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Answer Keys Part A
MathWorkbook
© Marshall Cavendish Education
Chapter 1
Numbers to 10,000
Practice 1.1: Counting
Pages 1–4
1 4,650 2 1,009 3 Two thousand, eight hundred thirty
4 Seven thousand, one hundred eighteen 5 Three
thousand, two hundred ninety–seven 6 One thousand,
eight hundred five 7 Three thousand, nine 8 Four
thousand, forty 9 9,000 10 1,400 11 6,835 12 3,260
13 3,206 14 5,068 15 2,070 16 5,009 17 monkey
18 2,065, 2,066, 2,067, 2,068, 2,069, 2,070
19 7,523, 7,533, 7,543 7,553 7,563, 7,573
20 3,307, 3,407, 3,507. 3,607, 3,707, 3,807
21 3,654, 4,654, 5,654, 6,654, 7,654 8,654
22
Practice 1.2: Place Value
Pages 5–10
1 3 thousands, 0 hundreds, 9 tens, 2 ones; or 3,000, or 0,
or 90, or 2 2 6 thousands, 5 hundreds, 0 tens, 0 ones;
or 6,000, or 500, or 0, or 0
3 5,000
400
20
6
4 3,000
400
60
7
5 9,000
800
50
4
6 6,000
0
50
5
7 4,000
700
0
3
8 1,000
400
20
0
9 7,000
200
90
8
10 tens; 40 11 8; 8 12 2,000; thousands 13 5; hundreds
14 1,643 1,000 600 40 3
1,643
One thousand, six hundred forty-three
1,643
15 9,304 9,000 300 4
9,304
Nine thousand, three hundred four
9,304
3,052
3,052
3,052 3,000 50 2
6,008
Six thousand, eight
6,008
6,008 6,000 8
5,800
Five thousand, eight hundred
5,800
5,800 5,000 800
16
17
18
19 2,034; 2,034 20 3,020; 3,020 21 400 22 1 23 90 24 7
25 8,000 26 5,000 27 70 28 5
Practice 1.3:
Comparing and Ordering Numbers
Pages 11–12
1 7,532 is greater than 7,392. 2 4,523 is less than 4,561.
3 < 4 < 5 < 6 >
7 8
109
11
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12 989, 2,340, 4,001 13 1,456, 2,456, 6,456
14 6,059, 6,359, 6,759 15 3,050, 3,052, 3,057
16 5,731, 5,713, 5,317, 5,137 17 3,761, 3,716, 3,671, 3,617
18 6,349 19 4,217 20 5,508 21 1,990
22
8,5156,5155,515
6,5036,1035,903
7,1167,0767,016
2,455 2,4852,445
2,243 8,2436,243
2,861 2,961 3,061
23
24
25
26
27
28 5,725, 5,735, 5,745, 5,755, 5,765, 5,775
29 8,625, 8,725, 8,825, 8,925, 9,025, 9,125
30 862, 962, 1,062, 1,162 1,262, 1,362
31 6,315 6,215, 6,115, 6,015, 5,915, 5,815
32 3,456 33 1,987 34 2,000 35 8,219 36 2,012 37 1,899
38
B
Put On Your Thinking Cap!
Page 17
1
2 5,621, 5,741, 5,861, 5,981 3 6,871, 5,861, 4,851, 3,841
4 2,828, 2,808, 2,818, 2,798, 2,808
5 400511622733844955
Page 18
9,830
Chapter 2
Mental Math and Estimation
Practice 2.1: Mental Addition
Pages 19–20
1 74
74 79
79
84
2 86
86
5
2
5
84
2
3 87
87 5
82
86
86 6
5
6
82
80
80
4
5 84 6 95 7 62 8 94
Practice 2.2: Mental Subtraction
Pages 21–24
1 39
39
32 77 32
Thousands Hundreds Tens Ones
5 6 2 3
6 6 2 2
7 6 2 1
8 6 2 0
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2 45
45 3
42 342
3
5
2
52
57
6767 2
69
52 5 57
69
4
5 22
22
28
6 28
48
48 1
49
49
6
1
6
7 61 8 24 9 16 10 14 11 58 12 28 13 35 14 49 15 45 16 36
17 55
8
4261
17
9
Practice 2.3: More Mental Addition
Pages 25–26
1 126
138
126
122
4 122
138 5
133
133
4
5
2
3
200
200
194
194
200
192
192
2 4
200 6 2
2 4
6 2
4
Practice 2.4:
Rounding Numbers to Estimate
Pages 27–30
1
9001,000
1,000
800 900
800
2
3
4
5
6a You need an exact answer.
$900 − $210 = $690
The two items cost $690.
6b You can estimate to find which two items she buys.
450 rounds to 500; 240 rounds to 200; 120 rounds to 100;
310 rounds to 300. $500 + $200 = $700; $700 is close
to $690. The two items she buys are the television set and
the washing machine.
7 836
200
600
200 600 800
800
800836
152
800
700
800 700 100
100
100152
8
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9 613
900
300
900 300 600
600
600613
10a $96 + $215 + $247 + $385 = $943
$96 is about $100; $215 is about $200; $247 is about $200;
$385 is about $400. $100 + $200 + $200 + $400 = $900
So, $96 + $215 + $247 + $385 is about $900.
$943 is close to $900, so the total cost is reasonable.
10b Yes, Mrs. Ramsey has enough money to buy all the items.
Practice 2.5:
Using Front-End Estimation
Pages 31–34
1 4 2 8 3 1 4 5 5 7 6 9
7 838
300 500 800
800
838
8 873
300 500 800
800873
9 759
200 400 600
600759
10 246
600 300 300
300
246
11 408
900 500 400
400
408
12 523
700 200 500
500
523
13 Answers vary. Sample: 439 is about 400. 558 is about
500. 400 + 500 = 900; The total length of the train and the
carriage is about 900 centimeters.
14 Answers vary. Sample: 356 is about 300. 104 is about
100. 300 – 100 = 200; About 200 centimeters of the wooden
pole is above the ground.
Math Journal
Pages 35–36
1 50 35
35 50
2 85
85
85 2 83
83
2
72 20 52
20 72
52 2 54
54
2 52
3
458 is nearer to 500 than 400.
458 is 500 when rounded to the nearest hundred.
400 500450
4 905 – 178 = 727
905 – 178
900 – 100 = 800
The estimated difference is 800.
727 is close to 800, so the answer is reasonable.
5 No. Answers vary. Sample: Using front-end estimation,
the estimated sum should be 500.
Put On Your Thinking Cap!Page 37
1 349 2 Accept 100 to 104; 195 to 204; 295 to 304; 395 to
404; 495 to 504; 595 to 604; 695 to 704; 795 to 804; 895 to
904; 995 to 999.
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Page 38
Problem Solving
1 356 is about 400 when rounded to the nearest hundred.
517 is about 500 when rounded to the nearest hundred.
400 + 500 = 900
She needs about 900 centimeters of fabric in all.
2 356 + 517 = 873
Mrs. Avilla needs a total of 873 centimeters.
900 – 873 = 27
27 centimeters of fabric will be left over.
Cumulative Review
Pages 39–44
1 nine thousand, nine hundred ninety-nine 2 one
thousand, forty-seven 3 six thousand, five 4 2,012
5 9,001 6 6,421 7 5,216, 6,216, 7,216, 8,216, 9,216
8 3,009, 3,109, 3,209, 3,309, 3,409
9 6,029, 6,019, 6,009, 5,999, 5,989
10 21, 2,021, 4,021, 6,021, 8,021
11
2,000
800
30
5
12 500 13 40; 5
14
15
16 4,702 17 6,588 18 6,886 19 4,702, 6,588, 6,886
20 7,641 21 1,467 22 4,167 23 7,146 24 89 25 74 26 82
27 41 28 6 29 17 30 131 31 192 32 900 33 7,600
34 3,000 35 2,000
36 650
500
200
500 200 700
700650
416
900
500
900 500 400
400416
37
38 949, 850 39 2 40 8 41 5 42 9
43 781
700
781
210
210
200
44
45 Estimate to get the answer. 125 rounds to 100, 264
rounds to 300. 100 + 300 = 400; The decorated float is
about 400 centimeters tall.
46 1,920 47 891 − 278 = 613; 800 − 200 = 600613
600613
48 293 + 108 = 401; 401 + 293 = 694
293 rounded to the nearest hundred is 300.
108 rounded to the nearest hundred is 100.
300 + 100 = 400
400 + 300 = 700
The school has 694 students. 694 is close to 700 so the
answer is reasonable.
Chapter 3
Addition up to 10,000
Practice 3.1:
Addition Without Regrouping
Pages 45–48
1 6,975 2 8,675 3 6,795 4 8,769 5 4,478 6 5,399
7 5,868
9,938
5 0 6
5 8 6 8
5 3 6 2
0 5 0
9 5 9 2
6 5 4 2
3
9,592
2,841
3 0 6
9 9 3 8
4 6 3 2
1 0 0
2 8 4 1
7 4 1
2
5
8
9
10
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11 9,986 12 8,489 13 3,009 14 6,039 15 2,063 16 8,900
17 2,968 18 4,776 19 7,376 20 Go o d A fterno on
21 4,897
4, 0 9 4 8 0 3
4, 8 9 7
22
5, 0 5 12, 1 3 6
7, 1 8 7
7,187
23
7, 4 2 31, 3 6 2
8, 7 8 5
8,785 24 9,148
6, 0 3 6 3, 1 1 2
9, 1 4 8
25 9,999
8, 9 9 9 1, 0 0 0
9, 9 9 9
Practice 3.2:
Addition with Regrouping in Hundreds
Pages 49–50
1 5,400 2 2,400 3 6,600 4 6,200 5 4,000 6 3,000 7 8,200
8 7,100 9 9,300
10 6,697
3, 8 7 6 2, 8 2 1
6, 6 9 7
1
11 5,537
3, 6 1 0 1, 9 2 7
5, 5 3 7
1
12 7,411
1, 9 0 0 5, 5 1 1
7, 4 1 1
1
13 8,399
1
5, 5 1 6 2, 8 8 3
8, 3 9 9
14 9,127
1
6, 3 2 5 2, 8 0 2
9, 1 2 7
Practice 3.3: Addition with Regrouping
in Ones, Tens, and Hundreds
Pages 51–54
1
2 1 12
1 2
5 2 1
8, 5 2 1
15
1 5
8
1 11
1 1
2 1,011 3 1,492 4 1,820 5 4,926 6 9,195 7 1,492 8 5,341
9 1,600 10 9,124 11 1492 12 6,835 + 2,795 = 9,630; 9,630
13 5,268 + 1,952 = 7,220; 7,220 14 2,156 + 3,152 = 5,308; 5,308
Put On Your Thinking Cap!Pages 55–56
1 Answers vary.
Sample answers:
2,035 5,3702,073 7,3093,592 7,5233,905 7,9505,037 9,2375,239 9,752
2, 0 3 57, 9 5 0
9, 9 8 5
2, 0 7 33, 9 0 5
5, 9 7 8
2 Answers vary.
Sample answers:
1,690 6,9041,896 8,1094,180 8,6494,691 8,9614,860 9,0846,849 9,416
1, 8 9 64, 6 9 1
6, 5 8 7
1 1
6, 8 4 91, 6 9 0
8, 5 3 9
1 1
Pages 57–58
1 6 2 4 3 Answers vary; Sample answer: Page A – 502,
322, 304, 214; Page B – 521, 323, 305, 125 4 64 + 36 =100
5 Answers vary. Sample answer: 65 + 48 + 37 = 150. 6 7
7 7,431 8 1,347 9 7,431 + 1,347 = 8,778
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Chapter 4
Subtraction up to 10,000
Practice 4.1:
Subtraction Without Regrouping
Pages 59–60
1 4,211 2 3,031
3 1,123
3 6 4 6
2 5 2 3
1 1 2 3
4 9,123
9 6 4 6
5 2 3
9 1 2 3
5 5,541
5 5 6 4
2 3
5 5 4 1
6 286 7 2,200 8
8, 4 2 1 – 3 1 0 8, 1 1 1
8,111
9
5, 4 9 3– 3, 2 9 1 2, 2 0 2
7, 5 6 8– 4, 0 2 2 3, 5 4 6
6, 9 7 4– 1, 8 1 3 5, 1 6 1
9, 7 8 6 – 7 2 9, 7 1 4
5,1619,714
2,2023,546
10
1211
Practice 4.2: Subtraction with
Regrouping in Hundreds and Thousands
Pages 61–62
1 1,900 2 716 3 2,921 4 332 5 5,631
1,483
32,10 8 4
1, 6 0 1 1, 4 8 3
81,515 744
21,13 9 4
1, 6 5 0 7 4 4
98
, 13 5 6 7, 8 4 1
1, 5 1 5
76
6,426
76,10 7 9
6 5 3 6, 4 2 6
8,183
98
,10 8 7 9 0 4
8, 1 8 3
9 10 11 1,700 12 4,520
13 2,989 14 3,851 15 1,524 16 1,402 17 2,331
18 YOU’RE GREAT
Practice 4.3: Subtraction with Regrouping
in Ones, Tens, Hundreds, and Thousands
Pages 63–66
1
9 1
1 16
18 9 1
7 11
6,8 9 1
1 161
11
67 1 1
11
67 1 1
2
8
6 8
5 6 8
4 17
4
2 14
2
3 12
2, 5 6 8
3 309 4 269 5 1,048 6 1,914 7 6,628 8 675
9 10 2,160 11 7,113
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12 1,221 13 4,840 14 7,947 15 5,582 16 504 17 5,176
18 1,864 19 1,308 20 6,987 21 STATUE OF LIBERTY
22 NEW YORK
Practice 4.4: Subtraction Across Zeros
Pages 67–68
1 236 2 1,642 3 4,563 4 485 5 2,363 6 2,528 7 3,444
8 5,001 9 2,654 10 strawberry
11
1,845
4,002 – 2,157 = 1,845
4, 0 0 2 2, 1 5 7
1, 8 4 5
3 9 91 1 1
Put On Your Thinking Cap!
Pages 69–70
1 68 − 26 = 42 2 400 120 280
476 – 196 = 280
3 6 4 1 5 6 6 5; 3
7
8,652 2,056 6,596
8, 6 5 2 2, 0 5 6
6, 5 9 6
5 141 1
8 Accept 7,410 – 5,632 = 1,778; 7,401 – 5,632 = 1,769;
7,140 – 5,632 = 1,508; 7,104 – 5,632 = 1,472;
7,041 – 5,632 = 1,409; 7,014 – 5,632 = 1,382.
Pages 71–72
1 Accept 91 and 191; 92 and 192; 93 and 193; 94 and 194;
95 and 195; 96 and 196; 97 and 197; 98 and 198; 99 and 199.
2 jewelry; dress 3a crayons, notebook, pencil 3b pencil
holder, notebook, pencil
Chapter 5
Using Bar Models: Addition and
Subtraction
Practice 5.1: Real-World Problems:
Addition and Subtraction
Pages 74 –76
1a 487
175
487 175 312
312
1b 487 + 312 = 799; Both grades collect 799 cans in all.
2a 2,169
4,320
2,1694,320 2,151
2,151
2b 2,151
1,493
1,4932,151 658
658
3a 1,452 379
1,452 379 1,831
1,831
3b 1,452
645
1,452 645 807
807
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Practice 5.2: Real-World Problems:
Addition and Subtraction
Pages 78–82
1a
1,287 879 408
408
men
?
women
1,287
879
?
1b 1,287 + 408 = 1,695; 1,695 adult spectators are at the
game.
2a
$4,756 $1,297 $3,459
$3,459
athletic
?
library
$4,756
$1,297
2b
$3,459 $948 $2,511
$2,511
$3,459
$? $948
3a
Monday
?
Wednesday
635
?
96
635 96 539
She prints 539 newsletters on Wednesday.
3b 635 + 539 = 1,174; She prints 1,174 newsletters in all.
4a
1,793 157 1,636
1,636
Mr. Tuzamoto
?
Ms. Jefferson
1,793
157
4b
1,636 698 938
938
1,636
? 698
5a
middle school
3,756
elementary school
?
?
455
3,756 455 4,211
The elementary school has 4,211 students.
5b 3,756 + 4,211 = 7,967; Both schools have 7,967
students.
Practice 5.3: Real-World Problems:
Addition and Subtraction
Page 84
1
2,500 2,000 4,500
pet store
3,500
farm
2,500
?
2,000
The farm donates 4,500 pounds of dog food.
4,500 3,500 1,000
The farm donates 1,000 pounds more dog food than the pet store.
Page 86
Math Journal
Answers vary.
Put On Your Thinking Cap!
Page 87
1 B and C; 456 + 195 = 651 2 A and C; 318 + 195 = 513
3 A; B 4 A; C 5 B; C 6 A; C
Page 88
1a 589 − 125 = 464; 464 cards 1b 464 − 201 = 263; 263
cards 2 $350 + $20 = $370; Peter raises $370. $350 + $370
+ $370 + $350 = $1,440; The boys raise $1,440 in all.
Cumulative Review for Chapter 3 to 5
Pages 89–92
1 8,817 2 5,900 3 8,223 4 5,911 5 4 6 5 7 5 8 3
9a 9b
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10
a. 5,476 – 1,496 = 3,980 3,980 people ride Bus E in March.
b. 5,476 + 3,980 = 9,456 9,456 people ride both buses in March.
1,496
5,475
Bus D
Bus E?
?
a
b
11 368
1,213
?
green apples
red apples
?
a. 1,213 – 368 = 845 845 of the apples are red.
b. 845 – 368 = 477 The supermarket has 477 more red apples than green apples.
a
b
12 2,500
?
?
Monday
Tuesday
532
2,500 + 532 = 3,0323,032 people were at the museum on Tuesday.2,500 + 3,032 = 5,532The total number of visitors for both days is 5,532.
13
754 – 98 = 656Peter has 656 songs.754 + 656 = 1,410They have 1,410 songs in all.
754
?
?
Michael
Peter
98
Chapter 6
Multiplication Tables of 6, 7, 8, and 9
Practice 6.1: Multiplication Properties
Pages 93–96
1 5 × 5 = 25 2 4 × 7 = 28 3 8 ×2 = 16
4
15
20
5
6 3 × 4 = 12; 4 × 3 = 12 7 1 × 6 = 6; 6 × 1 = 6
8
5 5
15
9 10
10
2 2
10
10 0 2 4 0
0 0
1 5 10 1
5 10
11
1312
14 Accept 8 2 or 2 8.
Answers vary.
16
Practice 6.2: Multiply by 6
Pages 97–100
1 5 × 6 = 30 2 6 × 6 = 30 3 6 4 5 5 7 6 6 7 10 8 6
9 61
20 4
24
7
230 1242
82
60 1248
30
60
10
11
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12
13 8 × 6 = 48; 48 wheels in all 14 4 × 6 = 24; 24 legs
15 9 × 6 = 54; 54 sides
Practice 6.3: Multiply by 7
Pages 101–108
1 6 × 7 = 42 2 7 × 7 = 49 3 7 4 9 5 5 6 7 7 10 8 7
9 2
820
28
49
63
35
2
35 14
70
1
70 7
10
11
12
13 14; 14 14 70; 70 15 28; 28
Practice 6.4: Multiply by 8
Pages 105–108
1 24
2 48 3 8 4 3 5 6 6 8 7 5 8 8; 8; 8
9 2
40 8
32
80
2
80 16
64
8
10
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11
40
56
40
2
16
7
12
13 1 × 8 14 7 × 8 = 56; 56 15 6 × 8 = 48; 48
Practice 6.5: Multiply by 9
Pages 109–112
1 18
2 63 3 9 4 4 5 9 6 6 7 9 8 9; 9
9
1
40
40
4
36
90
1
90
81
45
9
54
9
1
45
10
11
12
13 4 × 9 = 36; She pastes 36 stickers in all. 14 Answers
vary.
Practice 6.6: Division: Finding the
Number of Items in Each Group
Pages 113–114
1 45 ÷ 9 = 5; 45 ÷ 5 = 9 2 63 ÷ 7 = 9; 63 ÷ 9 = 7 3 48 ÷ 8
= 6; 48 ÷ 6 = 8 4 7; 7 5 6; 6 6 5;5 7 54 ÷ 9 = 6;
Each purse has 6 coins. 8 63 ÷ 7 = 9; Each box contains
9 seashells.
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Practice 6.7: Division:
Making Equal Groups
Page 115
1 9; 9 2 7; 7 3 3 4 9 5 7 6 8 7 64 ÷ 8 = 8; 8 tanks are
needed to hold 64 gallons of water. 8 36 ÷ 9 = 4; Donald
uses 4 bags.
Math Journal
Page 116
1
2 3
Put On Your Thinking Cap!
Page 117
1 70 63 56 49 42 35 28 21 14 7
2 80 92 64 56 48 40 32 24 16 8
3
36The number 36
does not belong in the
multiplication table of 8.
32The number 32
does not belong in the
multiplication table of 7.
4
Page 118
1
1
2
3
3
4
4
8
4
0
6
2
8
18 6 24
18
24 6 30
30 6 36
36 6 42
42 6 48
42
Chapter 7
Multiplication
Practice 7.1: Mental Multiplication
Pages 119–120
1 27 2 35 3 72 4 15; 1,500 5 28; 280 6 28; 2,800
7 48; 480 8 48; 4,800 9 180 10 1,800 11 140 12 1,400
13 240 14 2,400
Practice 7.2: Mental Multiplication
Pages 121–126
1 4
8
6
6 8 4
684
2
4
3
2 2 6
1 3
3 9
936
9 3 6
3 1 4
0 0
2 8
804
8 0 4
4 963 5 408 6 605
7
8 B, D, F, G, H, and I
9 143 × 2 = 286; 286 people ride the train in 2 hours.
10 213 × 3 = 639; The bakery sells 639 muffins in 3 days.
11 232 × 2 = 464; The website has 464 hits in both weeks.
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12 202 × 4 = 808; The grocery store sells 808 cartons of
milk in 4 weeks.
Practice 7.3: Multiplying Ones, Tens,
and Hundreds with Regrouping
Pages 128–134
1
8 0
3
6 30
30 3 0
1 5
3 5 8
80
2
2 832 8
32 3 2
8 32
328
3
8 40
40 4
7 35
4 35 39
39 3 9
390
9 03
4
0
4
5 20
20 2
1 4
2 4 6
1 4
460
6 04
2
0
5
2 86 89
1
4 16
16 1 6
2 8
968
1 8
9
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6
5 25
25 2
4 20
2 20 22
22 2
1 5
2 5
7
725
2 57
2 2
5
2
7
9 45
45 4
5 25
4 25 29
29 2
1 5
2 5
7
795
9 57
2 4
9
5
Practice 7.4: Multiplying Ones, Tens,
and Hundreds with Regrouping
Pages 135–138
1
1 7 5
K
9 7 2 8 3 7
9 1 2 6 2 48 9 1
7 7 5 9 9 59 9 2
D O E YN
2 187 × 4 = 748; The cars have 748 wheels in all.
3 198 × 3 = 594; They carry 594 books in all.
4 165 × 5 = 825; She feeds her hamster 825 food pellets in
165 days. 5 900 6 928 7 777 8 980
9–10
11
670
134 5 = 670
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Math Journal
Page 138
9 6 9Multiply 3 ones by 3.
3 3 ones = 9 ones
Multiply 2 tens by 3.
3 2 tens = 6 tens
Multiply 3 hundreds by 3.
3 3 hundreds = 9 hundreds
So, 3 323 = 969.
Put On Your Thinking Cap!
Page 139
1 4 2 4 3 2 4 5 5 2 6 3 7 2 8 4
Page 140
30 2 = 60 70 4 = 280 60 280 = 340
30 70
Cumulative Review for
Chapters 6 and 7
Pages 141–146
1 0 2 7 3 6 4 4 5 6 6 7 7 0 8 8 9 8 10 4
11 82
8 24
8 324
12 4 12
12 24
122
24
13 35
5 1
35 7
42
90
10 2
90 18
72
14
15 32
32 4 8
32 8 4
6 9 54
54 9 6
6
16
17
9
36
360
7
70
7,000
36
7018
19 30 20 50 21 80 22 120 23 1,000 24 800
25 848 740
2 1 2 4
8 4 8
1 4 8 5
7 4 0
26
27 864 28 753 29 42 × 4 = 168; Cheryl completes
168 exercises. 30 48 ÷ 8 = 6; There are 6 marbles in each
bag. 31 63 ÷ 9 = 7; He uses 7 pots. 32 49 ÷ 7 = 7;
He needs 7 bags. 33 153 × 5 = 765; She sells 765 carrots.
34 125 × 4 = 500; She buys 500 markers.
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Chapter 8
Division
Practice 8.1: Mental Division
Pages 147–148
1 5; 5 2 9; 9 3 7; 7 4 9; 9
5 56
8
8
36
4
40
6
2
200
45
9
900
6
7
8
9 60 10 50 11 20 12 30 13 40 14 70
Practice 8.2: Quotient and Remainder
Pages 149–150
1
5 2
5
2
8 0
8
0
2
3 5 4 6 5 8 6 8 7 8
8 10 9 9
10
8
3
11
7
1
12
9
4
Practice 8.3: Odd and Even Numbers
Pages 151–152
1 No; Answers vary. 2 No; Answers vary. 3 14 ÷ 2 = 7 R 0
4 23 ÷ 2 = 11 R 1 5 29 ÷ 2 = 14 R 1
6 14
remainder
remainder 1
23 297
8
30, 68, 76, 84, 92, 980
9 11, 59, 95, 123, 477 10 0, 2, 4, 6, 8 11 1, 3, 5, 7, 9
12 9,425 13 1,096
Practice 8.4: Division Without
Remainder and Regrouping
Pages 153–154
1
1 1
2 32
3 1
08
4
2
4
0
2
03
6
1
6
0
1
05
5
1
5
0
4 5
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6
Practice 8.5: Division with Regrouping
in Tens and Ones
Pages 155–156
1
C M R I
F A T J
2 02
1 6
12 1
0
6 08
2 6
18 1
0
6 03
2 7 R 2
21 2
2
8 02
2 3
12 1
0
4 09
1 7 R 1
282
1
5 03
1 2 R 3
101
3
5 05
1 5
25 2
0
6 02
3 6
121
0
2 3 4
6 7 85
9 TRAFFIC JAM
Math Journal
Page 156
1 False. When I divide one number by another, the answer
is called a quotient. Any number left is called a remainder.
2 False. When an odd number is divided by 2, there is
always a remainder of 1. 3 False. When an even number is
divided by 2, there is no remainder. 4 False. I divide the
tens first, then the ones.
Put On Your Thinking Cap!
Page 157
1 163656+
981
2
Page 158
4 R 84 R 242
65 R 2
42Thinking skill: Analyzing partand whole
Chapter 9
Using Bar Models:
Multiplication and Division
Practice 9.1: Real-World Problems:
Multiplication
Pages 159–160
1 95
95
285
285
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2
98 × 392
392
4
this year
last year
98 miles
?
3
School A
School B
76 bundles
?
76 × 5 = 380School B collects 380 bundles of newspaper.
Practice 9.2: Real-World Problems:
Two-step Problems with Multiplication
Pages 162–168
1a
milk
water
88 cartons
?
88 4 352
352
×
1b
352 88 264
264
–
milk
water
88 cartons
352 bottles
?
–
2
85
pottery
paintings
?
75 + 10 = 85The museum has 85 pieces of pottery.
85 × 3 = 255The museum has 255 paintings.
?
carvings
pottery
75 10
add
multiply
3
65 – 25 = 40The second graders have 40 books in boxes.
subtract
multiply
40 × 4 = 160The third graders collect 160 books.
65 books
?25books
second graders
third graders
40 books
?
4
? pencils
30 pencils
8 × 30 = 240
240 pencils
215 pencils ? pencils
240 – 215 = 25She needs 25 more pencils.
5
600 – 174 = 426
120 × 5 = 600There are 600 books in all.
120 books
? books
600 books
6
25
25 5
125
125
125 30 155
155
×
+
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7 28 stickers
Jill
Peggy
Luis
15 stickers
?
1 unit 28
4 units 28 × 4 = 112
Peggy has 112 stickers.
112 – 15 = 97
Luis has 97 stickers.
Practice 9.3:
Real-world Problems: Division
Pages 169–172
1 75 ÷ 5 = 15; Each child gets 15 marbles
2 63 hours
?
63 7 9
9
÷
3
9
72 8 9÷
72 buttons
8 8
? shirts
4
24 3÷
24
8
8
5
4 units 801 unit 80 ÷ 4 = 20
Luke takes 20 photos.
Elena
Luke
80 photos
?
6
9 units 541 unit 54 ÷ 9 = 6
Mr. Tang picked 6 peaches.
Mr. King
Mr. Tang
54 peaches
?
Practice 9.4: Real-World Problems:
Two-step Problems with Division
Pages 173–176
1
8
64 8 8÷
16
8 2 16×
8
divide
multiply
2
70 ÷ 5 = 14Alex has 14 pencils.
Alex
Lance
?
14 ÷ 2 = 7Each child gets 7 pencils.
multiply
divide
14 pencils
?
70 pencils
3
90 – 10 = 80Richard shares 80 pennies.
80 ÷ 4 = 20Each sister gets 20 pennies.
90 pennies
?10 pennies
divide
subtract
80 pennies
?
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4 64 rolls
?
32 rolls32 + 64 = 96He makes 96 rolls in all.
96 ÷ 4 = 24Each box has 24 rolls.
96 rolls
?
5 19 – 14 = 5Wayne collects 5 more stamps than Marcus each month.
65 ÷ 5 = 13In 13 months Wayne collects 65 more stamps than Marcus.
Marcus
Wayne
14 stamps
19 stamps
?
65 stamps
5 5
? months
Math Journal
Pages 177–178
1 Answers vary. Sample: Dr. Bob sees 89 patients in a week.
Dr. Jane sees twice as many patients as Dr. Bob. How many
patients do both doctors see?
2 My question: Answers vary. Sample: Baker Chang bakes
twice as many bread rolls as Baker Lee. Baker Chang bakes
98 bread rolls. How many bread rolls do they bake in all?
My methods: Answers vary. Sample:
Method 1 Method 2
98 ÷ 2 = 49 2 units → 98
49 × 3 = 147 1 unit → 98 ÷ 2 = 49
3 units → 49 × 3 = 147
Put On Your Thinking Cap!
Page 179
24 ÷ 2 = 12Pedro has 12 trading cards after receiving 5 cards from Timmy.
12 – 5 = 7
Timmy
Pedro24 cards
5
5
Timmy
Pedro24 cards
Page 180
6 × 3 = 18There are 18 nuggets on 6 sticks.
18 + 2 = 20Johanna has 20 nuggets in all.
20 ÷ 4 = 5No chicken nuggets will be left.She will need 5 sticks.
3 nuggets 2 nuggets
?
20 nuggets
4 4
? sticks
Cumulative Review for Chapters 8–9
Pages 181–186
1
183 381
831813
138
318
2
3 3
300
6
3
30
6
3
4
6 01 31 2 1
3 6 R 1 1 1 R 3 1 9 R 3
9 0 6 6 0
3 2
9 0 3 3 0
3 1
5 0 6 5 1
1 1 R 1
4 0 7 4 3
5 04 84 5 3
5
8
6
97
10
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11
125 × 3 = 375
Ian has 375 trading cards.
Roland
? trading cards
Ian
125 trading cards 12
250 ÷ 5 = 50
Each class receives 50 pencils.
? pencils
250 pencils
13a
Mike
2 feet
Pamela
? feet
? feet
3 × 2 = 6
Mike is 6 feet tall.
13b 6 – 2 = 4
Mike is 4 feet taller than Pamela.
14a 3 + 6 = 9
Mrs. Herra buys 9 boxes of fruit. ? boxes
6 boxes3 boxes
14b 65 × 9 = 585
Mrs. Herra buys 585 pieces of fruit.
65 pieces of fruit
? pieces of fruit
15
96 ÷ 6 = 16
Each jug holds 16 ounces of lemonade.
16 ÷ 2 = 8
Each glass holds 8 ounces of lemonade.
? ounces
96 ounces
? ounces
16 ounces
16
$56 × 2 = $112
The camera costs $112.
$56 + $112 = $168
The two items cost $168 in all.
watch
$?
camera
$56
$?
17
?
480 crayons
4 × 120 = 480
He has 480 crayons.
480 ÷ 6 = 80
80 crayons are in each box.
120 craons
?
18
275 – 15 = 260
Natalie uses 260 centimeters of ribbon to make 4 headbands.
260 ÷ 4 = 65
She uses 65 centimeters of ribbon for each headband.
? cm
275 cm
15
? cm
260 cm
cm
Mid-Year Review/Test Prep
Pages 187–200
1 C 2 D 3 A 4 B 5 A 6 B 7 D 8 B 9 C 10 D 11 B
12 D 13 D 14 A 15 C 16 3,014 17 5,000 18 Answers
vary. Sample: 129, 183, 347; Answers vary. Sample: 174,
318, 942 19 1,909 20 280 21 29; 1 22 900 23 26 24 600
and 900 25 212
26
14 7
14
7
14
14
14
27 9,101 28 2,141 29 616 30 Accept any two: 13; 17; 37;
73; 93; 97. 31 26 32 29 33 5,758 34 185 35 624
36a 600 − 285 = 315; Jolene has 315 glass beads.
36b 600 − 150 = 450; She has 450 wooden beads left.
37a
3,700 – 450 = 3,250Company B gets 3,250 hits.
?
3,700
Company A
Company B
450?
37b 3,700 + 3,250 = 6,950Both companies get 6,950 hits in all.
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38a 80 laps
? laps
80 ÷ 5 = 16He swims 16 laps in a day.
38b ? laps
16 laps
16 × 4 = 64He swims 64 laps in 4 days.
39a 88 stickers
4 4
? bookmarks
88 ÷ 4 = 22He puts stickers on 22 bookmarks.
39b
22 ÷ 2 = 11He has 11 friends.
22 bookmarks
2 2
? friends
40 162 pieces
?
162 × 5 = 810
786 pieces of pottery are not broken.
810 pieces
? pieces24pieces
810 – 24 = 786