Exploring Division and Practice Test on Division

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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. 10-NEM-GR4-WBAN/SI-CH10 11/3/03 12:55 PM Page 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

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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

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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

5. 10-NEM-GR4-WBAN/SI-CH10 11/3/03 12:55 PM Page 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

7. 10-NEM-GR4-WBAN/SI-CH10 11/3/03 12:55 PM Page 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

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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

9. 10-NEM-GR4-WBAN/SI-CH10 11/3/03 12:55 PM Page 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

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