Contributed by:

Using repeated subtraction to divide, Interpreting Remainders, Dividing 2-digits by 1-digit, Diving in parts, Dividing 3-digit numbers by 1-digit, and short exercise.

1.
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CHAPTER 10

1 Exploring Division

Goal Solve division problems using models.

You will need 40 bread tags, toothpicks, coins, At-Home Help

buttons, or something else to use as counters. The number you divide by in a

division equation is the divisor.

1. Use counters. Show how 40 band members

842

would group themselves as they march each divisor

way. Then sketch a diagram.

a) 2 equal columns b) 4 equal columns c) 5 equal columns

2. Use counters. Can 40 band members group themselves in equal

columns if they march each way? Why or why not?

a) 6 columns No, because 6 does not divide equally into 40.

b) 7 columns No, because 7 does not divide equally into 40.

c) 8 columns Yes, because 8 divides 5 times into 40.

3. Use counters. There are between 25 and 35 students working in

groups planting trees. Which numbers of students could there

be in each case?

a) All students are working in groups of 5. 25, 30, 35 (if between is considered

to include 25 and 35, otherwise 30)

b) All students are working in groups of 4. 28, 32

c) All students are working in groups of 3. 27, 30, 33

4. What number in each part of Question 3 is the divisor?

a) 5 b) 4 c) 3

Copyright © 2004 Nelson Answers Chapter 10: Dividing Greater Numbers 85

CHAPTER 10

1 Exploring Division

Goal Solve division problems using models.

You will need 40 bread tags, toothpicks, coins, At-Home Help

buttons, or something else to use as counters. The number you divide by in a

division equation is the divisor.

1. Use counters. Show how 40 band members

842

would group themselves as they march each divisor

way. Then sketch a diagram.

a) 2 equal columns b) 4 equal columns c) 5 equal columns

2. Use counters. Can 40 band members group themselves in equal

columns if they march each way? Why or why not?

a) 6 columns No, because 6 does not divide equally into 40.

b) 7 columns No, because 7 does not divide equally into 40.

c) 8 columns Yes, because 8 divides 5 times into 40.

3. Use counters. There are between 25 and 35 students working in

groups planting trees. Which numbers of students could there

be in each case?

a) All students are working in groups of 5. 25, 30, 35 (if between is considered

to include 25 and 35, otherwise 30)

b) All students are working in groups of 4. 28, 32

c) All students are working in groups of 3. 27, 30, 33

4. What number in each part of Question 3 is the divisor?

a) 5 b) 4 c) 3

Copyright © 2004 Nelson Answers Chapter 10: Dividing Greater Numbers 85

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CHAPTER 10

Using Repeated

2 Subtraction to Divide

Goal Use repeated subtraction to divide.

1. 72 muffins are to be put in packages of 5 At-Home Help

muffins each. To find how many packages When dividing larger numbers,

are needed, divide. you can use repeated

苶2

5冄7 苶 Start with 72 muffins subtraction.

50 10 At least 10 packages are needed. If you need to find 102 8, you

22 Now 22 muffins are left. know that the answer is at least

10 because 80 8 10. Then

20 4 4 more packages are needed

you can subtract to see how

2 Now 2 muffins are left. many more are needed. (See

10 4 14 packages are needed. Question 1 for an example.)

But 2 muffins are left over.

a) How many muffins were there at the beginning? 72

b) After they were packaged, how many muffins were left over? 2

c) What is the number in part b) called? remainder

d) Which number is the divisor? 5

e) Why was it known that at least 10 bags were needed? 5 x 10 = 50,

which is less than 72.

f) Why was it known that 4 more bags would be needed? 4 x 5 = 20,

which is less than the 22 left after subtracting 50.

2. 72 muffins were put in packages of 6. How many packages

are needed? How many muffins are left over?

12 needed

0 left over

3. Use repeated subtraction to divide. Show your steps.

1 2 R1 1 2 R1 13 1 6 R2

a) 4 冄苶4

苶苶 9 b) 7 冄苶8

苶苶5 c) 3 冄苶3

苶苶9 d) 6 冄苶9

苶苶8

-4 0 -7 0 -3 0 -6 0

9 15 9 38

-8 -1 4 -9 -3 6

1 1 0 2

86 Answers Chapter 10: Dividing Greater Numbers Copyright © 2004 Nelson

CHAPTER 10

Using Repeated

2 Subtraction to Divide

Goal Use repeated subtraction to divide.

1. 72 muffins are to be put in packages of 5 At-Home Help

muffins each. To find how many packages When dividing larger numbers,

are needed, divide. you can use repeated

苶2

5冄7 苶 Start with 72 muffins subtraction.

50 10 At least 10 packages are needed. If you need to find 102 8, you

22 Now 22 muffins are left. know that the answer is at least

10 because 80 8 10. Then

20 4 4 more packages are needed

you can subtract to see how

2 Now 2 muffins are left. many more are needed. (See

10 4 14 packages are needed. Question 1 for an example.)

But 2 muffins are left over.

a) How many muffins were there at the beginning? 72

b) After they were packaged, how many muffins were left over? 2

c) What is the number in part b) called? remainder

d) Which number is the divisor? 5

e) Why was it known that at least 10 bags were needed? 5 x 10 = 50,

which is less than 72.

f) Why was it known that 4 more bags would be needed? 4 x 5 = 20,

which is less than the 22 left after subtracting 50.

2. 72 muffins were put in packages of 6. How many packages

are needed? How many muffins are left over?

12 needed

0 left over

3. Use repeated subtraction to divide. Show your steps.

1 2 R1 1 2 R1 13 1 6 R2

a) 4 冄苶4

苶苶 9 b) 7 冄苶8

苶苶5 c) 3 冄苶3

苶苶9 d) 6 冄苶9

苶苶8

-4 0 -7 0 -3 0 -6 0

9 15 9 38

-8 -1 4 -9 -3 6

1 1 0 2

86 Answers Chapter 10: Dividing Greater Numbers Copyright © 2004 Nelson

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CHAPTER 10

3 Interpreting Remainders

Goal Decide how to treat the remainder in a division problem.

1. 75 students travel by minivan to an amusement At-Home Help

park. Each minivan can take 6 students. The meaning of the remainder

How many minivans are needed? depends on what the problem

13 asks.

4 different problems could be

2. 75 slices of pizza were eaten. Each pizza was solved by 75 6 12 R3.

The answers could be 12, 13,

cut into 6 slices. How many pizzas were eaten?

1212, and 3. (See an example of

1212 each in Questions 1 to 3.)

3. 75¢ is to be shared equally among 6 students.

a) How much will each student get?

12¢

b) How much money will be left over?

3¢

4. Tickets costing $3 each were bought with $125.

a) How many tickets were bought?

41

b) How much was the change?

$2

5. One car of an amusement park ride holds 4 people.

62 people take the ride. How many cars are needed?

16

6. 50 pictures are put in an album. Each page holds 4 pictures.

a) Exactly how many pages are used?

1212

b) How many pages are full?

12

c) How many pages are needed?

13

Copyright © 2004 Nelson Answers Chapter 10: Dividing Greater Numbers 87

CHAPTER 10

3 Interpreting Remainders

Goal Decide how to treat the remainder in a division problem.

1. 75 students travel by minivan to an amusement At-Home Help

park. Each minivan can take 6 students. The meaning of the remainder

How many minivans are needed? depends on what the problem

13 asks.

4 different problems could be

2. 75 slices of pizza were eaten. Each pizza was solved by 75 6 12 R3.

The answers could be 12, 13,

cut into 6 slices. How many pizzas were eaten?

1212, and 3. (See an example of

1212 each in Questions 1 to 3.)

3. 75¢ is to be shared equally among 6 students.

a) How much will each student get?

12¢

b) How much money will be left over?

3¢

4. Tickets costing $3 each were bought with $125.

a) How many tickets were bought?

41

b) How much was the change?

$2

5. One car of an amusement park ride holds 4 people.

62 people take the ride. How many cars are needed?

16

6. 50 pictures are put in an album. Each page holds 4 pictures.

a) Exactly how many pages are used?

1212

b) How many pages are full?

12

c) How many pages are needed?

13

Copyright © 2004 Nelson Answers Chapter 10: Dividing Greater Numbers 87

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CHAPTER 10

4 Dividing 2 Digits by 1 Digit

Use base ten blocks and pencil and paper to divide a

Goal

2-digit number by a 1-digit number.

1. 5 people share 68 strawberries. At-Home Help

a) Without dividing, tell if there will be any The number you divide into

berries left over. How do you know? parts is the dividend.

53 4 13 R1

Yes, there will be berries left over because 5 only

dividend

divides equally into numbers ending in 5 or 0.

b) Estimate the number that each person 10冧

3

10 3 13

will get. 苶3

4冄苶5苶

40

For example, 13. 13

12

c) Sketch a picture to show the sharing. 1

The remainder is 1.

d) Record the division. Show all the steps.

1 3 R3

5 冄苶6苶8苶

- 50

18

- 15

3

e) How many berries did each person get? How many were left over?

13 berries

3 left over

2. Divide. Show your work.

1 1 R1 1 1 R1 1 6 R2 1 1 R5

a) 6 冄苶6

苶苶7 b) 5 冄苶5

苶苶6 c) 3 冄苶5

苶苶0 d) 8 冄苶9

苶苶3

-60 -5 0 -3 0 -8 0

7 6 20 13

-6 -5 -1 8 -8

1 1 2 5

88 Answers Chapter 10: Dividing Greater Numbers Copyright © 2004 Nelson

CHAPTER 10

4 Dividing 2 Digits by 1 Digit

Use base ten blocks and pencil and paper to divide a

Goal

2-digit number by a 1-digit number.

1. 5 people share 68 strawberries. At-Home Help

a) Without dividing, tell if there will be any The number you divide into

berries left over. How do you know? parts is the dividend.

53 4 13 R1

Yes, there will be berries left over because 5 only

dividend

divides equally into numbers ending in 5 or 0.

b) Estimate the number that each person 10冧

3

10 3 13

will get. 苶3

4冄苶5苶

40

For example, 13. 13

12

c) Sketch a picture to show the sharing. 1

The remainder is 1.

d) Record the division. Show all the steps.

1 3 R3

5 冄苶6苶8苶

- 50

18

- 15

3

e) How many berries did each person get? How many were left over?

13 berries

3 left over

2. Divide. Show your work.

1 1 R1 1 1 R1 1 6 R2 1 1 R5

a) 6 冄苶6

苶苶7 b) 5 冄苶5

苶苶6 c) 3 冄苶5

苶苶0 d) 8 冄苶9

苶苶3

-60 -5 0 -3 0 -8 0

7 6 20 13

-6 -5 -1 8 -8

1 1 2 5

88 Answers Chapter 10: Dividing Greater Numbers Copyright © 2004 Nelson

5.
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CHAPTER 10

Solve Problems By Guessing

5 and Testing

Goal Use a guess-and-test strategy to solve problems.

1. Jalissa has 66 chairs to arrange for the show. At-Home Help

She makes 5 equal rows and has 1 chair left Guessing and testing is a useful

over. How many chairs are in each row? strategy for solving problems.

For example, a number between

13

25 and 35 is divided by 7 and

the remainder is 3. To find the

number, think:

35 7 5, but there is no

2. Derek has between 40 and 50 clothespins to remainder.

7 4 28

put equally in 2 bags.

To have a remainder of 3,

a) How many clothespins could there be if use 28 3 31.

there are none left over? So 31 7 4 R3.

The number is 31.

40, 42, 44, 46, 48, 50 (if between is considered

to include 40 and 50, otherwise 42, 44, 46, 48)

b) How many clothes pins could there be if there is 1 left over?

41, 43, 45, 47, 49

3. Chloe has 87 books to place on 7 shelves. How many more books

does she need to have an equal number on each shelf?

4

4. Ryan used between 50 and 60 cards to make an array with 4 rows.

He has 1 card left over. How many cards did he start with?

Find more than one answer.

If he started with 53 cards, there would be 13 in each row with 1 left over.

If he started with 57 cards, there would be 14 in each row with 1 left over.

Copyright © 2004 Nelson Answers Chapter 10: Dividing Greater Numbers 89

CHAPTER 10

Solve Problems By Guessing

5 and Testing

Goal Use a guess-and-test strategy to solve problems.

1. Jalissa has 66 chairs to arrange for the show. At-Home Help

She makes 5 equal rows and has 1 chair left Guessing and testing is a useful

over. How many chairs are in each row? strategy for solving problems.

For example, a number between

13

25 and 35 is divided by 7 and

the remainder is 3. To find the

number, think:

35 7 5, but there is no

2. Derek has between 40 and 50 clothespins to remainder.

7 4 28

put equally in 2 bags.

To have a remainder of 3,

a) How many clothespins could there be if use 28 3 31.

there are none left over? So 31 7 4 R3.

The number is 31.

40, 42, 44, 46, 48, 50 (if between is considered

to include 40 and 50, otherwise 42, 44, 46, 48)

b) How many clothes pins could there be if there is 1 left over?

41, 43, 45, 47, 49

3. Chloe has 87 books to place on 7 shelves. How many more books

does she need to have an equal number on each shelf?

4

4. Ryan used between 50 and 60 cards to make an array with 4 rows.

He has 1 card left over. How many cards did he start with?

Find more than one answer.

If he started with 53 cards, there would be 13 in each row with 1 left over.

If he started with 57 cards, there would be 14 in each row with 1 left over.

Copyright © 2004 Nelson Answers Chapter 10: Dividing Greater Numbers 89

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CHAPTER 10

6 Estimating with 3-Digit Dividends

Goal Use multiplication and division facts to estimate quotients.

1. Choose the correct answer. At-Home Help

To estimate 290 ÷ 7, this fact is useful. Using basic facts and extending

A. 30 5 6 C. 28 7 4 them helps you to estimate

quotients.

B. 27 9 3 D. 25 5 5

For example, you know

18 3 6, so

2. Choose the correct answer.

180 3 18 tens 3

If I know 36 4 9, then I know . 6 tens

E. 36 tens 4 90 G. 360 40 90 60

This helps you to estimate that

F. 36 tens 4 9 H. 360 4 900 185 3 is about 60.

3. Doug wants to read a 168-page book in 6 days.

a) What fact will help him to estimate how many pages he needs

to read each day?

180 ÷ 6 = 30

b) About how many pages should he read each day?

30

4. Emma has

• 125 blue beads • 200 red beads • 160 yellow beads

To make 1 bracelet, she needs

• 4 blue beads • 6 red beads • 5 yellow beads

Estimate how many bracelets she can make with each

colour of bead.

a) blue b) red c) yellow

Answers will vary. For example:

30 30 30

5. Estimate each quotient. Explain your thinking.

Answers will vary. For example:

苶1

a) 6冄苶6苶7

苶 苶0

b) 8冄苶5苶9

苶

100 because 600 ÷ 6 = 100. 60 because 480 ÷ 8 = 60.

90 Answers Chapter 10: Dividing Greater Numbers Copyright © 2004 Nelson

CHAPTER 10

6 Estimating with 3-Digit Dividends

Goal Use multiplication and division facts to estimate quotients.

1. Choose the correct answer. At-Home Help

To estimate 290 ÷ 7, this fact is useful. Using basic facts and extending

A. 30 5 6 C. 28 7 4 them helps you to estimate

quotients.

B. 27 9 3 D. 25 5 5

For example, you know

18 3 6, so

2. Choose the correct answer.

180 3 18 tens 3

If I know 36 4 9, then I know . 6 tens

E. 36 tens 4 90 G. 360 40 90 60

This helps you to estimate that

F. 36 tens 4 9 H. 360 4 900 185 3 is about 60.

3. Doug wants to read a 168-page book in 6 days.

a) What fact will help him to estimate how many pages he needs

to read each day?

180 ÷ 6 = 30

b) About how many pages should he read each day?

30

4. Emma has

• 125 blue beads • 200 red beads • 160 yellow beads

To make 1 bracelet, she needs

• 4 blue beads • 6 red beads • 5 yellow beads

Estimate how many bracelets she can make with each

colour of bead.

a) blue b) red c) yellow

Answers will vary. For example:

30 30 30

5. Estimate each quotient. Explain your thinking.

Answers will vary. For example:

苶1

a) 6冄苶6苶7

苶 苶0

b) 8冄苶5苶9

苶

100 because 600 ÷ 6 = 100. 60 because 480 ÷ 8 = 60.

90 Answers Chapter 10: Dividing Greater Numbers Copyright © 2004 Nelson

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CHAPTER 10

7 Dividing in Parts

Goal Divide in steps using simpler numbers.

1. Barb, Cameron, and Rory have coin collections. At-Home Help

Barb has the greatest number, 390 coins.

285 3 can be found by

She has 5 times as many coins as Cameron. renaming 285 as 270 15

She has 3 times as many as Rory. because 270 3 is 90

and 15 3 is 5.

a) Why is renaming 390 as 350 + 40 useful in So 285 3 is 90 5, or 95.

finding out how many coins Cameron has?

Both 350 and 40 can be related to multiplication facts:

350 ÷ 5 = 70 and 40 ÷ 5 = 8.

苶5

b) Calculate 5冄苶3苶0

苶 5冄苶4

苶0

苶.

78

c) How many coins does Cameron have? 78

d) Why is renaming 390 as 350 40 not useful in finding out

how many coins Rory has?

3 does not divide equally into 350 or 40.

e) Why is renaming 390 as 300 90 useful?

3 divides equally into both 300 and 90.

f) Why is renaming 390 as 360 30 useful?

3 divides equally into both 360 and 30.

g) Find the number of coins Rory has, using the renaming

in part e) or f).

130

2. Divide into parts and find the quotient.

103 62 R4 142

苶1

a) 6冄苶6苶8

苶 苶0

b) 8冄苶5苶0苶 苶1

c) 5冄苶7苶0

苶

Copyright © 2004 Nelson Answers Chapter 10: Dividing Greater Numbers 91

CHAPTER 10

7 Dividing in Parts

Goal Divide in steps using simpler numbers.

1. Barb, Cameron, and Rory have coin collections. At-Home Help

Barb has the greatest number, 390 coins.

285 3 can be found by

She has 5 times as many coins as Cameron. renaming 285 as 270 15

She has 3 times as many as Rory. because 270 3 is 90

and 15 3 is 5.

a) Why is renaming 390 as 350 + 40 useful in So 285 3 is 90 5, or 95.

finding out how many coins Cameron has?

Both 350 and 40 can be related to multiplication facts:

350 ÷ 5 = 70 and 40 ÷ 5 = 8.

苶5

b) Calculate 5冄苶3苶0

苶 5冄苶4

苶0

苶.

78

c) How many coins does Cameron have? 78

d) Why is renaming 390 as 350 40 not useful in finding out

how many coins Rory has?

3 does not divide equally into 350 or 40.

e) Why is renaming 390 as 300 90 useful?

3 divides equally into both 300 and 90.

f) Why is renaming 390 as 360 30 useful?

3 divides equally into both 360 and 30.

g) Find the number of coins Rory has, using the renaming

in part e) or f).

130

2. Divide into parts and find the quotient.

103 62 R4 142

苶1

a) 6冄苶6苶8

苶 苶0

b) 8冄苶5苶0苶 苶1

c) 5冄苶7苶0

苶

Copyright © 2004 Nelson Answers Chapter 10: Dividing Greater Numbers 91

8.
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CHAPTER 10

8 Dividing 3 Digits by 1 Digit

Use base ten blocks and pencil and paper to divide a

Goal

3-digit number by a 1-digit number.

1. A class drinks 165 cartons of milk starting on At-Home Help

Monday and ending on Friday. They drink the

267 7 38 R1

same number of cartons each day. How many

38

cartons do the students drink each day? 苶6

7冄苶2苶7

苶

210

33 57

56

1

2. 780 tickets were sold for 4 performances of a play.

The same number of tickets were sold for each performance.

How many tickets were sold for each performance?

195

3. Carolyn’s class baked 276 cupcakes for a bake sale. They want

to package all the cupcakes. Should they put them in packages

of 6 or 8? Show your work.

packages of 6

276 ÷ 6 = 46, but 276 ÷ 8 = 34 R4.

4. Divide.

a) 184 4 c) 511 7

46 73

b) 336 6 d) 616 8

56 77

92 Answers Chapter 10: Dividing Greater Numbers Copyright © 2004 Nelson

CHAPTER 10

8 Dividing 3 Digits by 1 Digit

Use base ten blocks and pencil and paper to divide a

Goal

3-digit number by a 1-digit number.

1. A class drinks 165 cartons of milk starting on At-Home Help

Monday and ending on Friday. They drink the

267 7 38 R1

same number of cartons each day. How many

38

cartons do the students drink each day? 苶6

7冄苶2苶7

苶

210

33 57

56

1

2. 780 tickets were sold for 4 performances of a play.

The same number of tickets were sold for each performance.

How many tickets were sold for each performance?

195

3. Carolyn’s class baked 276 cupcakes for a bake sale. They want

to package all the cupcakes. Should they put them in packages

of 6 or 8? Show your work.

packages of 6

276 ÷ 6 = 46, but 276 ÷ 8 = 34 R4.

4. Divide.

a) 184 4 c) 511 7

46 73

b) 336 6 d) 616 8

56 77

92 Answers Chapter 10: Dividing Greater Numbers Copyright © 2004 Nelson

9.
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CHAPTER 10

Test Yourself

Circle the correct answer.

1. Which division equation matches the diagram?

A. 8 6 48 B. 48 8 8 C. 48 8 6 D. 48 12 4

2. 4 students are sharing 56 minutes of computer

time equally. How many minutes does each student get?

E. 14 F. 16 G. 18 H. 20

3. 57 students will receive certificates of achievement in

mathematics. The certificates come in packages of 5.

How many packages need to be bought?

A. 8 B. 9 C. 10 D. 12

4. What is the remainder when 89 is divided by 8?

E. 9 F. 1 G. 5 H. 11

5. 7 classes are sharing the planting of 500 spring bulbs equally.

What is a reasonable estimate of the number of bulbs

each class will plant?

A. 30 B. 70 C. 90 D. 100

6. 132 students will be divided into teams of 4 for the science fair.

How many teams will there be?

E. 15 F. 27 G. 33 H. 44

7. 264 students are sitting in 8 equal rows for the assembly.

How many students are in each row?

A. 22 B. 33 C. 44 D. 55

8. Chloe is reading a 326-page book. She has read the same number

of pages each day for 7 days. How many pages does she have left?

E. 4 F. 6 G. 8 H. 10

Copyright © 2004 Nelson Answers Chapter 10: Dividing Greater Numbers 93

CHAPTER 10

Test Yourself

Circle the correct answer.

1. Which division equation matches the diagram?

A. 8 6 48 B. 48 8 8 C. 48 8 6 D. 48 12 4

2. 4 students are sharing 56 minutes of computer

time equally. How many minutes does each student get?

E. 14 F. 16 G. 18 H. 20

3. 57 students will receive certificates of achievement in

mathematics. The certificates come in packages of 5.

How many packages need to be bought?

A. 8 B. 9 C. 10 D. 12

4. What is the remainder when 89 is divided by 8?

E. 9 F. 1 G. 5 H. 11

5. 7 classes are sharing the planting of 500 spring bulbs equally.

What is a reasonable estimate of the number of bulbs

each class will plant?

A. 30 B. 70 C. 90 D. 100

6. 132 students will be divided into teams of 4 for the science fair.

How many teams will there be?

E. 15 F. 27 G. 33 H. 44

7. 264 students are sitting in 8 equal rows for the assembly.

How many students are in each row?

A. 22 B. 33 C. 44 D. 55

8. Chloe is reading a 326-page book. She has read the same number

of pages each day for 7 days. How many pages does she have left?

E. 4 F. 6 G. 8 H. 10

Copyright © 2004 Nelson Answers Chapter 10: Dividing Greater Numbers 93