ANSWER KEY MATH TEXTBOOK
C A L V E R T E D U C A T I O N
05MAKA Textbook
12
Chapter 1
Whole Numbers
Page 4
Quick Check
1 Ninety-five thousand, seven hundred eighteen
2 78,213 3 30,000 + 1,000 + 400 + 80 + 5 4 20 5 30
6 50 7 70 8 21,345 9 9,991 10 900 11 1,200 12 2,900
13 9,000 14 900 + 500 = 1,400 15 900 – 200 = 700
16 500 + 400 = 900 17 700 – 300 = 400
Pages 6–13
Guided Practice
1
400,000500,000
800,000
Six hundred thousandSeven hundred thousand
Nine hundred thousand
2
five hundred fifty-seven thousand, six hundred seventy-six
557,676
500,000
7,000
70
50,000
600
6
five hundred thousand
fifty thousand
seven thousand
six hundred
seventy
six
5
7
5
6
6
7
3 686,044; six hundred eighty-six thousand, forty-four
4 Three hundred twenty-five thousand, one hundred
seventy-six 5 Four hundred thirty-eight thousand, eight
hundred thirty-four 6 Nine hundred six thousand,
ninety-six 7 Six hundred eighty thousand, eight hundred
six 8 Seven hundred thousand, seven 9 Nine hundred
ninety-nine thousand, nine hundred ninety-nine
10
9,000,000
Four million
Eight million
11 4 4,000,000;
four million
0
300
600,000
5,000
70
9
three hundred
six hundred thousand
five thousand
seventy
nine
0
7
6
3
5
9
4,605,379
four million, six hundred five thousand, three hundred seventy-nine
12 6,340,581
six million, three hundred forty thousand, five hundred eighty-one
13 One million, two hundred thirty-four thousand, five
hundred sixty-seven 14 Two million, six hundred fifty-
three thousand, three hundred fifty-six 15 Four million,
four hundred four thousand, forty-four 16 Eight million,
eight hundred eighty-eight thousand, eight hundred
eighty-eight 17 Five million, ninety thousand, nine
hundred nine 18 Seven million, six thousand, sixty
Page 14
Let’s Practice
1 200,106 2 9,000,520 3 5,002,012 4 two hundred fifteen
thousand, nine hundred five 5 eight hundred nineteen
thousand, two 6 six million, four hundred thirty
thousand 7 five million, nine thousand, three hundred
Pages 14–15
Let’s Explore!
3a –8 3b –50 3c –173 3d –2,469
1.2: Place Value
Pages 16–18
Guided Practice
1 600,000 2 0 3 1 4 tens 5 ten thousands 6 2,000
7 200,000 8 20,000 9 thousands 10 hundred thousands
Answer Keys Part A
MathTextbook
© Marshall Cavendish Education
ANSWER KEY MATH TEXTBOOK
C A L V E R T E D U C A T I O N
05MAKA Textbook
13
11 ten thousands 12 60,000 13 100,000 14 50 15a 7
15b 200,000 15c ten thousands 16 200,000
17 6,000,000 18 50,000
Page 19
Let’s Practice
1 50 2 500 3 50,000 4 500,000 5 9 6 600,000
7 300,000; thousands 8 20,000 9 6,000,000 10 600
11 600,000 12 60,000 13 7 14 3 15 300 16 2,000,000
1.3: Comparing Numbers to
10,000,000
Pages 21–23
Guided Practice
1 greater
>
9 8
2 3 04,730,589; 4,703,9854,730,589; 4,703,985
3 < 4 > 5 > 6 < 7 32,468 324,688 3,246,880
8 1,064,645 1,600,456 1,604,654
9
10
Pages 23–24
Let’s Practice
1 568,921 2 71,690 3 816,300 4 12,500 5 199,981
714,800 901,736 6 645,231 645,321 654,987 7 925,360
360,925 36,925 8 474,108 474,089 445,976
9 20,000
20,000
20,000
20,000; 660,356
10 200,000
200,000
200,000
200,000; 3,230,875
11 Rule: Count back by 10,000. 315,410; 285,410
12 Rule: Count on by 1,010,000. 5,420,000
1.4: Rounding and Estimating
Pages 25–31
Guided Practice
1
9,000
9,0009,000; 8,000
2 7,000 3 8,000 4 8,000
5 125,231 125,780
125,780 rounds to 126,000; 125,231 rounds to 125,000.
6 6,000 7 10,000 8 7,000 9 12,000 10 66,000 11 90,000
12 326,000 13 600,000 14a 3,500 14b 79,500
15a 7,499 15b 50,499 16 7,000 + 2,000 = 9,000
17 6,000 – 3,000 = 3,000 18 6,000 + 6,000 + 4,000 =
16,000 19 10,000 – 2,000 – 7,000 = 1,000
20 4,000
7,0006,175; 6,000
1,100; 1,000
4,000; 7,000; 6,000; 17,000
17,000; 1,000; 18,000
18,000
879; 175; 200; 800; 100; 1,100
21 15,000 22 20,000 23 19,000 24 17,000
25 9,0002,215; 2,000
9,000; 2,000; 7,000
215; 800; 200; 600600; 1,000
7,000; 1,000; 8,000
8,000
26 3,000 27 4,000 28 4,000 29 3,000 30 5,000
31 8,000
3,860; 3,0008,000; 3,000; 5,000
275; 800; 200; 600
600; 1,000
5,000; 1,000; 4,000
4,000
32 2,000 33 3,000 34 2,000 35 8,000
ANSWER KEY MATH TEXTBOOK
C A L V E R T E D U C A T I O N
05MAKA Textbook
14
Pages 33–35
Guided Practice
36 6,0006,000; 42,000
42,000
14,000
37 14,000 38 54,000
39 6,400
6,400; 800
8006,400; 7,200
40 600 41 700
Let’s Practice
1 80,000 2 229,000 3 550,000 4a 7,500 4b 60,499
5 2,000 6 18,000 7 17,000 8 12,000 9 6,000 10 3,000
11 24,000 12 45,000 13 900 14 900
Page 35
Put on Your Thinking Cap!
1 Any number from 25 to 29 and 31 to 34 2a 2 × 100 − 2
= 198 2b 6 × 100 − 6 = 594 2c 8 and 4 2d 9
Page 38
Chapter Review/Test
1 periods 2 word form; million 3 front-end estimation
with adjustment 4 compatible numbers 5 5,896,413
6 five million, eight hundred ninety-six thousand, four
hundred thirteen 7 5,000,000 + 800,000 + 90,000 + 6,000
+ 400 + 10 + 3 8 900,000 9 2,000,000 10 ten thousands
11 > 12 < 13 Rule: Count back by 500,000. 7,084,671;
6,584,671 14 Rule: Count on by 1,100,000. 3,600,534;
4,700,534 15 2,000 16 527,000 17 11,000 18 15,000
19 3,000 20 3,000 21 45,000 22 24,000 23 800 24 900
25 three million, eight hundred fifty-one thousand, eight
hundred eight square miles 26 Canada, United States,
France, Thailand, Hong Kong, Singapore 27 Canada and
United States 28 France and Thailand
Chapter 2
Whole Number Multiplication and
Division
Page 44
Quick Check
1 8,000,000; 700,000; 50,000; 3,000; 900; 20; 4; Eight
million, seven hundred fifty-three thousand, nine
hundred twenty-four 2 5,000,000; 900,000; 5,000; 400;
70; 8; Five million, nine hundred five thousand, four
hundred seventy-eight 3 +; 163 4 −; 202 5 ×; 98 6 ÷; 16
7 ÷; 27 8 1,000 9 10,000 10 15,000 11 200 × 6 = 1,200
12 800 × 4 = 3,200 13 900 × 3 = 2,700 14 100 × 9 = 900
15 900 × 5 = 4,500 16 300 × 6 = 1,800 17 180 ÷ 3 = 60
18 250 ÷ 5 = 50 19 540 ÷ 6 = 90
2.1: Using a Calculator
Page 49
Hands-On Activity
1 9,442 2 1,699 3 10,602 km 4 $1,385
Page 50
Hands-On Activity
1 103,305 2 95,718 3 43 4 271 5 1,200 m2 6 14.5 oz
2.2: Multiplying by Tens, Hundreds,
or Thousands
Pages 53
Hands-On Activity
2
4
3
1
4
0
5
8 0
0
1 2,310 2 23,450 3 41,080 To multiply a whole number by 10, just write a zero after the number.
Guided Practice
1 600 2 1,350 3 5,030 4 28,760 5 60,820 6 60,100 7 10
8 10 9 528 10 7,460
Page 55
Hands-On Activity
� 6 � 60
42 252 2,520
65
861
1 10 2 6; 10 3 6; 10
ANSWER KEY MATH TEXTBOOK
C A L V E R T E D U C A T I O N
05MAKA Textbook
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Pages 55–56
Guided Practice
11 � � 10
�
12 � (307 � ) � 10
� � 10
�
13 13,700 14 177,300 15 325,800
Page 58
Hands-On Activity
Millions HundredThousands
TenThousands Thousands Hundreds Tens Ones
174 1 7 4
174 � 100 1 7 4 0 0
174 � 1,000 1 7 4 0 0 0
3,298 3 2 9 8
3,298 � 100
3,298 � 1,000
1 17,400 2 174,000 3 329,800 4 3,298,000
Left speech bubble: To multiply a whole number by 100,
just write two zeros after the number. Right speech
bubble: To multiply a whole number by 1,000, just write
three zeros after the number.
Page 59
Guided Practice
16 2,700 17 61,500 18 967,000 19 18,000 20 487,000
21 5,346,000 22 100 23 1,000 24 490 25 168
Page 60
Hands-On Activity
791 79,100 791,0001,757 175,700 1,757,000
1 100 2 7; 100 3 7; 100 4 1,000 5 7; 1,000 6 7; 1,000
Pages 60–63
Guided Practice
26 288; 28,800 27
86186,100
7 100
28 30; 30,000
29 18 � 6,000 � (18 � ) �
� � 1,000
�
30 40,500 31 745,600
32 5,809,500 33 4,805,600 34 292,000 35 7,240,000
36 1,962,000 37 7,263,000
38 228 rounds to , and 57 rounds to 60.
� 60 � ( � 6) � 10
� � 10
�
39 14,000 40 12,000 41 8,000 42 18,000 43 30,000
44 16,000 45 1,238 rounds to 1,000, and 56 rounds to .
1,000 � � (1,000 � ) �
� �
�
46 4,000
47 28,000 48 270,000 49 80,000
Page 63
Let’s Practice
1 4,120 2 79,200 3 740,000 4 42,180 5 570,500
6 507,000 7 36,000 8 80,000 9 600,000 10 30,000 beads
2.3: Multiplying by 2-Digit Numbers
Pages 65–69
Guided Practice
1 Estimate the value of 97 � 53.
97 rounds to , and
53 rounds to .
� � The estimate shows the answer
is .
9 7� 5 3
multiply 97 by ones
multiply 97 by tens
add
ltiply. Show your work.
2 6,480 3 1,000 4 2,380 5 228 6 2,860 7 2,736 8 9,405
9 7,735
10 Check!
1,02835,98037,008
27
70500 35,000
37,008 reasonable
11 40,860 12 16,800 13 45,570 14 4,956 15 10,836
16 14,112
17 Check!
36,820184,100220,920
42 209,000 180,000
220,920 reasonable
209,000
18 62,300 19 354,780 20 46,928 21 343,440 22 115,056
23 119,145
ANSWER KEY MATH TEXTBOOK
C A L V E R T E D U C A T I O N
05MAKA Textbook
16
Page 69
Let’s Practice
1 600 2 2,870 3 15,000 4 34,400 5 37,170 6 140,000
7 148,000 8 153,000 9 1,792 10 1,976 11 45,353
12 56,373 13 278,478 14 56,520
2.4: Dividing by Tens, Hundreds,
or Thousands
Page 72
Hands-On Activity
1 36 2 158
Guided Practice
1 9 2 38 3 190 4 4,365 5 2,304 6 5,360 7 10 8 10
9 49,000 10 16,800
Page 73
Hands-On Activity
9 90
540 60 6
720
810
1 10 2 10; 9 3 10; 9
Page 74
Guided Practice
11 85; 17 12 7,200 � 80 � (7,200 � ) �
� � 8
�
13 4 14 14
15 316 16 140
Page 76
Hands-On Activity
TenThousands Thousands Hundreds Tens Ones
700 7 0 0
700 � 100 7
3,600 3 6 0 0
3,600 � 100
8,000 8 0 0 0
8,000 � 1,000
54,000 5 4 0 0 0
54,000 � 1,000
1 7 2 36 3 8 4 54
Left speech bubble: To divide a multiple of 100 by 100,
just drop the two zeros. Right speech bubble: To divide a
multiple of 1,000 by 1,000, just drop the three zeros.
Page 77
Guided Practice
17 4 18 15 19 205 20 10 21 124 22 3,230
Page 78
Hands-On Activity
6 600
1,200 200 2
4,200
5,400
1 100 2 100; 6 2 100; 6
8 8,000
32,000 4,000 4
48,000
64,000
1 1,000 2 1,000; 6 2 1,000; 8
Pages 79–80
Guided Practice
23 24; 6 24 35; 5 25 4 26 9 27 8 28 6 29 9
30 51 31 4,200; 4,200; 100; 6 32 1,000 ÷ 20 = 50
33 6,000 ÷ 30 = 200 34 5,000 ÷ 100 = 50
35 3,600 ÷ 400 = 9
Page 80
Hands-On Activity
Sample answers:
Divisors for 4,500:
Number Can be divided by Answer
4,500 10 4,500 ÷ 10 = 450
4,500 300 4,500 ÷ 300 = 15
4,500 1,500 4,500 ÷ 1,500 = 3
Divisors for 420:
Number Can be divided by Answer
420 10 420 ÷ 10 = 42
420 30 420 ÷ 30 = 14
420 70 420 ÷ 70 = 6
Divisors for 2,000:
Number Can be divided by Answer
2,000 20 2,000 ÷ 20 = 100
2,000 200 2,000 ÷ 200 = 10
2,000 1,000 2,000 ÷ 1,000 = 2
ANSWER KEY MATH TEXTBOOK
C A L V E R T E D U C A T I O N
05MAKA Textbook
17
Divisors for 40:
Number Can be divided by Answer
40 10 40 ÷ 10 = 4
40 20 40 ÷ 20 = 2
40 40 40 ÷ 40 = 1
Divisors for 88,000:
Number Can be divided by Answer
88,000 80 88,000 ÷ 80 = 1,100
88,000 400 88,000 ÷ 400 = 220
88,000 4,000 88,000 ÷ 4,000 = 22
Page 81
Let’s Explore!
1 4.3 2 7.35
Let’s Practice
1 87 2 900 3 71 4 820 5 3 6 97 7 25 8 101 9 27 10 82
11 2 12 6 13 6,800 ÷ 20 = 340 14 3,600 ÷ 12 = 300
2.5: Dividing by 2-Digit Numbers
Pages 82–88
Guided Practice
1 3 2 80 3 57 R 70
4 20
48
64
17
1
4 1
20
20
4small
60
The quotient is 15 and the remainder is 2.
5 30
96
6430
2 30
30
30
2big
90
The quotient is 2 and the remainder is 30.
6 4 R 1 7 4 R 1 8 5 R 4
9
86 0 0
8 12
1 2
The quotient is 8 and the remainder is 12.
10 5 R 18 11 6 R 36 12 8 R 69 13 8 R 66
14
12
01
7
5 2
01 52
1
1
5
The quotient is 15
and the remainder is
2.
15 13 R 10 16 19 R 5 17 12 R 33 18 35 R 18
19
510 4
0 9
1 53
5 65 3
9
9
1
The quotient is
91 and the
remainder is 53.
20 90 R 31 21 79 R 13 22 44 R 42 23 87 R 80
24 3 6 6, 4 7 9
R
36 � hundred
36 � tens
36 �
The quotient
is 179 and the
remainder is
35.
25 334 R 13 26 165 R 7 27 142 R 29 28 117 R 55
Page 89
Math JournalStep 1: Round 32 to the nearest ten. Then estimate the
quotient.
32 rounds to 30.
6 × 30 = 180
The quotient is about 6.
63 0 1 8 7
1 8 0
Step 2: Check if the estimated quotient is too big or too
small.
The estimated quotient, 6, is too big. Use 5 as a
quotient.
Step 3: Work out the division using 5 as a quotient.
The quotient is 5 and the remainder is 27.
63 2 1 8 7
1 9 2
53 2 1 8 7
1 6 02 7
ANSWER KEY MATH TEXTBOOK
C A L V E R T E D U C A T I O N
05MAKA Textbook
18
Let’s Practice
1 3 2 1 R 20 3 1 R 22 4 13 R 10 5 8 6 10 R 81 7 8 R 9
8 8 R 16 9 90 10 177 R 1 11 125 R 25 12 146 R 27
2.6: Order of Operations
Pages 90–93
Guided Practice
1 20 2 66 3 31 4 23 5 40 6 84 7 2 8 120 9 153 10 55
11 25 12 14 13 46 14 15 15 8 16 23 17 77 18 10
19 184 20 64 21 9 22 42
Page 94
Let’s Explore!
1 The answers are the same.
2 Number sentence Partner A’s answers Partner B’s answers
9 � 6 � 5
48 � 4 � 2
36 � 6 � 3
14 � 4 � 2
50 � 8 � 2
Page 95
Let’s Practice
1 110 2 105 3 80 4 2,650 5 133 6 271 7 280 8 6
2.7: Real-World Problems:
Multiplication and Division
Pages 96–101
Guided Practice
1 100 ÷ 15 = 6 R10; There are 6 bags of potatoes. 10
pounds of potatoes are left.
2 17225
2522
1 71221
1726
67
3 2,2502,250; 6,750
6,750
4 Amount paid � number of payments � amount for each payment
� 45 � $478
� $
Then, fi nd the cost of the car.
Cost of car � total amount paid � amount she still has to pay
� $ � $3,090
� $
Which operation will you use to fi nd how much she would pay for each of the 60 payments?
$ � $
She would pay $ for each of the 60 equal payments.
Cost of the car:
(45 � $478) � $3,090
� $
.� �
5 Total number of hours � h
Parking fee for the fi rst hour � $
Parking fee for the second hour � $
Parking fee from 11 A.M. to 2 P.M. � � $ � $
Total parking fee � $ � $ � $ � $
Mr. Lee paid $ .
Page 102
Let’s Practice
1 41 barrels; 20 gallons of water are left 2 341 stamps
3 245 small boxes 4a 366 packages 4b $732
4c $1,460.50 5 111 cans 6a $1.60 6b 20 ounces
Pages 104–107
Guided Practice
6
247
191319
13
1339
13 39 5252
7 208; 1,6641,664
ANSWER KEY MATH TEXTBOOK
C A L V E R T E D U C A T I O N
05MAKA Textbook
19
8 140140
140 690690
9 Number of Cars Number of
MotorcyclesNumber of
WheelsAre there
50 Wheels?10 10 40 � 20 � 60 No (too many)
9 11 36 � � 58 No (too many)
12 32 � 24 � 56 No (too many)
5 15 20 � 30 � 50
There are motorcycles.
Pages 107–108
Let’s Practice
1 $620 2 $4 3 $58 4 108 pencils 5 $3 6 16 cows 7 196
stamps 8 15 9 956 milliliters
Page 109
Put On Your Thinking Cap!
Method 1: (1,234 × 80) − 1,234 = 97,486
Method 2: (1,234 × 78) + 1,234 = 97,486
79 groups
groups
1,234 �
1,234 � 79
I can rewrite 79 as �1 or � 1.
1,234 � 79 � (1,234 � ) �
1,234 � 79 � (1,234 � ) �
1,234 1,234 1,234
1,234 1,234 1,234
79
�1 �1
Pages 112–113
Chapter Review/Test
1 factors; product 2 dividend; divisor; quotient;
remainder 3 numeric expressions 4 order of operations
5 7,180 6 50,200 7 863,000 8 32,880 9 197,700
10 7,480,000 11–13 Answers may vary. Sample answers
as shown. 11 150,000 12 400,000 13 270,000 14 38,598
15 98,496 16 459,745 17 68 18 70 19 241 20 30
21 23 22 8 23 about 200 24 about 90 25 about 14
26 9 R 16 27 295 R 5 28 228 R 13 29 71 30 216 31 64
32 3,332 33a 1,800 balloons 33b 63 large packets
33c $180
Chapter 3
Fractions and Mixed Numbers
Pages 119–121
Quick Check
1 ¾ ; ¼ 2 5⁄9; 7⁄9 3 2⁄7; ½ 4 5⁄12; 1⁄10
5 2 wholes 4 parts = 24⁄5 6 6 7 3 8 4⁄5 9 ¾ 10 1⁄6; ½ ; ⅔ ;
¾ 11 2; 3; 7 12 14; 18; 10 13
63
2323
2 23
2
68
2
14 3¼ 15 34⁄5 16 ¾ 17 1⁄5
18 ⅞ 19 2¼ 20 ½ 21 1⁄14
22 2⁄9 23 24⁄9 24 0.7 25 0.03
26 0.89
3.1: Adding Unlike Fractions
Page 123
Guided Practice
1 7 4
1114
7 4
2
9 812 12
912
812
17
12 5
12
12 12
1 512
Hands-On Activity
1 ¾ 2 19⁄20 3 11⁄12
Page 124
Guided Practice
3 0 + ½ = ½ 4 1 + 1 = 2 5 0 + ½ + 1 = 1½
Page 125
Let’s Explore!
1 Since both ⅓ and ⅜ are less than ½ , their sum is less
than 1. 2 Since both 5⁄9 and 6⁄11 are greater than ½ , their
sum is greater than 1. 3 5⁄11 is slightly less than ½
whereas 4⁄7 is slightly more than ½ . So, we cannot tell by
estimating if the sum of 5⁄11 and 4⁄7 is greater than or less
than 1.
Math Journal
a Model 3 b Model 1: The wrong number of units is
shaded to show ½ . Model 2: The wrong number of units
is shaded to show 1⁄7.
ANSWER KEY MATH TEXTBOOK
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Page 126
Let’s Practice
1 12
910
25
2 7⁄12 3 14⁄15 4 19⁄24 5 ¾ 6 ½ 7 5⁄12 8 11⁄18 9 17⁄30
10 11⁄6 11 19⁄24 12 ½ + 1 = 1½ 13 ½ + ½ = 1
14 0 + ½ + 1 = 1½
3.2: Subtracting Unlike Fractions
Page 128
Guided Practice
1
10 3
7
10
310 3
2 3 212 12
12
7
3 212
12
12 12
3 212 12
Hands-On Activity
1 3⁄14 2 7⁄18 3 3⁄20
Page 129
Guided Practice
3 1 − ½ = ½ 4 1 − 0 = 1 5 ½ − ½ = 0
Let’s Explore!
1 3⁄7 is less than ½ . Subtracting a fraction less than ½
from 1 will give a fraction greater than ½ . So, the
difference between 1 and 3⁄7 is greater than ½ .
2 7⁄12 is greater than ½ . Subtracting a fraction greater
than ½ from 1 will give a fraction less than ½ . So, the
difference between 1 and 7⁄12 is less than ½ . 3 11⁄12 is
about 1 whereas ¼ is about 0. So we can estimate that the
difference between 11⁄12 and ¼ is greater than ½ .
Page 130
Let’s Practice
1 Accept: 45
12
310
810
510
310
45
12
310
2 ⅛ 3 1½ 0 4 1⁄18 5 ½ 4 6 18⁄35 7 ⅓ 6 8 17⁄42 9 7⁄24 10 23⁄30
11 219⁄24 12 1 − ½ = ½ 13 ½ − 0 = ½ 14 1 − 1 = 0
3.3: Fractions, Mixed Numbers, and
Division Expressions
Pages 132–133
Guided Practice
1 4
14
; ¾ ; ¾ ; 34
2 4⁄5; 3 7⁄9 4 ⅝ 5 7⁄11 6 3; 7 7 8; 12 8 3; 10 9 5; 6
10 14 24 2
7
13
2
2
37261
11 19⁄2 = 9½ 12 4¾ = 10¾
13 49⁄5 = 94⁄5 14 5⁄2 = 2½
Page 136
Let’s Practice
1 4; 7 2 5; 11 3 9; 13 4 10⁄12; 5⁄6 5
22
12
112
1
21
6 2⅓ 7 2¾ 8 34⁄7 9 1½ = 5½ 10 8⁄3 = 2⅔
3.4: Expressing Fractions, Division
Expressions, and Mixed Numbers as
Decimals
Pages 137–138
Guided Practice
1 8; 0.8 2 35; 0.35 3 2.4 4 2.68 5 3.6 6 5.35 7a 11⁄5
yards 7b 1.2 yards
ANSWER KEY MATH TEXTBOOK
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Page 139
Let’s Practice
1 0.6 2 0.85 3 0.36 4 0.64 5a 31⁄5 quarts 5b 3.2 quarts
6a 9¾ yards 6b 9.75 yards 7 1¾ , 1.75 8 13⁄10, 1.3 9 11⁄5,
1.2 10 24⁄5, 2.8 11 2¼ , 2.25 10 112⁄25, 1.48
3.5: Adding Mixed Numbers
Pages 141–143
Guided Practice
1
9 8
9 818 18
1718
5
2 4 36 6
16
76
6
34
3 6½ + 9½ = 16 4 12 + 5½ = 17½ 5 8½ + 10 = 18½
6 32 + 15 = 47 7 17 + 37½ = 54½
Page 143
Let’s Explore!
1 Since ¼ and 4⁄9 are less than ½ , their sum must be less
than 1. So, the sum of 1¼ and 34⁄9 must be less than 5.
2 Since 5⁄9 and 7⁄12 are greater than ½ , their sum must be
greater than 1. So, the sum of 35⁄9 and 27⁄12 must be
greater than 6. 3 ⅜ is less than ½ whereas 3⁄5 is greater
than ½ . We cannot tell if the sum of ⅜ and 3⁄5 is greater
than or less than 1. So, we cannot tell by estimating if the
sum of 3⅜ and 53⁄5 is greater than or less than 9.
Page 144
Let’s Practice
1 313⁄20 2 717⁄24 3 9¼ 4 339⁄40 5 9½ 8 6 81⁄18
7 1½ + 3½ = 5 8 5 + 7 = 12 9 44 + 69½ = 113½
3.6: Subtracting Mixed Numbers
Pages 145–148
Guided Practice
1 5 39
29
3
3
2 810
3 2
1
510
310
3
183 183
1518
101828 15
1813
1518
10
4 8 − 3½ = 4½
5 23½ − 17 = 6½
Pages 148–149
Let’s Practice
1 2¼ 2 31⁄6 3 2⅝ 4 111⁄12 5 13⁄24 6 31⁄6 7 75⁄21
8 29⁄10 9 2⅝ 10 211⁄12 11 625⁄36 12 6½ − 4½ = 2
13 40 − 13½ = 26½
3.7: Real-World Problems:
Fractions and Mixed Numbers
Pages 150–152
Guided Practice
1 5
12125
52
2
52
2
2 29
16 1 2
29
16
718
418
318
718
1 2
3
1 2
3
3 112
112
112
56
56
2
2
2 4
4
Let’s Practice
1 11⅔ pounds 2 19⁄20 3 21⁄15 quarts 4 113⁄18 pounds 5 15⁄24
pints 6 105⁄12 pounds
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Page 154
Math Journal
a Leah’s and Marta’s answers are incorrect.
b
15182918
1118 11
18
1118
1418
18
18
11
1
Page 155
Put On Your Thinking Cap!
Pages 158–159
Chapter Review/Test
1 least common multiple 2 equivalent fractions;
mixed number 3 benchmark 4 division expression
5 13⁄14 6 7⁄15 7 ⅜ 8 19⁄36 9 ½ − ½ = 0 10 1 + ½ + 0 = 1½
11 ¾ 12 3⅓ 13 0.25 14 0.72 15 41⁄5, 4.2 16 5¼ , 5.25
17 27⁄18 18 63⁄10 19 5¼ 20 18⁄9 21 4½ + 2½ = 7
22 9 − 2½ = 6½ 23a 1¾ pounds 23b 3½ pounds
23c 15⁄6 pounds
Chapter 4
Multiplying and Dividing Fractions
and Mixed Numbers
Pages 163–164
Quick Check
Answers vary. Sample answers as shown. 1 4⁄6; 6⁄9 2 6⁄8; 9⁄12
3 10⁄12; 15⁄18 4 ½ 5 3⁄5 6 9⁄16 7 2⁄15 8 22⁄7 9 33⁄11 10 4¼
11 3⅔ 12 44⁄9 13 24⁄7 14 59⁄9 15 42⁄5 16 0.75 17 0.65
18 0.84 19 3 20 3¾ 21 13½ 22 53 3
9
39
23
baseball cards soccer cards basketball cards
24 27 25 36
4.1: Multiplying Proper Fractions
Page 166
Guided Practice
1 ¼ 13 × 3
4 = 3
12 = 1
4
2
25 × 5
8 = 10
40 = 1
4
3 1⁄6 4 1⁄6
Page 167
Hands-On Activity
Step 3 3⁄16 Step 6 3⁄16; yes; The products are equal.
Page 168
Let’s Explore!
1 12 8572 84
Finding the product of two whole numbers is the same as
multiplying one number by the number of times given by
the second number. So, the product of any two numbers
is greater than each of the numbers.
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2 3 3
3 58 5
14 54
Finding the product of two proper fractions is the same
as finding a fractional part of another fraction. A proper
fraction is always less than 1, so a fractional part of a
proper fraction will always be less than the original
fractions.
Page 168
Let’s Practice
1 2⁄7 2 ⅓ 3 ½ 4 7⁄20 5 ¼ 6 ⅜
4.2: Real-World Problems:
Multiplying with Proper Fractions
Page 170–173
Guided Practice
1 Method 1
The model shows that:
units gal
unit gal
units gal
a Michelle uses gallon of paint.
b There is gallon of paint left.
Method 2
a 34 � � 12
20
�
Michelle uses gallon of paint.
b 45 � �
There is gallon of paint left.
gal
gal
2
The model shows that:Number of units given to the neighbor �
Total number of units in 1 whole �
jam
a She gives of the strawberries to her neighbor.
b She has of the strawberries left.
Method 2
a 1 � �
of Janice's strawberries is left after she makes jam with 35 of them.
34 � � 6
20
�
She gives of the strawberries to her neighbor.
b � � �
�
She has of the strawberries left.
Page 174
Let’s Practice
1 ½ 2 ⅓ 3 ⅓ yard 4 ⅓ 5 ¼ 6 ⅓ 7 1⁄6
4.3: Multiplying Improper Fractions
by Fractions
Page 176
Guided Practice
1 7⁄15 2 ½ 3 6⁄5 = 11⁄5 4 40⁄21 = 119⁄21 5 15⁄2 = 7½
6 63⁄10 = 63⁄10 7 135⁄16 = 87⁄16 8 12
Let’s Practice
1 1 2 2 3 15⁄4 = 3¾ 4 10 5 119⁄5 = 234⁄5 6 55⁄9 = 61⁄9
7 28⁄3 = 9⅓ 8 253⁄30 = 813⁄30
4.4: Multiplying Mixed Numbers and
Whole Numbers
Page 178
Guided Practice
1 21
3 � 5 � � 5
�
� 333 �
� 11 �
�
213 �
So, 213 � 5 is the
same as groups
of .
the
oups
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Page 179
Hands-On Activity
Step 2d 14
Let’s Explore!
1 2¼ 2 4⅛ 2 � � 4
2 � � 12
Page 180
Let’s Practice
1 4½ 2 4⅔ 3 126 4 362⁄5 5 2006⁄7
4.5: Real-World Problems: Multiplying
with Mixed Numbers
Pages 181–183
Guided Practice
1
920
420
4545
1804
2 12 734
7
25
89.2589.25
89
89
514
3574
14
3 1 bottle qt
3 bottles 3 �
� qt
3 bottles contain quarts
of olive oil.
1 qt of olive oil $5
qt of olive oil � $5
� � $5
�
The total cost of the olive oil is $ .
Page 184
Let’s Practice
1 14 cups 2 31½ 3 37⅛ ounces 4 351¼ pounds 5 $67.50
6 $306
4.6: Dividing a Fraction by a Whole
Number
Pages 186–187
Guided Practice
1 1⁄10; 1⁄10; � �
�
�
Each piece is feet long.
; � 3
5 �
�
�
Each piece is feet long.
2 3⁄11; ⅓ ; 3⁄11
Page 188
Hands-On Activity
1 Counta the total number of parts,
b the number of colored parts.
14 � 3 �
� 3 �
�
Page 189
Let’s Practice
1 1⁄12 2 1⁄16 3 2⁄21 4 2⁄11 5 2⁄9 6 3⁄14 7 4⁄27 square yards
8 3⁄10 9 1⁄12 10a ⅓ 6 pound 10b 7⁄36 pound
4.7: Real-World Problems: Multiplying
and Dividing with Fractions
Pages 191–196
Guided Practice
1 23 of 12 units � �
� units
14 of 12 units � �
� units
;
The model shows that:
units plants
1 unit � � plants
Kim has pumpkin plants.
plants
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2 2
2
52
15
5 10
3
2 103 15
;
3154 315
4 4721
2
47212
; 15
155
1010
4
3 80
9 80 720
720
4 1; 1⁄16; 1⁄16
Page 197
Let’s Practice
1a 160 tickets 1b 128 tickets 2 $600 3 50 minutes
4 90 centimeters 5 7⁄50 meter 6 24 apples
Page 198
Math Journal
Amol got the answer 23 by dividing the
denominator 9 by 3.
Bart got the answer6
20 by adding the
numerators and the denominators separately.
÷ division
3227
×
×+ addition
2 49 11899
Page 199
Put On Your Thinking Cap!
1a
3 3 3 3
4 kg 8 kg 12 kg 16 kg
54
11
1b
2 54 students
3 Number of toy cars bought by Brad = 1½ × 10 = 15
Total number of toy cars bought = 10 + 15 = 25
25 toy cars → $75
1 toy car → $75 ÷ 25 = $3
The cost of each toy car was $3.
Pages 202–203
Chapter Review/Test
1 improper fraction 2 mixed number 3 common factor
4 reciprocal 5 2⁄7 6 3⁄5 7 3⁄20 8 11⁄12 9 8 10 2⅔ 11 42
12 53⅔ 13 44⅝ 14 1⁄18 15 7⁄24 16 ⅓ 0 17 3⁄19 18 ⅜
19 $61.25 20a 7⁄10 square yard 20b 7⁄20 square yard
21 198
Chapter 5
Algebra
Page 207
Quick Check
1 > 2 < 3 = 4 2 5 3 6 × 7 × 8 True 9 False 10 True
11 False 12 True 13 4 14 21 15 9 16 60 17 22 18 6
5.1: Using Letters as Numbers
Pages 210–215
Guided Practice
1
x 5
x 4
x 8
x 10
2 z + 5
3 8 + z 4 z − 7 5 10 − z 6 z + 9 7 9 + z 8 z − 11 9 11 − z
10
20232
422410
11 4 × k ; 4 groups of k ; k × 4 ; k groups of 4 (any three)
12 7j ; 7 groups of j ; j × 7 ; j groups of 7 (any three)
13 5p ; 5 × p ; p × 5 ; p groups of 5 (any three)
14 8q ; 8 × q ; q × 8 ; 8 groups of q (any three)
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15
7n4n
10560
14080
200300
150225
10n15n
16
432
864
16m6m8m12
17
3p
p 4
3p – 8
– 11 – p
1
5
5
10
13
18 39,655 19 354 20 3,191 21 987
Page 216
Let’s Explore!
1 3 ; 7; They are equivalent expressions. 2 2 ; 5; They are
equivalent expressions. 3 + ( +
Page 217
Math Journal
Answers vary.
Pages 217–218
Let’s Practice
Answers vary. Sample answers as shown.
1 5w 2 15v 3 x⁄3 or 1⁄3 × x 4 y ÷ 4 or y⁄4 5 (z + 4) ÷ 5 or 1⁄5 × (z + 4) 6 (a – 7) 2 or a – 7 7 9 + b 8 b − 4
9 10 − b 10 3b 11 7b 12 b⁄5 13 b⁄2 14
15 6b − 11 16 b⁄3 + 8 17 x + 5 ; 23 18 x − 3 ; 15
19 2x; 36 20 x⁄2; 9 21 n − 6 ; 18 22 n⁄4; 6 23 10n ; 240
24 + ; 7 25 19,291 26 17,065 27 6,959 28 91,620
29 4,581
5.2: Simplifying Algebraic Expressions
Pages 220–223
Guided Practice
1 2x 2 3y 3 5a 4 6b 5 7c 6 5a; 2a; 3a 7 4a 8 5x 9 7z
10 9y 11 6b 12 16c 13 0 14 0 15 0
16
5a � 2a �
a a a a a
17 3a 18 4a
19 x 20 4x 21 0 22 4y 23 x 24 0 25 10a 26 7a
27 2b + 10 28 7b + 8 29 9 + 2s 27 6s + 5
Page 225
Let’s Practice
1 7a 2 8a 3 12a 4 2x 5 x 6 0 7 6y 8 7y 9 2a + 5
10 2b + 8 11 3s + 1 12 12 + 6r
5.3: Inequalities and Equations
Pages 227–234
Guided Practice
1 = 2 > 3 < 4 >
5 6 612 2422
less than
6 = 7 > 8
7 73030 665
5
9 r = 11 10 q = 9
11
7 718
18186
6
3 3
18
12 9
99 9
9
11
1111 11
1111
11 11202020
2 220
1010
20
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Page 235
Let’s Practice
1 < 2 > 3 = 4 < 5 = 6 > 7 < 8 < 9 < 10 > 11 j = 6
12 k = 2 13 m = 8 14 n = 3
5.4: Real-World Problems: Algebra
Pages 236–239
Guided Practice
1a m + 15; m + m + 15 = 2m + 15 1b 165
2a
(y + 200); (y + 200)2
(y + 200)2
y + 200 2b 140
3a 18 182736
29>
Lenny
3b 7 716
– y 1616
16
– y
Pages 239–240
Let’s Practice
1a 3r 1b 3r – 4 1c 11 years old 2a 3x dollars
2b (100 – 3x) dollars 2c $55 3a 4z 3b 4z + 5 3c 9z + 5
4a 26 < 29; The steel pipe is longer. 4b p = 5
5a dollars14m 5b $84 6a q⁄10 quart 6b 22.5 quarts
Page 241
Math Journal
1 Answers vary. 2 No, it is not correct. a does not stand
for 1 apple. It stands for an unknown number. So a can be
any number. The correct way to think of a + a = 2a is that
any number added to itself is equal to twice the number.
Put On Your Thinking Cap!
Solution: Let the number that Grace thinks of be m.
(1) m × 2 = 2m (2) 2m + 12 (3) 2m + 12 – 2m = 12
Grace will get 12.
Pages 244–245
Chapter Review/Test
1 variable 2 algebraic expression 3 evaluate 4 inequality;
equation 5 solve 6 x + 4 7 8 − x 8 7x 9 x⁄2 10 11 11 4
12 81 13 1 14 3a 15 a 16 4a 17 2a + 4 18 < 19 >
20 = 21 > 22 p = 5 23 p = 4 24 p = 8 25 p = 10
26a men: 3 × m = 3m; children: 3m − 6,352 26b 43,663
27a Andy 27b 8
Chapter 6
Area of a Triangle
Pages 249–250
Quick Check
1 b and c; d and f; a and e 2 Yes 3 No 4 16 cm2 5 6 in.2
6 36 in.2 7 9 cm2 8 32 cm2 9 30 ft2
6.1: Base and Height of a Triangle
Page 253
Guided Practice
1 CB; AD 2 JH; GK 3 MN; LO 4 RT; ST 5 BE; AC
6 QR; PQ 7 XU; YZ
Page 254
Hands-On Activity
Step 4 They are all perpendicular to the base.
Pages 254–255
Let’s Practice
1 AC; BD 2 RS; PQ 3
baseBC
4 height
5 AB
AC
BC
CF
BE
AD
6 ZW
7 ZW; XY
6.2: Finding the Area of a Triangle
Pages 257–259
Hands-On Activity
1-Step 2 JEFK
DG
height
HEFI
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2-Step 2
PS
WQRV
UQRT
height
The area of triangle DEF is half the area of the
corresponding rectangle HEFI or half its base times
height.
The area of triangle PQR is half the area of the
corresponding rectangle UQRT or half its base times
height.
The formula for area of triangle applies to acute and
obtuse triangles.
Step 1 2.4 cm Step 2 yes
Page 260
Guided Practice
1 136 cm2 2 182 in.2 3 475 cm2 4 483 yd2 5 868 ft2
6 90 m2
Pages 260–261
Let’s Practice
1 28 cm2 2 96 in.2 3 290 yd2 4 182 m2 5 594 cm2
6 338 in.2 7 126 ft2 8 400 in.2 9 105 yd2
Page 262
Let’s Explore!
They are equal; heights; area
Put On Your Thinking Cap!
Area of triangle ABD = 12 × 8 × 11
= 44 cm2
Area of triangle ABE = 44 ÷ 2
= 22 cm2
A
B
E
D
C
11 cm
8 cm
Page 264–265
Chapter Review/Test
1 perpendicular 2 base; height 3 area 4 acute triangle
5 BC; AD 6 QR; PS 7 FD; ED 8 MN; PO 9 240 cm2
10 27 in.2 11 10 m2 12 27 ft2 13 18 cm 14 54 cm2
15 36 cm2
Chapter 7
Ratio
Page 268
Quick Check
1 8 2 9 3 1 out of 3 parts 4 4 out of 8 parts
5 15 520 5
34
6 4 424 4
16
7 14 8 2 9 4 10 18
7.1: Finding Ratio
Pages 270–273
Guided Practice
1 2 : 5 2 5 : 2
The ratio :
tells us that ‘there are
yellow pennants
to blue pennants’
or ‘there are
blue pennants to
yellow pennants’.
The ratio : tells us that ‘there are
blue pennants to yellow pennants’
or ‘there are yellow pennants to
blue pennants’.
3 1 : 5 4 5 : 1 5 2 : 5 6 5 : 2 7 5 : 8 8 8 : 5
9
7 8
15 88
Pages 274–275
Let’s Practice
1 11 : 8; 3 : 29;1. Sample answers:
Ratio
Mass of mussels to mass of lobsters 2 : 11
Mass of shrimp to mass of scallops 5 : 8
Mass of crabs and lobsters to mass of scallops
and shrimp
14 : 13
Mass of lobsters to mass of shellfish in total 11 : 29
Mass of shellfish in total to mass of scallops 29 : 8
2 AB
3 A B
4 A : B = 2 : 5 and B : A = 5 : 2 or A : B = 20 : 50 and
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B : A = 50 : 20 5 Accept 12 : 15 and 15 : 12 or 4 : 5 and
5 : 4. 6 7 : 5 7 35 : 53
7.2: Equivalent Ratios
Pages 278–281
Guided Practice
1 6 : 12 2 3; 6; 3 :6 3 1; 2; 1 : 2 4 6 : 12; 3 : 6; 1 : 2 5 1 : 2
6 6 : 12 7
4 43 1
44
8
3 33 5
9 5 5
15
55 15
10
3 83 8
3 83 84 24
4 2411
Page 281
Hands-On Activity
Step 2 Answers vary. Step 3 They are equivalent ratios.
Step 4 These ratios are also equivalent ratios because the
number of cubes in each group is the common factor of
the terms of the ratios.
Page 282
Let’s Practice
1 15 2 40 3 15 : 40 4 3 : 8 5 They are equivalent ratios.
6 2 : 7 7 9 : 4 8 1 : 4 9 7 : 2 10 21 11 12 12 9 13 14
14 5 15 68 16 140 17 4
7.3: Real-World Problems: Ratios
Pages 283–288
Guided Practice
1
4
4 5
5
3 3 2 5 : 4
3 56 : 24 = 7 : 3
The ratio of the total number of umbrellas and raincoats
sold to the number of raincoats sold is 7 : 3.
4 56 – 24 = 32; The number of umbrellas sold was 32.
32 : 24 = 4 : 3; The ratio of the number of umbrellas sold to
the number of raincoats sold is 4 : 3.
5 30 + 18 = 48; Gerald donated a total of 48 quarters.
48 : 16 = 3 : 1; The ratio of the total number of quarters
Gerald donated to the number of dimes he donated is 3 : 1.
6 The total number of quarters Gerald donated is 48.
48 + 16 = 64; Gerald donated a total of 64 coins.
48 : 64 = 3 : 4; The ratio of the total number of quarters
Gerald donated to the number of coins he donated is 3 : 4.
7196 + 56 = 252; The total number of stamps in Stanley’s
collection is 252.
196 : 252 = 7 : 9; The ratio of the number of U.S. stamps
to the total number of stamps Stanley has is 7 : 9.
8
Portion 1
Portion 2
? mL
mL
3 units mL
1 unit � � mL
7 units � � mL
The total volume of both portions is milliliters.
Method 2
The volume of portion 1 is milliliters.
120 � �
The total volume of both portions is milliliters.
3 : 4
� 120 :
� 40� 40
3 � 40 � 1204 � 40 �
20
Page 289
Math Journal
Answers vary.
Let’s Practice
1 24 : 35 2 2 : 5 3 7 : 6 4 56 cm 5 87 6 3 : 7
7.4: Ratio in Fraction Form
Page 291
Guided Practice
1 5 : 6 or 5⁄6 2 5 : 11 or 5⁄11
Let’s Explore!
1 It is the first term of the same ratio in ratio form.
2 It is the second term of the same ratio in ratio form.
The first term of a ratio is the numerator of the same
ratio in fraction form. The second term of a ratio is the
denominator of the same ratio in fraction form.
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Pages 292–293
Guided Practice
3 ½ ; ½ 4 2⁄1; 2 5 7 : 4 or 7⁄4 6 7 : 11 or 7⁄11
Page 294
Math Journal
Answers vary.
Pages 294–295
Let’s Practice
1 2 : 7 or 2⁄7 2 2⁄7 3 7⁄2 4 4⁄9 5 5⁄4 6 4⁄5 7 9⁄4 8 9⁄5 9 5⁄7
10 5⁄7 11 7⁄5 12 5⁄12 13 12⁄7
7.5: Comparing Three Quantities
Pages 297–300
Guided Practice
1
5 4 6
3 3 3 3
3
2
3 2 5
4 4 4
3
3
15 21
3
3
153213
3
3 3 3
4 3 : 4 5 1 : 3
Page 300
Hands-On Activity
Step 2 3 : 12 : 18 = 1 : 4 : 6
Page 301
Let’s Practice
1 5 : 15 : 20
� : :
� � �
2 4 : 18 : 24
� : :
� � �
3 12 : 16 : 28
� : :
� � �
4 36 : 45 : 72
� : :
� � �
5 1 : 4 : 5
� 3 : :
� � �
6 32 : 56 : 16
� : : 2
� � �
7 12; 48 8 28; 35 9 5; 2 10 3; 20
7.6: Real-World Problems: More Ratios
Pages 303–308
Guided Practice
1
1 4 15
200 200 200
1 4 15
2 Length of Z
1 unit � � cm
Total number of units � 4 � 2 � 1 �
� �
The total length of the three pieces of ribbon is centimeters.
3 car paym
electric
grocery
6 units $432
1 unit $ � � $
Total number of units � 5 � 4 � 6 � 15
� $ � $
The total amount of all three bills was $ .
4 Total number of units � � �
From the model:
a The ratio of the number of coins Sally has to the number of coins Layla has to the total number of coins they have is : : .
b 7 units coins
1 unit � � coins
units 10 � 128 � coins
They have coins altogether.
5 The ratio of the distance Raul ran to the distance he swam to the total distance of the biathlon is : : .
Distance Raul ran
Total distance of the biathlon �
The distance Raul ran is times the total distance of the biathlon.
units
unit
units
The total distance of the biathlon was meters.
Totof 5 �
iathlon.
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Pages 309–310
Let’s Practice
1 1 : 3 : 8 2 2 : 3 : 7 3 30 centimeters 4a 480 milliliters
4b 1,440 milliliters 5a Anna 5b $2,100 6a 120 6b 240
7a 3⁄2 7b 2⁄5 7c 3⁄5 7d Lilian: 10 years old. May: 15 years
old. 8a 5 : 2 : 7 8b 5⁄7 8c 21 lb 9a 3⁄1 9b ¾ 9c ¼
9d 6 square meters 10a 5 : 1 : 6 10b 5⁄6 10c 1⁄6 10d 210
Page 311
Math Journal
Accept reasonable explanations and models. The ratio of
the number of white balloons to the number of pink
balloons is 6 : 15 or 2 : 5.
Let’s Explore!
2 Answers vary. Sample: 2 : 3 : 5 = 8 : 12 : 20
1. Sample answers:
7 : 3 = 35 : 15
25 : 10 = 5 : 2
2. Rewrite the given numbers as products.
2 3 5 6 = 2 × 3 7
8 = 2 × 4 9 = 3 × 3 10 = 2 × 5 12 = 2 × 6 14 = 2 × 7
= 3 × 4
15 = 3 × 5 20 = 2 × 10 21 = 3 × 7 25 = 5 × 5 35 = 5 × 7
= 4 × 5
Identify the common factors of the given numbers. Use
guess and check to find equivalent ratios whose terms
are all on the list. For example, 8, 12, and 20 have a
common factor of 4. Dividing each of them by 4 gives
2, 3, and 5.
Page 312
Put On Your Thinking Cap!
1a $12 1b 48 quarters 2 $1.90
Page 314–315
Chapter Review/Test
1 ratio ; terms 2 equivalent ratios 3 simplest form
4 greatest common factor
5 A B
6 A B
7 A : B = 5 : 4
8 A : B = 3 : 7 9 1 : 2 10 3 : 2 11 2 12 24 13 2 14 7
15 1/3 16 8/3 17 1 : 3 : 7 18 2 : 5 : 4 19 15 : 9 20 20; 35
21 10 : 6 22 8 : 11 23a 40 cm 23b 100 cm 23c 35 cm
Page 319
Let’s Practice
1 3,500 2 14,000 3 560,000 4 7,008,000
2.6.a: Evaluating Expressions with
Parentheses, Brackets, and Braces
Pages 320–321
Guided Practice
1 [28 – (5 + 7)] × 4 = 64
Step 1: 5 + 7 = 12
Step 2: 28 − 12 = 16
Step 3: 16 × 4 = 64
2 96 ÷ {24 ÷ [12 − (6 − 2)]} = 32
Step 1: 6 − 2 = 4
Step 2: 12 − 4 = 8
Step 3: 24 ÷ 8 = 3
Step 4: 96 ÷ 3 = 32
Let’s Practice
1 [59 − (15 + 9)] × 3
[59 − 24] × 3
35 × 3
105
2 168 ÷ [(12 − 5) × 2]
168 ÷ [7 × 2]
168 ÷ 14
12
3 108 ÷ {36 ÷ [12 ÷ (3 × 2)]}
108 ÷ {36 ÷ [12 ÷ 6]}
108 ÷ {36 ÷ 2}
108 ÷ 18
6
4 420 ÷ {[15 − (8 − 3)] × 2}
420 ÷ {[15 − 5] × 2}
420 ÷ {10 × 2}
420 ÷ 20
21
5 56 − [5 × 7 − (14 ÷ 8 ÷ 2)]
56 − [5 × 7 − (14 ÷ 4)]
56 − [5 × 7 − 18]
56 − [35 − 18]
56 − 17
39
6 (500 − 230) +[(58+ 23) − 7 × 9]
270 ÷ [(58+ 23) − 7 × 9]
270 ÷ [81 − 7 × 9]
270 ÷ [81 − 63]
270 ÷ 18
15
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4.0: Multiplying with Whole Numbers
and Proper Fractions
Page 322
Let’s Explore!
1 Sample answer: Finding 5 × 6 by finding 5 groups of 6,
so the product is greater than the factor 6. You could also
find 6 × 5 by finding 6 groups of 5, so the product is
greater than the factor 5.
2 Sample answer: The product of two whole numbers
(greater than 1) is greater than either factor. Either way
you multiply the two numbers, you are finding the
number of items in several groups, which means that the
product is greater than both the factors.
3 Sample answer: The product ⅓ × 6 means to find a
fractional part of 6, so the product is less than the factor 6.
However, the product 6 × ⅓ means to find 6 groups of
1/3, so the product is greater than the factor ⅓.
4 Sample answer: The product of a proper fraction and a
whole number is less than the whole number factor
(because you are finding a part of the whole number) but
greater than the fractional factor (because you are finding
equal groups of the fraction).
4.6.a: Dividing a Whole Number by a
Unit Fraction
Page 324
Let’s Practice
1 35 2 54 3 60 4 96
5 3 � 19 � 3 � 9 � 27 jugs
6 4 � 18 � 4 � 8 � 32 square yards
4.7.a: Real-World Problems: Dividing a
Whole Number by a Unit Fraction
Page 326
Let’s Practice
1 7 � 2 � 5 gallons
5 � 16 � 5 � 6 � 30
He can water 30 potted plants.
2 3 � 5 � 8 bottles of ceramic glaze
8 � 14 � 8 � 4 � 32
He can coat 32 pieces of sculpture.
6.0: Finding the Area of a Rectangle
with Fractional Side Lengths
Page 328
Let’s Practice
11 5
7 yd
67 yd
3049 yd2
2 58 in.
38 in.
1564 in2
3
34 ft
27 ft
314 ft2
4
49 yd
23 yd
827 yd2
