trips a day? ____________________________________
EXCEL Which would you rather have: a. 8 pieces of P100 bill or 6 pieces of P1,000 bill? Why? ____________________________ b. 10 pieces of P500 bill or 12 pieces of P200 bill? Why? ______________________________________
ESTIMATING PRODUCTS EXPLORE:
P 87.00 EACH
P 185.00 EACH
About how much are 6 notebooks? About how much are two pocket books? What will you do to solve these problems? Young Ji International School/College
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The word about tells you that you do not need to give an exact number amount. You only have to make estimate.
Study the following examples.
1. estimate the product of 6 and 87 To estimate , round off the number to its highest place value before multiplying. You do not need round off the one- digit number. 87 is rounded off to 90 x6
x6
______________
___________ 540= estimated product
Thus, six notebooks cost about P540 87 x6 ___________ 522 Since P540 is close to P522 we say that the estimation is reasonable. This means that the estimated answer is close to the exact or actual answer. 2. Estimate the product of 32 and 68. 68
is rounded off to 70
70
x32
is rounded off to 30
x 30
_______ 136
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___________ 2,100- estimated product
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204 _____________ 2,176- exact product The estimated product is reasonable since it is close to the exact product. Try some more examples. Estimate each product 1.
37
40
x5
x5
2.
__________ __________ _________
81
80
x4
x4 __________
EMPHASIZE To estimate Product Round off each factor to the highest place value before multiplying. A one-digit factor does not need to be rounded off Multiply the nonzero digit, then write as many zeros as there are in the two factors. A. ESTIMATE THE PRODUCTS. Follow the given example. 47
50
x 4x 4 200 1. 56
2. 38
3. 71
5. 93
6. 49
x 6x 7x 9 4. 88 x 5x 4x 17 Young Ji International School/College
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7. 51
8. 68
9. 79
x 4x 28x 36
Circle the letter of the pair of factors that will give the estimated product on top. 10.
11.
800
2,400
a. 28 x 48
a. 26 x 81
a. 42 x 25
b. 42 x 35
b. 18 x 78
b. 27 x 86
c. 38 x 17
c. 48 x 67
c. 31 x 86
13.
14.
15.
4,800
25,000
12,000
a. 57 x 82
a. 36 x 410
a. 44 x 386
b. 51 x 79
b. 29 x 390
b. 49 x 487
c. 54 x 91
c. 42 x 386
c. 42 x 386
B. Put a check 1.
47
x
4 200____
4.
12. 12.
1,600
61
x 68 1,200____
if the estimate ia reasonable, cRoss if 2.
75 x
3. 8
640_____
5.
not.
75 x 48
2,800____
58 x 41
2,400_____
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6. 8 5 x 29 2,700____
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Estimate each product. 7.
63 x 19
8. 7 5 x37
9.6 1 x 48
10. 8 6 x 61
C. Solve each problem by estimating the product. 1. A box of crayons costs P65. About how much will Yoly pay if she buys 5 boxes of crayons? ____________ 2. Hanah wants to buy coloring pens at P69 each. About how much will she pay for 18 pieces of coloring pens? __________
3. Roco wants to find out if his P2,000 is enough to buy 18 CDs of cartoon movies at P75 each. ___________________ 4. Gino spends P78 for transportation each day. About how much does he spend in a mounth? ______________________ 5. A group of 5 persons went to a restaurant for their get-together party. If each person paid an amount between P260 and P285, about how much did they spend for the party?
EXCEL: Bastil, jeric and Ziggy were given tickets to sell for the school fair. The three boys sold 79,82 and 75 tickets respectively. What multiplication sentence should you write to estimate the total number of tickets sold? Third Quarter Lesson 1: Rational Numbers Fractions Concept of Fractions Nico and Nica are twins. They are celebrating their ninth birthday.
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Mother cut the blueberry cake into ten equal slices. If Nico and Nica took the two slices, what part of the cake have they taken? Explore This is how the blueberry cake is cut into 10 equal slices. 2 out of 10 slices is “two-tenths” or 2 10
of the whole cake
3 out of 10 slices is “three-tenths.” We write:
3 10
4 out of 10 slices is “four-tenths.” We write:
4
What do we call 5 out of 10 slices? ____
10
7 out of 10 slices?______ 8 out of 10 slices?______ 9 out of 10 slices? Mother cut the chocolate cake into 8 equal parts. 1
Father ate “one- eighth” or of the cake. 8
Three children got their share. They ate 3 parts of the chocolate cake “threeeighths” or 2
,
3 8
4 13
, , , are called fractions. A fraction is made up of a numerator,
10 10 8 8
denominator, and a fraction line. Fraction line
2 10
numerator (number of slices taken)
denominator ( total number of slices) The fractions above indicate part(s) of a whole. Fractions also indicate part(s) of a group or a set.
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Examples: 1. There are 5 small groups of children playing. If 3 groups are boys what fraction of the children are boys? 3 out of the 5 groups of children are boys is written as: 3
fraction line ------ numerator (number of groups of boys) 5
denominator (total number of groups of children) We write:
3 5
We say: three- fifths
2. Look at the set of fruits.
What fraction of the fruits are oranges?
More Examples: 1. 4/6 of “four-sixths” of the rectangle is shaded. 2. 2/9 or “two-ninths” of the shapes are squares. 3. ¾ or “ three- fourths” of the circles are not shaded. Young Ji International School/College
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Study further the illustration below. Each part of the orange is 1/5 or “one-fifth”. 5 parts are 5/5 of “five- fifths”. 5/5 or “five-fifths” is equal to one. Therefore, 5/5 = 1.
A fraction is a number that tells a part of a whole, a group, or a set. A fraction is made up of numerator, a denominator, and a fraction line. The numerator tells how many equal parts are considered. The denominator tells how many equal parts there are in all. The fraction line separates the numerator and the denominator. ½, 1/3, ¼, 1/5, etc. mean “1 out of a certain part.” They are called unit fractions.
A. Tell whether each illustration shows a fraction. Put a check () on the blank if it does and a cross () if it does not.
1. ________
2. _________
3. _________
4. __________
5. __________
6. __________
What part is shaded? Write the missing number in each fraction.
7.
8.
6/9
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4/9 Page 55
9. 1/4 10. 1/4 B. Shade the fractional parts as indicated. 1.
five- sixths
2.
two- fourths
3.
three- fifths
4. one- third
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5.
one- half
Complete each fraction name in words. 6. 7/9 is _________ - ninths 7. 6/12 is _______ - twelfths 8. 3/10 is three- _______. 9. 4/7 is four- __________. 10. 1/11 is one- ___________. C. Read each given situation then answer the questions. 1. A long piece of wood was cut into 9 equal pieces. 5 pieces were painted green. What part was painted green? __________ 2. I collected 12 seashells. I gave 7 seashells to my bestfriend. What part of the seashells did I give to my bestfriend? _________ 3. 15 club officers, 10 are girls. What fraction of the club officers does the number of girls represent? ____________ 4. 40 children in a class. One stormy day, 10 children were absent. What part of the class was absent? _______________. 5. If the pie is cut into 8 equal parts, what fraction represents the whole pie? __________ What is the fraction equal to? ______________.
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EXCEL Work with a partner. Illustrate each given fraction as indicated. 1. 4/6 (part of a whole) 2. 5/10 (part of a set)
Lesson 2 Fractions Less Than One, Equal to One and More Than One Study the illustrations below. A
B
What do we call each part of the
What do we call 4 parts of the
watermelon?
C
watermelon?
In figure C, there are 8 of Âź parts. What is the fraction for the shaded portion? Many students think that all fractions are less than 1. Some fractions are less than 1, some are equal to 1, and others are greater than 1. Young Ji International School/College
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Hereâ&#x20AC;&#x2122;s how you tell how large a fraction is. Start with the bottom number. The bottom number tells you how many equal parts are in each whole group. How many parts are in each of these whole groups?
4
3
2
8
6 The top number tells how many parts we use. How many parts are shaded in each of these whole groups?
3
2
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1
5
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If a fraction equals 1 you use the same number of parts in each whole group. If the bottom number is 4, you use 4 parts in each group.
If you had 1 whole parts would you use?
group shaded in, how many
Thatâ&#x20AC;&#x2122;s right, 4 parts. So the fraction 4 /4 equals 1 whole group. The fraction 4/4 equals 1. If a fraction equals 1 you use the same number of parts in each whole group. If the bottom number is 3, you use 3 parts in each group.
If you had 1 whole group shaded in how many parts would you use? Good job, 3 parts. So the fraction 3/3 equals 1 whole group. 3/3 equals 1. If a fraction equals 1 you use the same number of parts in each whole group. If a bottom number is 8, you use 8 parts in each group.
If you had 1 whole group shaded in how many parts would you use? Young Ji International School/College
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Yes, 8 parts So the fraction 8/8 equals 1 whole group. 8 equals 1. A. Which of the following fractions equal 1? 3 5
7
1 5
7
, ,
½
7
,
9
6/5
100
,
100
10/11
3/3
4/1
You can look at a fraction and tell if the number is less than 1 whole, equals 1 whole, or less than 1 whole. The bottom part tells how many parts are in each whole group. This fraction has 6 parts in each whole group. If the fraction equals 1, how many parts would we use?
6/6 equals 1 whole group. If a fraction has 6 parts and we use more than 6 parts, then we have more than one whole group. This fraction has 8 parts. So we have more than 1 whole group.
8/6 is more than 1 whole group. So the fraction 8/6 is more than one whole group.
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If a fraction has 6 parts and the top number in a fraction uses less than 6 parts, then we have less than one whole group. This fractions uses 3 parts. So we have less than one whole group.
3/6 is less than one whole group. So the fraction 3/6 is less than one whole group. A. Identify the fractions that are less than one whole, equal to 1 whole, or greater than one whole. 1. 5/1
2. 4/4
3.9/7
4.7/9
5. 100/100
6. ½
7. 6/5
8.10/11
9.4/1
10. 3/3
A fraction whose numerator is less than the denominator is called Proper Fraction. Its value is less than one. A fraction whose numerator is the same as or greater than the denominator is called improper fraction. It’s value is equal to more than one. A mixed number is made up of a whole number and a proper fraction. An improper fraction can be expressed as a mixed by dividing the numerator by the denominator. A mixed number can be expressed as an improper fraction by multiplying the whole number by the denominator and adding the product to the numerator then just copy the denominator.
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A. Write P for proper fraction. IM for improper fraction, and MN for mixed number. ______ 1.3/12
________ 6. 13/5
______ 2.15/14
_________ 7. 10/10
______ 3.6 ______ 4.2
1
_________ 8. 7
7 2
1 2
_________ 9. 5/9
3
______ 5.18/7
_________ 10. 1
4 5
A. Write a fraction to show how much of the shape is shaded. 1.
2.
4.
3.
6. 5
7.
8.
9.
10.
11.
12.
13.
14.
15.
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16.
17.
Write an improper fraction for the parts that are shaded.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19. 5 wholes and 3 sevenths
= _______________
20. 10 and 7 tenths
= _______________
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Write a mixed number to show what part of each illustration is shaded.
g. sevenwholes and 7 eighths = _________________ h. eightwholes and one- half = __________________ 3
10. 9 and = _________________ 4
Write each fraction as a whole number or a mixed number. 1. 2. 3. 4. 5.
13 13 14 5 16 7 21 5 32 3
= _______________
6.
= _______________
7.
= _______________
8.
= ______________ = ______________
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9.
51 12
18 18 35 35 40 9
= _______________ = _______________ = _______________
= ________________ 10.
60 10
= _____________
Page 65
Change each mixed number to an improper fraction. 2
11. 4 = _________ 9
4
14. 7 = _________ 7
1
2
6
3
12. 5 = ____________ 13. 6 = _____________ 1
15. 9 = ____________ 8
Excel Fractions Draw a picture to show the fraction. 1. 1
2. four-fifths
3. two-fourths
5. seven-eighths
6. 2/2
8. six-sevenths
9. 1
2
4. 3 6
7.
8 10
10. one-half
3
11. 2
12. four-sixths
3
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Lesson 3: Equivalent Fractions Equivalent Fractions Equivalent Fractions have the same value, even though they may look different. These fractions are really the same: 1 2 4 = = 2 4 8 Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value. The rule to remember is: "Change the bottom using multiply or divide, And the same to the top must be applied" So, here is why those fractions are really the same: ×2 1 2
×2 2 4
=
×2
=
4 8
×2
And visually it looks like this: 1
2
/2
4
/4
=
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/8
=
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Dividing Here are some more equivalent fractions, this time by dividing: ÷3 18 36
=
÷3
÷6 6 12
=
1 2
÷6
Choose the number you divide by carefully, so that the results (both top and bottom) stay whole numbers . If we keep dividing until we can't go any further, then we have simplified the fraction (made it as simple as possible)
You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.
You only multiply or divide, never add or subtract, to get an equivalent fraction.
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ď&#x201A;ˇ
Only divide when the top and bottom would still be whole numbers.
Write the equivalent fractions. ď &#x2020; Equivalent fractions are fractions whose size or value are the same
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To determine whether a fraction is equivalent to another fraction, multiply or divide both numerator and denominator by the same nonzero number.
To check the equivalence of fractions, use the cross product method. To find the missing term, get the product of the first pair of terms, then divide by the other given term.
EXPERIENCE Young Ji International School/College
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Refer to the drawings. Write the equivalent fractions.
Write 4 equivalent fractions for each 1/6,
2/5,
3/7,
4/3
B. Shade the box of the Yes (ď &#x160;) column if the fractions are equivalent and the No (ď &#x152;) column if they are not. Young Ji International School/College
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Yes
No
1. 1/8 = 2/16 2. 3/5 = 9/20 3. 20/30 = 2/3 4. 15/25 = 4/5 5. 8/24= 1/2 Yes
No
6. 8/9 = 16/18 7. 36/40 = 9/10 8. 26/28 = 13/14 9. 2/16 = 1/7 10. 10/35 = 2/8 Solve for the missing terms to make the fractions equivalent. 11. 10/15 = _12_ = 13
____
12. 9/10 = 18 60
13. 16_ 16
14._
15.
4
C. Each group must be a set of equivalent fractions. Cross out the fraction that does not belong to the set. 1. 3/5, 6/10, 9/15, 14/20….. 3. 1/8, 2/16, 3/25, 4/32… 5.
1/9, 2/18, 3/27, 4/35….
7.
5/10, 10/20, 15/25, 25/30…
9. 4/6, 9/12, 2/3, 6/9…
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2.
5/6, 20/25, 10/12, 15/18….
4.
2/6, 3/12, 6/12, 8/24…. 6. 8.
4/8, 8/14, 12/21, 16/28… 1/3, 5/15, 7/21, 9/28…
10. 7/8, 14/16, 21/24, 24/36….
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EXCEL Read and understand the problem. Answer the question. Father has 2 pieces of agricultural land, each one hectare big. If he gave 2/12 of one land to his eldest son and 1/6 to his youngest son, did the two sons receive the same size of land? Why or why not? Illustrate in the box.
FRACTIONS in LOWEST TERMS EXPOSE Alex, Bong, and Carlo each has chocolate bar Read what they said:
I ate 4/8 of my chocolate bar.
ate 2/4 of my chocolate bar
I ate ½ of my chocolate bar.
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A fraction is in its simplest form (this is also called being expressed in lowest terms) if the Greatest Common Factor (GCF), also called the Greatest Common Divisor (GCD), of the numerator and denominator is 1. For example, 1/2 is in lowest terms but 2/4 is not. Equivalent Fractions: Equivalent fractions are different fractions that are equal to the same number and can be simplified and written as the same fraction (for example, 3/6 = 2/4 = 1/2 and 3/9 = 2/6 = 1/3). To reduce a fraction to lowest terms (also called its simplest form), divide both the numerator and denominator by the GCD. For example, 2/3 is in lowest form, but 4/6 is not in lowest form (the GCD of 4 and 6 is 2) and 4/6 can be expressed as 2/3. You can do this because the value of a fraction is not changed if both the numerator and denominator are multiplied or divided by the same number (other than zero). Experience A. Check () the biggest common divisor of each fraction. 1. 14/18 ( 2, 7, 9) 2. 20/24 ( 6, 5, 4 )
4. 21/24 ( 3, 7, 8 ) 5. 50/60 ( 5, 6, 10 )
3. 20/25 ( 5, 6, 7 ) B. Write each fraction is simplest form. 1. 2/18=
6. 18/30=
2. 3/24=
7. 35/45=
3. 10/60=
8. 60/100=
4. 21/27=
9. 28/32=
5. 32/64=
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10. 8/64=
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C. Shade the if the fraction is in its lowest terms and the if not. 1. 15/22
6. 12/30
2. 20/27
7. 9/27
3. 13/39
8. 16/17
4. 8/32
9. 18/29
5. 18/35
10. 21/63
D. Cross out the fraction in each set that is not in simplest form. 1. 4/6, 1/3, 2/3 4. 3/8, 8/12, 5/11 7.
1/6, 6/7, 3/18
2.7/10, 10/20, ½
3.5/6, 4/9, 5/10
5. 9/12, ¾, 4/13
6. 2/5, 4/10, 5/21
8. 14/21, 3/28, 12/31
9. 7/28, 5/24, 4/21
10. 10/11, 15/30, 11/12 EXCEL Read each problem then do as indicated. 1. Sixteen out of forty children in class are boys. Express the fractional part of the class that are girls in lowest terms.
2. Olga is holding a card with the fraction 24/30. Find the fraction equivalent to it with the numerator 4.
3. Nora is holding another card with the fraction 25/35. Find the fraction equivalent to it with the denominator 7.
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Comparing and Ordering Fractions Your students may need to be reassured that fractions are just numbers and, like other numbers, they can be compared, ordered, and used in computation. The main difference between fractions and whole numbers, of course, is that fractions are parts of a whole. They have a numerator, a word that means "enumerate," or "count," and a denominator. The word denominator is related to denominate, which means "to name." Just as you wouldn't say that 7 inches are greater than 6 feet because 7 > 6, you wouldn't say that 7 eighths are greater than 6 fourths by comparing only the 7 and the 6. Fractions come in three basic forms.
Proper fractions have a numerator that is always less than the denominator. In arithmetic, using positive numbers, proper fractions represent the numbers between 0 and 1. , , and are all proper fractions. Improper fractions have a numerator that is greater than the denominator. Improper fractions can be rewritten as fractions or mixed numbers. There is nothing "wrong" with improper fractions; in fact they're sometimes easier to compute with than mixed numbers. , , and are improper fractions. Mixed numbers have a whole-number part and a fractional part (usually proper). Mixed numbers can be rewritten as improper fractions. 1 and 8 are mixed numbers.
Students have learned how to write numbers in different forms, and they need to do the same with fractions. An important rule about numbers is that if you multiply or divide a number by 1, you don't change the value of the number. This is the Property of One. Students also know the division rule that states when you divide a number by itself, the quotient is 1. So any number divided by itself equals 1. One nice thing about fractions is that they provide you with an infinite number of forms of the number 1: , , , , and so on, or even
a
fraction
over
a
fraction,
such
as .
In order to work with fractions, students often need to find equivalent fractions—that is, fractions with different numbers but the same value. If you're working with and you'd really rather be working with eighths, multiply by . Since 1 = , then has the same value as even though it's written as . When denominators are different, students may use benchmarks to compare them. A very easy benchmark is . If the numerator of a fraction is less than half Young Ji International School/College
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of the denominator, the fraction's value is less than . Similarly, if the numerator is more than half of the denominator, the fraction's value is greater than . For example: > and < , so must be greater than . When denominators are different, you may also model with a diagram or manipulative. 1. a ruler marked in eigths or sixteenths of an inch
2. same-length number lines, each dedicated to all the fractions between 0 and 1 with the same denominator
3. a collection of wax-paper fraction squares
4. Fraction strips (See page 328 in the text.) 5. coins and dollar bills 6. two-color counters and yarn loops When denominators are different and benchmarks don't help, students should find equivalent
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fractions with like denominators. Look for a denominator that can be used to name both fractions. Then multiply the fraction you wish to change by a form of oneâ&#x20AC;&#x201D;such as , , , and so onâ&#x20AC;&#x201D; that produces the denominator you want. Just as inches can name measurements given in feet and yards, sixteenths can name fractions given in eighths and fourths. can be written as by can be written as by multiplying by .
multiplying by .
Since and are both forms of 1, you haven't changed the value of either fraction, just the form. With an understanding of how to compare fractions, you can introduce the idea of ordering fractions. Suggest that students use the same logic to order fractions as they do to order whole numbers. Have them compare pairs of fractions and be sure every pair is related in the same way. For example, to order , , and from least to greatest, first find an equivalent fraction to that has a denominator of 8. =
=
is equivalent to .
Then compare the numerators. < < , so < < . Students can also use a number line to determine where the fractions fall in relation to each other.
is closest to the left. is closest to the right. So < < .
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ou can introduce the addition and subtraction of fractions with like denominators by explaining to students that it is similar to adding and subtracting with whole numbers. However, the sum or difference is written over the denominator. When the denominators of fractions are the same, you can say the fractions have the same name. When this is true, you can add or subtract the numerators without changing the denominator. So 3 fifths plus 3 fifths equals 6 fifths. This way of thinking only works for addition and subtraction
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C. Arrange the fractions in ascending order. 1. 7/8, 2/8, 1/8, 5/8
___________________________
2. 10/12, 8/12, 6/12, 11/12
__________________________
3. 3/6, 3/8, ¾, 3/5
___________________________
4. 3/5, 3/10, 2/5, ¼
___________________________
5. 1/5, 3/20, 2/4, 1/10
___________________________
Arrange the fractions in descending order. 6. 2/15, 5/15, 1/15, 6/15
___________________________
7. 8/21, 10/21, 4/21, 2/21
__________________________
8. 4/7, 4/8, 4/6, 4/5
___________________________
9. ½, ¾, 7/8, 6/10
__________________________
10. 2/3, 7/9, ¾, 5/6
___________________________
EXCEL Choose the fraction that will make the comparison correct. Write your answer on the right wing of the butterfly. 1. 2/6
¼, 1/3, ½
2. 3/5
2/7, 2/3, 2/6
3. 5/9
4/5, ¾, ½
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Lesson 6: Addition and Subtraction of Similar Fractions It's easy to add and subtract like fractions, or fractions with the same denominator. You just add or subtract the numerators and keep the same denominator. The tricky part comes when you add or subtract fractions that have different denominators. To do this, you need to know how to find the least common denominator. In an earlier lesson, you learned how to simplify, or reduce, a fraction by finding an equivalent, or equal, fraction where the numerator and denominator have no common factors. To do this, you divided the numerator and denominator by their greatest common factor. In this lesson, you'll learn that you can also multiply the numerator and denominator by the same factor to make equivalent fractions. Example 1
In this example, since 12 divided by 12 equals one, and any number multiplied by 1 equals itself, we know 36/48 and 3/4 are equivalent fractions, or fractions that have the same value. In general, to make an equivalent fraction you can multiply or divide the numerator and denominator of the fraction by any non-zero number. Since only like fractions can be added or subtracted, we first have to convert unlike fractions to equivalent like fractions. We want to find the smallest, or least, common denominator, because working with smaller numbers makes our calculations easier. The least common denominator, or LCD, of two fractions is the smallest number that can be divided by both denominators. There are two methods for finding the least common denominator of two fractions: Example 2
Method 1: Write the multiples of both denominators until you find a common multiple. The first method is to simply start writing all the multiples of both denominators, beginning with the numbers themselves. Here's an example of this method. Multiples of 4 are 4, 8, 12, 16, and so forth (because 1 × 4=4, 2 × 4=8, 3 × 4=12, 4 × 4=16, etc.). The multiples of 6 are 6, 12,…--that's the number we're looking for, 12, because it's the first one that appears in both lists Young Ji International School/College
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of multiples. It's the least common multiple, which we'll use as our least common denominator. Method 2: Use prime factorization. For the second method, we use prime factorization-that is, we write each denominator as a product of its prime factors. The prime factors of 4 are 2 times 2. The prime factors of 6 are 2 times 3. For our least common denominator, we must use every factor that appears in either number. We therefore need the factors 2 and 3, but we must use 2 twice, since it's used twice in the factorization for 4. We get the same answer for our least common denominator, 12. Example 3 prime factorization of 4 = 2 × 2 prime factorization of 6 = 2 × 3 LCD = 2 × 2 × 3 = 12 Now that we have our least common denominator, we can make equivalent like fractions by multiplying the numerator and denominator of each fraction by the factor(s) needed. We multiply 3/4 by 3/3, since 3 times 4 is 12, and we multiply 1/6 by 2/2, since 2 times 6 is 12. This gives the equivalent like fractions 9/12 and 2/12. Now we can add the numerators, 9 + 2, to find the answer, 11/12. Example 4
A. Find the sum. Express the sum in lowest terms, if needed. 1.
5 10
+
3 10
= ____
3
1
2
9
9
9
4. + + = _____
2.
2 12
+
3 12
= ______
1
3
7
7
5. 2 + 5 = _______
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3.
1 15
+
3 15
+
4 15
= ______
2
4
8
8
6. 3 + 4 = _____
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Solve For the missing addend. 2
5
6
6
7. + =
8. +
5
7
9
9
9. + + = 1
2
4
4
11. 2 + = 4 13. +
3 12
+
4 12
=
1 20
10.
9
=
20
5 11
+ =
8 11
2
4
5
5
12. 3 + = 4 8
13.
12
1 25
+
6
+=
25
9 25
Find the difference mentally. 6
3
8
8
1. - = _____ 4.
9 11
-
7 11
2.
= ____
4
3
6
6
2 10
1
-
10
7
5
9
9
= _______
3.
5. - = _____
7.10 - 7 = _____
3
1
7
7
6.
10 12 8 13
-
8. 9 - 7 = _____
3 12 5 13
= _____ = _____ 5
9.12
11
- 10
2 11
= _____
Subtract. Express the difference in lowest terms. 10. 12.
18 25 16 20
14. 15
-
13 25 10 20
4 10
10
11.
= ____
13. - - = ______
- 10
2
10
= ______
15
-
4
= ____
15
5
1
2
8
8
8
5
2
6
6
= ______
15. 18 - 15 = _____
C. Read each problem carefully. Write a number sentence then solve. Write all final answers in simplest form. 1
1. Jean does leisure reading thrice a week. On Mondays, she spends hour, on 1
6
2
Wednesdays, another hour on Fridays, hour. What part of an hour does Jean 6 6 spend in leisure in reading. 2. Joanne has planned to read 4
6 10
of the whole book in a day but she was able to
read only of the book. What fractional part of the book has she not yet read.3. 10
Her friend Dulce enjoys jogging every weekend. She covers
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1 4
of a kilometer on
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2
Saturday and of a kilometer on a Sunday. What distance does Dulce jog on 4 weekend? 7
4
4. Emma needs of a cartolina for her Art project. Fe needs of a cartolina for 8 8 her Filipino project. How much more of a cartolina does Emma need than Fe. 5. Gina needed
4 5
kilogram of pork and 3
2 5
kilogram of chicken for their Cooking
class. If she used kilogram of meat for the chicken- pork adobo, how much 5 meat was left? EXCEL Work with a partner. Write at least 2 story problems about addition and subtraction of similar fractions. Show it first to your teacher for checking. Then ask your classmates to solve them. Lesson 7: ADDITION AND SUBTRACTION OF DISSIMILAR FRACTIONS In lesson 6, we learned how to add or subtract fractions whose denominators are the same. 1
2
2
5
What if you will be asked to get the sum of and
? or the difference of
5 6
3
and ? 4
EXPOSE To get sum of
1 2
and
2 5
, let us illustrate.
1
5
2
10
2
4
5
10
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We cannot just add ½ and 2/5, because they have different denominators. Let us study how to get the Smallest Common Dividend of two or more numbers. Using the given fractions above, let us study further. dissimilar
What are the multiplies of 2? 2, 4, 6, 8, 1 2
=
â&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Ś.
5 10 4}
fractions{+ 2 = 5
10
similar fractions What are the multiplies of 5?
10
5,
10
, 15, 20 â&#x20AC;Śâ&#x20AC;Ś.
Use 10 as the smallest common dividend. 5 10 +
4 10 đ?&#x2018;&#x153;đ?&#x2018;&#x153;
5 The fractions 10
can 4
now be added because they have the same denominator
10 9
The sum is already in its simplest form.
10
A. Complete the addition process. 3
1.) = 8
2.) 2/7 = O/28
40
3.) 1/6 = O/18
+ 1/5 = O/40+ ž = O/28+ 2/9 = O/18 ď Łď Łorď Łď Ł 4.)7 and 2/7 = 7 and _/35 + 3 and 1/5 = 3 and _/35 = Young Ji International School/College
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5. 10 and 1/5 = 10 and _/20 + 15 and ¼ = 15 and _/20 B. Get the smallest common dividend (SCD) first then rename the fractions and solve for the sum. 6. 1/6 + 2/5=
7. 7/10 + 1/5 =
SCD: _______
SCD: _______
8. ¾ + 2/9=
9. 5 and 5/16 + 6 and ¼ =
SCD: _______
SCD: ________
10. 15 and 2/7 + 20 and ½ = SCD: _____ B. Complete the subtraction process. 1. 5/8 = __/8 – ½ = __/8
2. 4/10 = __/30 – 1/3 = __/30 =2/30 or
=
3. 2/3 = __/15 – 3/5 = __/15
4. 5 and 2/3 = 5 and __/24
=
- 3 and 3/8 = 3 and __/24 =2
5. 9 and 5/6 = 9 and ___/18 -- 4 and 4/9 = 4 and __/18 = Find the difference. Express all answers in simplest form. 6. 6/10 =
7. 5/9 =
8. 11/12
-- ¼ =
-- 1/3 =
--- 2/4
________
__________
_________
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9. 6 and 5/14 =
10. 10 and 2/3 =
--- 2 and 2/7 =
--- 7 and 2/4 =
--------------------------
----------------------------
C. Read each problem carefully. Write an equation, solve and express the final answer in simplest form. 1. Mother bought ¼ kg of tomatoes and 1/3 kg of cabbage. a. How many kilograms of vegetables did Mother buy? b. Which are heavier, tomatoes or cabbage? By how much? 2. Father is doing carpentry work he needs 3/8 kg. Of one- inch nail and 2/6 kg of two- inch nails. How many kilograms of nails doe’s father need in all?
3. Father weighs 50 and 2/5 kg. Mother weighs 40 and 3/15 kg. How much heavier is Father than Mother?
EXCEL Rename 1 as a fraction then find the difference of the following: 1.
1- 2/7 =?
2.
1- 5/10= ?
3. 1- 6/15 =? What is the missing addend in the equation below? ¼ + 1/5 + = 1
LESSON 8: FRACTION OF A NUMBER On the table is a basket of fruits. If there are 15 fruits and 1/5 of these are oranges, the rest are bananas, how many oranges are there? Young Ji International School/College
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What is 1/5 or 15? Let us illustrate 1/5 of 15.
We divided 15 into 5 equal groups. One group is 1/5. 1/5 of 15= 3. Therefore, there are 3 stars in the basket So, what is 4/5 of 15? 4 groups of threeâ&#x20AC;&#x2122;s is 12. 4/5 or 15 = 12= There are 12 bananas in the basket. Analyze these: 1/5 of 15 is the same as 1/5 x 15/1 = 1 x 5 = 15/5 = 3 5x 1 2/5 of 15 is the same as 2/5 x 15/1 = 2x15 = 30/5 = 6 5 3/5 of 15 is the same as 3/5 x 15/1 = 3 x 15= 45/5 = 9 5 4/5 of 15 is the same as 4/5 x 15/1 = 4 x 15 = 60/5 = 12 Another example: I bought 18 marbles. I gave my best friend 2/6 of these marbles. How many marbles did I give away?
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Divide 18 marbles into 6 equal groups. There are 3 marbles in each group. There are 6 marbles in 2 groups. We solve: 2/6 of 18
2/6 x 18/1 = 2x18= 36/6= 6 6
Therefore, 6 marbles were given away. Can you illustrate 3/10 of 20 in the box below? What is the value?
EXPERIENCE A. Divide the objects into equal portions then fill in the box.
1.
2.
1/3 of 12= 4.
7. 1/9 of 18= Young Ji International School/College
½ of 14 =
1/5 of 15 =
5.
1/6 OF 18=
3.
6.
¼ OF 20=
1/3 OF 15=
8. 1/8 of 16= Page 89
B. Group the objects. Write your answer on the circle. 1.
2.
4/6 of 18=
2/3 of 12=
3.
4. 3/7
4/5 of 20 =
of 21=
5. 5/8 of 16=
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C. Find the value each. 1. 1/3 of 27= ________________ _____________
3. 3/5 of 10=
2. 2/4 of 16 = _______________
4. 4/6 of 18= ____________
Read each problem then solve. 5. Kathy has 25 popsicle sticks. Of these, three- fifths are green. How many green popsicle sticks does Kathy have?
6. Alex has 30 colored seashells. 1/6 of them are brown. How many brown seashells does Alex have? Excel Work with a partner. (You may use Philippine coins and bills.) Do what is asked. 1. What is 1/10 of P100? 2. What is the value of 2/5 of P200? 3. Find 2/3 of P90.
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Chapter 7: Decimals and Money Lesson 1: Place Value of Decimals
EXPOSE: The shoppers were attracted to the Christmas trees on display? There were 10 Christmas trees. Of these, 6 were tall and 4 were small. What attraction represents the tall Christmas trees display? In how many ways can this number be written? 6 out of 10 Christmas trees on display were small. It can be written as a fraction 6/10. It can also be written as a decimal 0.6. 4 out of 10 Christmas trees on display were small. It can be written 4/10 as a fraction and 0.4 as a decimal. Study the chart below. Fraction 6/10 4/10
Written as decimal 0.6 0.4
Read as Sis- tenths Four- tenths
If one whole is divided into 10 equal parts, 1 part is called 1/10 or one tenth (0.1) If one whole is divided into 100 parts, one part is called 1/100 of one- hundredth (0.01) Let us study further. 1 whole
and
5 tenths
We write: 1 and 5/10 or 1.5 We read or say: one and five- tenths Young Ji International School/College
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Number like 0.6 and 1.5 are called decimal numbers or simply decimals. We can use the place value chart for easy reading of any decimals number. Whole number Ten
Ones 0 0 4 5
Decimal Tenths .9 .5 .6 .4
Hundredths 4 8
Read as: Nine- tenths Fifty- four hundredths Four and six- tenths Five and forty- eight hundredths
Decimal point ( read as “and”) To analyze the decimal 5.48: a. The value of 5 is 5 ones of 5. The digit 5 is in the ones place. b. The value of 4 is 4 tenths. The digit 4 is in the tenths place. c. The value of 8 is 8 hundredths. The digit 8 is in the hundredths place. A decimal number, like fraction shows parts of a whole. A fraction with the denominator 10 or 100 can be written as a decimal number. The number before the decimal point indicates the whole number. If the number is less than 1, we add zero (0) before the decimal point. Examples: 0.6, 0.06 The decimal point is read as “and”. Example: 6.5 is read as six and five- tenths EXPERIENCE A. Write the decimal number for the shaded parts shown. 1.
2.
__________
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___________
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3.
4.
______________
______________ 5.
_______________ Write the following in decimal form. 6. nine and nine- tenths
________________
7. thirty- eight hundredths 8. seventeen hundredths
________________ ________________
9. ten and nine hundredths 10. one hundred two and three tenths
________________ ________________
B. Write the following decimal numbers in words. 1. 0.78
_________________________
2. 12. 05
_______________________
3. 6. 99
________________________
4. 130. 04
______________________
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5. 25. 25
_______________________
Write a decimal for each fraction. 6. 16/100 =
___________________________
7. 4 and 3/10 =
__________________________
8. 9 and 2/100=
__________________________
9. 35/100 = ____________________________ 10. 2 and 56/100=
____________________________
C. Refer to the given decimal number. Complete the sentences that follow.
98.76 1. The digit ________ is in the ones place. Its value is _________. 2. The digit ________ is in the tens place. Its value is ______________. 3. The digit ________ is in the tenths place. Its value is ___________. 4. The digit ________ is in the hundredths place. Its value is _______. 5. The decimal numeral is written and read as ________________________________________________________________ Read each problem and do what is asked. Seven out of ten grade 3 soccer players passed the training. Write a fraction for the number of players that passed the training.
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7. There are 100 parents in the assembly. 45 of them are fathers. Write a decimal for the number of fathers present in the assembly.
8. Write these amounts of money in words. a. P 5.05
___________________________________
b. P 10. 95
____________________________________
c. P 206. 10
___________________________________
EXCEL 1. Solve the number puzzle. Answer: _____________ 706 The number is less than 1. The digit in the tenths digit is two less than the hundredths digit. 2. Using the digits 0, 1, 2, 3 and 4, form a decimal number whose value is less than 125. Answer: __________________
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LESSON 2: COMPARING AND ORDERING DECIMALS In March, the school nurse usually records the pupils’ heights and weights. Anna’s height is 120.7 cm. Nico’s height is 120.9 cm. Who is taller, Anna or Nico?
We have learned how to compare similar fractions. This time, we will have fractions whose denominators are either 10 or 100. Examples: 5/10 < 8/10
12/100 > 11/100
If we change them to decimals, we write 0.5 < 0.8 and 0.12> 0.11. To answer the question above, we will compare the two decimal numbers 120.7 and 120.9. 1.
120.7
Align the decimal points.
120.9 2.
120 120
. .
Compare the digits.
7
a. The whole numbers are the same.
9
b. Compare the tenths digits. 120.7 < 120.9 Therefore, Nico is taller than Anna. Example: 1. Write the decimals in ascending order. 0.65
3.81
0.7
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2.9
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Steps: a. Align the decimal points. 0.65 3.81 0.7 2.9 b. Compare the ones 3.81 > 2.9 c. Compare the tenths. 0.7 > 0.65
d. Find out the least and the greatest decimals. 0.65 3.81 0.7 2.9 Therefore, in ascending order, the arrangement is: 0.65
0.7
2.9
3.81
2. To arrange the same set of decimals above in descending order is: 3.81
2.9
0.7
0.65
Can you try these yourself? 1. Compare:
5.67 ď Ł 5.7 ;
2. Arrange from greatest to least: 0.3
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0.15 ď Ł 0.09 0.24
1.8
2.01
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To compare decimals: a. Align the decimal points. b. Compare the greatest place value, if they are the same, compare the next greatest place value. c. The first greater digit shows the greater decimal. Putting zero (0) after the last to the right of a decimal point, the value of the digit remains the same. Example: 3.9 = 3.90 To order decimals: a. Align the decimal the decimal points. b. Compare two decimals at a time. c. Arrange the decimals accordingly. A. Encircle the greater decimal. 1.
0.28 0.82
4.
2.12
2. 2.21
0.9
0.69
3.
5.
5.06
6.05
1.01 0.99
Compare. 6.
3.5 0.35
7. 6.7 6.07
9.
4.8 4.80
10.
8.
8.17 87.70
8.06 6.08
B. Ring the greatest decimal and underline the least decimal in each set. 1.
0.48
0.3
0.46
0.29
2.
3.75
3.99
2.8
3.7
3.
4.07
4.1
4.8
4.5
4.
5.7
4.78
6.01
6.16
5.
0.93
0.36
0.8
0.08
C. Arrange each set of decimals in ascending order. Write numbers 1, 2, 3, 4 in each . 1.
0.18
0.81
0.87
0.08
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2.
3.
0.59
5.9
9.5
0.05
4.64
4.46
4.04
4.06
EXCEL Do as indicated. 1. Write a decimal to make each sentence true. 28.06 < 5. 24 > 2. Arrange the given numerals from least greatest. 3 and 4/100
Two and four- tenths
4/100
0.64
LESSON 3: MONEY and DECIMALS EXPOSE The grade 3 classes supported the project “SagipKaklase”, to help their classmates who were victims of the typhoon. Section 1 did their own collection. They were able to collect bills and coins as follows. 2 five hundred- peso bills 5 twenty- peso bills 10 ten- peso coins 4 twenty- five centavo coins
How do we read and write these amounts? Are you familiar with the Philippine bills and coins? Young Ji International School/College
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P500 This is five- hundred- peso bill. Two of these make one thousand pesos or P1000.00 P20 This is a twenty- peso bill. 5 of these make one hundred pesos or P100.00 10 peso
This is a ten- peso coin. 10 of these make P100.00
25 peso one peso or P1.00
This is a twenty- five centavo coin. 4 of these make
Let’s find out the amount of collection section 1 had. P 1,000.00 100.00 + 100.00 1.00_____ This is read as “one thousand two hundred one peso.”
P1201.00
Reading and writing money is similar to reading and writing decimal numbers. We also use a decimal point to separate the pesos from centavos. is read as “six pesos and fifty- five centavos”.
Examples: P6.65 0.75
is read as “seventy- five centavos”. It can also be written using the centavo sign (75¢). P29.60
pesos centavos decimal point (read as “and”) We also compare money values the same way as we do with decimal numbers. Examples: 1. P56.65 P55.70 Compare the digits in the ones place. Young Ji International School/College
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6>5 Therefore, P56.65 > P55.70. 2. P48.50 P58.60 Compare the tens digits. 4<5 Therefore, P48.50 < P58.60. 3. P125.75 P125.80 Compare the tenths digits. 7<8 Therefore, P125.75 < P125.80. 4. P3.76 P3.7 Compare the hundredths digits 6>1 Therefore, P 3.76, P3.76>P3.71. EMPHASIZE We use the P (peso) and ¢ (centavo) signs to write amounts of money. In reading an amount of money, the number before the decimal point is read as peso (s) and the number after the decimal point is read a centavo(s). The decimal point is read as “and”, similar to reading decimal numbers. The symbols >, =, < are used to compare money values. A. Read each amount orally. 1. P10.58
4. P50.10
2. P12.05
5. P100.60
3. P15.15
6. P500.75
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Write each amount in words. 7. P1000.00
_______________________________________
8. P975.00
________________________________________
9. P640.50
________________________________________
10.P200.10
_______________________________________
B. Write each amount using peso notation. 1. Nine pesos and fifty centavos. ___________________ 2. Twenty pesos and sixty centavos. _________________ 3. Fifty pesos and fifteen centavos. ___________________ 4. Three hundred twenty- five pesos ___________________ 5. Four hundred pesos and forty centavos ________________ C. Compare. Write >, =, or < in each ☼. 1.
P38.80
☼
P38.08
2.
P59.95
☼
P95.59
3.
P20.00
☼
two ten- peso coins
4.
75¢
☼
4 twenty- five centavo coins
5.
P100.00
☼
2 fifty- peso bills
Find the value of the following. Use peso notation. 6. P500, P20, P20= _____________ 7. P500, ¢25 = _________________ 8. P500, P500= ________________ Get 3 classmates to work with you.
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Show different combinations of Philippine coins and bills to come up with the amount P400.50.
LESSON 4: ADDITION and SUBTRACTION of DECIMALS and MONEY EXPOSE For recess, Rina bought a sandwich that cost P25.50 and a glass of pineapple juice that cost P15.50. a. How much did Rina spend in all for recess? b. If she gave the cashier a fifty- peso bill, how much change did she receive? EXPLORE To find the total amount Rina spent, we add. Follow these steps using shortcut method. Step 1
Step 2
Step 3
Step 4
Arrange the numbers in vertical order. Align the decimal points. Add the hundredths.
Add the tenths.
Regroup. Add ones.
Regroup. Add the tens.
P25.50. +15.50 1.00
P25.50 +15.50 41.00 Decimal point aligned with the other decimal points.
P25.50 +15.50 00
P25.50 +15.50 0
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Rina spent P41.00 for the sandwich and juice. Other examples: 1. Father walks 1.75 km on a Saturday and 2.2 km on a Sunday. How far does Father walk on a weekend? Solution: 1.75 +2.20Annex a zero. 3.95 Therefore, Father walks 3.95 km on a weekend. 2. Karen has saved P112.50. Kiara has saved P160.75. How much more has Kiara saved than Karen? Solution: P160.75 -112.50 P48.25 Threfore, Kiara has saved P48.25 more than Karen.
To add/subtract decimals and money. Arrange the numbers in vertical order; align the decimal points. Annex zero, if needed, to fill the empty places. Add or subtract the same way with whole numbers. Regroup when needed. Write the decimal point in line with the other decimal points.
EXPERIENCE A. Arrange the decimals in column and add. 1. 13.6 + 2.9= _____________ 2. 9.5 + 3.08 = ______________
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3. 35 + 65.92= ______________ 4. 18.24 + 16.83= _____________ 5. 21.6 + 14.09 + 6.7= ______________ 6. P50.854 + P60.15= _______________ 7. P98.05 + P12.75= ________________ 8. P8.20 + P31.35= _________________ 9. P65.10+ P82.25= ________________ 10. P125.70+ P306.80= ________________ B. Arrange the decimals in vertical order and subtract. 1. 16.3 – 12.8= ______________________ 2. 25.16 – 8.90= _____________________ 3. 34.9 – 18.7 = ______________________ 4. 132.6 – 94.8= ______________________ 5. 555 – 400.9= _______________________ 6. P24.60 –P10.90= ___________________ 7. P35.75 – P20.75= ____________________ 8. P67.10 – P54.80= ____________________ 9. P85.95 – P51.60= ____________________ 10. P150.00- P75.00= ___________________ C. Do what is indicated. Write your answer in the blank. 1. Find the sum of 24.64, 35.9, and 48.62. ______________________________________________________________ 2. Subtract six and three-tenths from ten and nine tenths. Young Ji International School/College
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______________________________________________________________ 3. Add five pesos and fifty centavos to eighteen pesos then subtract fifteen pesos and ninety- five centavos. _____________________________________________________________ 4. Solve for N. (52.9 + 6.16)- 38.88= N _____________________________________________________________ 5. Find the total amount of the following: 3 twenty- peso bills 2 fifty-peso bills 1 two hundred-peso bill__________________________________________ Excel From the given decimal numbers, make: a. 3 pairs that have a total 10
b. Three pairs that have a difference
of P5.00 9.6 1.8 6.1 0.4 3.9 8.2
P15.50 P13.80 P8.80 P1.40 P20.5 P6.40
________________
_______________
________________
_______________
________________
_______________
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LESSON 5: WORD PROBLEMS INVOLVING ADDITION AND SUBTRACTION OF DECIMALS AND MONEY EXPOSE Jenny spent 1.75 hours, surfing the net and paid P26.25. Jason spent 2.15 hours and paid P33.50. a. How many hours did the two children spend surfing the net? b. How much more did Jason spend in surfing the net than Jenny? EXPLORE Do you remember the 4- Point Checklist in solving problems? Let use these to answer the questions above. 4-Point Checklist or steps in Problem solving. 1. Read and Understand the problem. What are the given facts? 1.75 hours and 2.15 hours What is asked in the problem? How many hours did the two children spend surfing the net? 2. Plan to solve the problem. What operation(s) should be used? addition What is the number sentence? 1.75 + 2.15= 3. Solve. 1.75 + 2.15= 3.90 4. Check the answer. Is the answer reasonable? Yes Therefore, the two children spent 3.90 of 3.9 hours. Let us find the answer to the second question. Given Facts P26.25—spent by Jenny
Operation(s) to be used/Number Sentence P33.50- P26.25= N
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Solve
Final Answer
P33.50
Jason spent P7.25 more than what Jenny spent. Page 108
P33.50--- spent by Jason
-P26.25 P7.25
EMPHASIZE
To solve word problems, follow the 4 steps: identify the given facts Write a number sentence Solve Check and label the final answer
EXPERIENCE A. Solve each problem by answering the given questions. 1. Aliya bought the book “Diary of a Wimpy Kid” for P299.00 and a plastic cover for P25.50. How much did Aliya spend in all? a. What are the given facts? ____________________________ b. What is asked? _________________________ c. What is the number sentence? ________________________ d. What is the answer? _______________________________ 2. Her sister Kiara bought a pocketbook for P495.95. How much change did she receive from her P500.00 bill? a. What are the given facts? __________________________ b. What is asked? ______________________ c. What is the number sentence? ______________________ d. What is the answer? __________________________ 3. For their Science project, Adam bought an illustration board that cost P35.90, 10 pieces of art paper for P19.50 and a tube of paste for P10.75. What is Adam’s total expense? a. What are the given facts? _________________________ b. What is asked? ____________________________________ Young Ji International School/College
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c. What is the number sentence? ______________________ d. What is the answer? __________________________ 4. Jade started saving for the Christmas party. She needs to buy gifts for her parents, brothers, and sisters which will cost P215.00. If she has saved P132.50, how much does she still need? a. What are the given facts? _______________________ b. What is asked? ________________________________ c. What is the number sentence? __________________________ d. What is the answer? _____________________________________ B. Fill in the boxes to solve each problem. 1. From Antipolo City to Balintawak is 29.5 km far. From Balintawak to Sta. Maria, Pangasinan is 153 km far. How far is it from Antipolo City to Sta. Maria, Pangasinan? Number Sentence
Solution
Answer
2. Father bought 12 liters of gasoline for P651.12. How much change did he get if he gave the cashier a thousand- peso bill? Number Sentence
Solution
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Answer
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3. Jun joined the “bikathlon”. He was able to bike 20.75 km far. If the winner biked 21.90 km far, how much farther did the winner bike than Jun? Number Sentence
Solution
Answer
4. Nico jogged 3.65 km on Monday, 2.79 km on Wednesday and 3.7 km on Friday. How many km did Nico jog on those three days? Number Sentence
Solution
Answer
C. Read the given problem. Use the data to solve. The Simon family puts up a garage sale of the following items:
P50.95
P99.95
P100.75
P65.50
P10.70
1. Ernie bought a pair of pants and t-shirt. How much did he pay?
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2. Bert bought jacket and a pair of slippers. How much change did he get if he gave the cashier a two-hundred peso- bill. 3. How much more does the pair of pants cost than the jacket?
4. How much less does the t-shirt cost than the bag?
5. Which 3 items willType equation here. you buy if you gave 3 hundred- peso bills to get a change of P33.80?
EXCEL Read the given situation carefully. Lolo Jose owns two pieces of land with the measurements shown below? A.
B. 12 m 15 m
18m
a. If he encloses both using barbed wire, would piece of land A needed longer wire than piece of land B? b. Why or why not? Prove your answer.
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