Math Gr4 Ch9

Chapter 9
Divide by a One-Digit Number
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9

Lesson 9-1 Division with Remainders
Lesson 9-2 Divide Multiples of 10, 100, and
1,000
Lesson 9-3 Problem-Solving Strategy: Guess
and Check
Lesson 9-4 Estimate Quotients
Lesson 9-5 Two-Digit Quotients
Lesson 9-6 Problem-Solving Investigation:
Choose a Strategy
Lesson 9-7 Three-Digit Quotients
Lesson 9-8 Quotients with Zeros
Lesson 9-9 Divide Greater Numbers

9-1 Division with Remainders

Five-Minute Check (over Chapter 8)
Main Idea
California Standards
Example 1
Example 2
Example 3


• I will carry out division with and without
remainders.


Preparation for Standard 4NS3.2
Demonstrate an understanding of, and the ability to
use, standard algorithms for multiplying a multi-digit
number by a two-digit number and for dividing a multi-
digit number by a one-digit number; use relationships
between them to simplify computations and to check
results.


José wants to change the buttons on his school
uniform shirts. Each shirt has 7 buttons. He bought
a package of 84 buttons. On how many shirts will
he be able to change the buttons.

There are 84 buttons. Each shirt has 7 buttons. Find
84 7.


Step 1 Divide the tens.

7 84 Can 8 tens be divided
equally into groups of 7?

1
7 84 Yes, there is one ten in
each group.


Step 2 Multiply, subtract, and compare.
1
7 84 Multiply. 7 1 = 7
– 7 Subtract. 8 – 7 = 1
1 Compare. 1 < 7

Step 3 Bring down the ones.
1
7 84 Bring down 4 ones.
– 7
14 14 ones in all.


Step 4 Divide the ones.

1 2 Divide. 14 7=2
7 84 Put 2 in the quotient.
– 7
14 Multiply. 2 7 = 14
– Subtract. 14 – 14 = 0
14
0 Compare. 0 < 7

Answer: So, José will be able to change the buttons
on 12 shirts.


Victor is making care packages with his charity
group for students in college. He has a package
of 54 travel size soaps. 2 soaps go in each care
package. How many care packages will he be
able be able to fill with soap?

A. 17
B. 22
C. 25
D. 27


Find 48 ÷ 6.


6 48 Divide.
6 does not divide into 4.

So, there are no tens in
each group.



8 R0 Divide. 48 6 = 8
6 48 So, 8 ones is in each group.
– 48 Multiply. 8 6 = 48
0 Subtract. 48 – 48 = 0
Compare. 0 < 6
Remainder = 0

Answer: So, 48 6 = 8.


Find 77 5.

A. 5 R2

B. 15 R2

C. 10 R0

D. 15 R0


Markus wants to go to the go-cart park with his
friends. The group rate is $63 for 5 guests. How
much will each person need to pay for their share
of the group price?


1 Divide. 6 5 = 1
5 63 So, one tens is in each group.
– 5 Multiply. 5 1 = 5
1 Subtract. 6 – 5 = 1
Compare. 1 < 5



1 2 Bring down the ones.
R3
5 63 Divide. 13 5 = 2
– 5 Put 2 in the quotient.
13 Multiply. 5 2 = 10
– 10
Subtract. 13 – 10 = 3
3
Compare. 3 < 5
Remainder = 3

Answer: So, each person will have to pay a little
over $12.


Six friends went to the movies together. The total
cost for the movies is $44. How much does each
person have to pay?

A. a little over $6

B. exactly $6

C. a little over $7

D. exactly $7

9-2 Divide Multiples of 10, 100, and 1,000

Five-Minute Check (over Lesson 9-1)
Main Idea
Example 1
Example 2


• I will use basic facts and patterns to divide
mentally.


Standard 4NS3.2 Demonstrate an
understanding of, and the ability to use, standard
algorithms for multiplying a multi-digit number by a
two-digit number and for dividing a multi-digit
number by a one-digit number; use relationships
between them to simplify computations and to
check results.


The factory line just completed 600 wheels for
their tricycles. How many tricycles can they make
with the 600 wheels?
Each tricycle has 3 wheels, so you need to divide
600 by 3.


One Way: Use a Multiplication Pattern

3×2=6 6÷3=2
3 × 20 = 60 60 ÷ 3 = 20
3 × 200 = 600 600 ÷ 3 = 200


Another Way: Use a Basic Fact

6÷3=2 basic fact
60 ÷ 3 = 20
600 ÷ 3 = 200

Answer: So, the factory can make 200 tricycles.


Fred collects coins and puts them in an album. He
has 400 coins. If 8 coins fit on a page, how many
pages does he have filled in the album?

A. 5

B. 40

C. 50

D. 500


Find the quotient of 3,200 and 80.

One Way: Use a Multiplication Pattern

8 × 4 = 32 32 ÷ 8 = 4
80 × 4 = 320 320 ÷ 80 = 4
80 × 40 = 3,200 3,200 ÷ 80 = 40


Another Way: Use a Basic Fact

The basic fact for 3,200 ÷ 80 is 32 ÷ 8.

32 ÷ 8 = 4 basic fact
320 ÷ 80 = 4
3,200 ÷ 80 = 40

Answer: So, the quotient is 40.


Find the quotient of 6,300 and 70.

A. 90

B. 900

C. 9,000

D. 80

9-3 Problem-Solving Strategy: Guess and Check

Main Idea
Example 1: Problem-Solving Strategy


• I will solve problems by using the guess and
check strategy.


Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.


Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.


Ruben bought 3 gifts for his sisters. Two of the
gifts cost the same. The other gift costs $3 more
than the other two. If the total amount or money
spent was $27, how much did each gift cost?


Understand
What facts do you know?
• There are 3 gifts, and two gifts cost the same.
• One gift is $3 more than the other two.
• Ruben spent $27 on all 3 gifts.

What do you need to find?
• The cost of each gift.


Plan
You can guess and check to solve the problem.


Solve
Use gift + gift + (gift + $3) = $27 and make
logical guesses.

Start with numbers smaller than $10 because
$10 × 3 = $30 and the total is less than $30.


Solve
Try $9.
$9 + $9 + ($9 + $3) = $30 No, too large.

Try $8.
$8 + $8 + ($8 + $3) = $27 yes

Answer: So, two gifts cost $8 each and the third
gift costs $8 + $3, or $11.


Check
Subtract the cost of each gift from the total cost.

First gift: $27 – $8 = $19
Second gift: $19 – $8 = $11
Third gift: $11 – $11 = $0

So, the answer is correct.

9-4 Estimate Quotients

Main Idea and Vocabulary
Example 1
Example 2


• I will estimate quotients.

• compatible numbers


check results.


A small wading pool holds 225 gallons of water
and it takes 3 hours to fill. About how many
gallons are put into the pool in one hour?
Estimate the quotient of 225 and 3.


One Way: Compatible Numbers

225 ÷ 3

210 ÷ 3 = 70 3 × 7 = 21


Another Way: Basic Facts

225 ÷ 3

3 × 7 = 21
3 × 70 = 210
210 ÷ 3 = 70


Answer: So, about 70 gallons of water are put into
the pool in one hour.


Estimate 310 5.

A. 5

B. 50

C. 6

D. 60


The hotdog stand at the school carnival earned
$1,315 today and sold only $4 combination meals.
About how many meals did they sell?


One Way: Compatible Numbers

$1,315 ÷ $4

$1,200 ÷ $4 = 300 4 × 3 = 12


Another Way: Basic Facts

$1,315 ÷ $4

4 × 3 = 12
4 × 30 = 120
4 × 300 = 1,200
$1,200 ÷ $4 = 300


Answer: So, they sold about 300 meals.


Estimate 1,700 8.

A. 100

B. 200

C. 300

D. 400

9-5 Two-Digit Quotients

Main Idea
Example 1
Example 2


• I will divide a two-digit dividend by a one-digit
number.


Preparation for Standard 4NS3.2
Demonstrate an understanding of, and the ability
to use, standard algorithms for multiplying a multi-
digit number by a two-digit number and for
dividing a multi-digit number by a one-digit
number; use relationships between them to
simplify computations and to check results.


Standard 4MR2.1 Use estimation to verify the
reasonableness of calculated results.


There are 96 cans of tennis balls in 4 boxes. How
many cans are in each box?

Estimate 96 ÷ 4 100 ÷ 4 = 25

2 Divide. 9 4 = 2
Put 2 in the quotient.
4 96
–8 Multiply. 4 2 = 8
1 Subtract. 9 – 8 = 1
Compare. 1 < 4



2 4 Bring R0 the ones.
down
4 96 Divide. 16 4 = 4
–8 Put 4 in the quotient.
1 6 Multiply. 4 4 = 16
– Subtract. 16 – 16 = 0
16
0 Compare. 0 < 4
Remainder = 0

Answer: So, 96 4 = 24. The answer is reasonable
because it is close to the estimate of 25.


There are 102 packs of crackers in 5 cases. How
many packs are in each case?

A. 22

B. 20 R2

C. 12

D. 10 R2


Shelley and 6 of her friends are using beads to
make necklaces. She has 338 beads to share.
How many beads will each of them get?

There are 338 beads and 7 friends (Shelley and 6 of
her friends).

Divide 338 ÷ 7.

Estimate 338 ÷ 7 350 ÷ 7 = 50


Step 1 Estimate to place the first digit.

x
7 338 7 338



4 Divide. 33 7 = 4
– 28
Multiply. 7 4 = 28
5 Subtract. 33 – 28 = 5
Compare. 5 < 7



R2
7 338 Divide. 58 7 = 8
– 28 8 in the quotient.
Put
58 Multiply. 7 8 = 56
– Subtract. 58 – 56 = 2
56
2 Compare. 2 < 7
Remainder = 2

Answer: So, each person will get 48 beads and 2 will
be left over. The answer, 48 R2, is close to the
estimate, so the answer is reasonable.


Lupe and 5 of his friends are looking at baseball
cards at his house. If Lupe has 491 baseball
cards, and he splits them evenly between him and
his friends evenly to look at, how many cards does
each person get?

A. 81 R5

B. 81 R3

C. 72 R0

D. 71 R5

9-6 Problem-Solving Investigation: Choose a Strategy

Main Idea
Example 1: Problem-Solving Investigation


• I will choose the best strategy to solve a problem.


Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.


Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.


CINDY: I had some stamps. I bought
6 more stamps. I traded 4 of my
stamps for 8 of my friend’s stamps.
I now have 32 stamps.

YOUR MISSION: Find how many stamps
Cindy started with.


Understand
What facts do you know?
• Cindy bought 6 stamps.
• She traded 4 stamps for 8 stamps.
• She now has 32 stamps.

What do you need to find?
• Find the number of stamps Cindy started with.


Plan
You need to find how many stamps Cindy
started with. So, the work backward strategy
is a good choice.


Solve
Start with the end result, then work backwards
one step at a time.

End result stamps Cindy has now
stamps Cindy received from
a friend


Solve

stamps Cindy gave to a friend

stamps Cindy bought

Answer: 22 stamps


Check
Look back at the problem. Cindy gained 14
stamps and lost 4. This means she has 10 more
stamps then she started with. If she now has 32
stamps, then she started with 22 stamps. The
answer is correct.

9-7 Three-Digit Quotients

Main Idea
Example 1
Example 2


• I will divide a three-digit dividend by a one-digit
number.


check results.


A teacher orders pencils in large plastic jars. Each
jar holds 276 pencils. To how many students can
he give 2 pencils?

Estimate 276 2 280 ÷ 2 = 140

Step 1 Divide the hundreds.
1 Divide. 2 2 = 1
0 Subtract. 2 – 2 = 0
Compare. 0 < 2



13 Bring down the tens.
2 276 Divide. 7 2 = 3
07 Multiply. 3 2 = 6
–6 Subtract. 7 – 6 = 1
1 Compare. 1 < 2



2 276 Divide. 16 2 = 8
07
–6
16 Multiply. 8 2 = 16
– 16 Subtract. 16 – 16 = 0
0 Compare. 0 < 2

Answer: So, 138 students can receive 2 pencils. Since
the answer, 138, is close to the estimate of
140, the answer is reasonable.


Find 322 2.

A. 61

B. 161

C. 111

D. 121


The principal wants to form reading groups of 4 for
567 students. How many groups will be formed?

To find how many groups will be formed, divide
567 by 4.

Estimate 567 4 560 ÷ 4 = 140


14 1 R3
4 567
–4
16
– 16
07
– 4
3

Answer: So, 141 groups will be formed with 3 people
left over. The answer is close to the estimate
of 140, so the answer is reasonable.


A group of 892 volunteers want to split up into
groups of 8 to do different community service
projects. How many groups will be formed?

A. 112 R4

B. 121 R4

C. 111 R4

D. 111 R5

9-8 Quotients with Zeros

Main Idea
Example 1
Example 2


• I will divide with zeros in the quotients.


results.


Rita is using 315 beads to make beaded necklaces
for 3 of her friends. If each necklace has the same
number of beads, how many beads will each
necklace have?
You need to find 315 ÷ 3.

1 Divide. 3 3 = 1
0 Subtract. 3 – 3 = 0
Compare. 0 < 3



10 Bring down the tens.
3 315 Divide. Since 1 < 3, there is not enough
–3 to divide. So, put 0 in the quotient.
–0 Subtract. 1 – 0 = 1
1 Compare. 1 < 3



3 315 Divide. 15 3 = 5
01
–0
15 Multiply. 3 5 = 15
– 15 Subtract. 15 – 15 = 0
0 Compare. 0 < 3

Answer: So, each necklace will have 105 beads.


Felix bowled 327 in 3 games of bowling. If he
scored the same for each game, what was his
score for each game?

A. 118

B. 108

C. 119

D. 109


The camping club spent $217 on 2 large tents. How
much did each tent cost?

To find the cost of each tent, you need to find 217 ÷ 2.

Estimate 217 2 220 ÷ 2 = 110


10 8 R1
2 217
–2
01
– 0
17 Remember to divide, multiply,
– 16
subtract, and compare. Then
1 bring down the next number in
the dividend.
Answer: So, the camping club spent a little over $108
for each tent. The answer is close to the
estimate of 110, so the answer is reasonable.


A ski club spent $408 on 4 pairs of skis. What is the
cost of each pair?

A. $102

B. $103

C. $112

D. $113

9-9 Divide Greater Numbers

Main Idea
Example 1
Example 2


• I will divide four- and five-digit quotients by a
one-digit number.


results.


Mrs. Chi wants to bundle 4 muffins in a package for
a fundraiser at school. Parents donated 4,576
muffins. How many bundles will be ready to sell?

To find the number of bundles, you need to find
4,576 4.

Step 1 Divide the thousands.
1 Divide. 4 4 = 1
4 4,576 Put 1 in the quotient.
0 Subtract. 4 – 4 = 0
Compare. 1 < 4



1,1 Bring down the hundreds.
4 4,576 Divide. 5 4 = 1
–4
– 4 Subtract. 5 – 4 = 1
1 Compare. 1 < 4


Step 3 Divide each place.

1,14 4
4 4,576 For each
–4 place, multiply, subt
05 ract, and bring
– 4 down.
7 1
– 16
1 6
– 16
0

Answer: So, 1,144 bundles will be ready to sell.


A cookie bake sale sold 5,705 cookies. If there were
5 cookies in every bundle that they sold, how many
bundles of cookies did they sell?

A. 1,101

B. 1,141

C. 1,241

D. 1,242


The school play earned $62,530 for the week. If
admission costs $5 a ticket, how many tickets did
they sell?
To find the number of tickets sold, find 62,530 5.

Estimate $62,530 $5 $60,000 ÷ $5 = 12,000


Divide each place.

12,506
5 62,530 For each place, divide,
–5 multiply, subtract, and
12 compare. Then bring
– 10 down the next digit in
5 2 the dividend.
– 25
0 3
– 0
3 0
– 30
0


Answer: So, they sold 12,506 tickets. The answer
is close to the estimate of 12,000, so the
answer is reasonable.


A baseball team made $33,615 after selling tickets
for two weeks. If admission is $3, how many tickets
did they sell?

A. 10,205

B. 10,215

C. 11,215

D. 11,205

9

Five-Minute Checks

9

Lesson 9-1 (over Chapter 8)
Lesson 9-2 (over Lesson 9-1)

9
(over Chapter 8)

Multiply 3,270 25.

A. 1,510,350

B. 79,450

C. 81,750

D. 22,890

9
(over Chapter 8)

Multiply 5,741 53.

A. 45,928

B. 302,173

C. 1,521,123

D. 304,273

9
(over Chapter 8)

Multiply 98,304 24.

A. 2,169,296

B. 2,359,296

C. 589,824

D. 1,259,296

9
(over Chapter 8)

Multiply $34,811 45.

A. $1,566,495

B. $87,979

C. $313,295

D. $1,466,495

9
(over Lesson 9-1)

Divide 68 2.

A. 43

B. 66

C. 34

D. 64

9
(over Lesson 9-1)

Divide 78 3.

A. 39

B. 62

C. 76

D. 26

9
(over Lesson 9-1)

Divide 59 5.

A. 11 R4

B. 10 R9

C. 12

D. 12 R1

9
(over Lesson 9-1)

Divide 97 8.

A. 21 R1

B. 12 R1

C. 11 R9

D. 10 R7

9
(over Lesson 9-2)

Divide 3,600 4.

A. 9,000

B. 922 R2

C. 1,200

D. 900

9
(over Lesson 9-2)

Divide 490 7.

A. 70

B. 155 R5

C. 140

D. 170

9
(over Lesson 9-2)

Divide 2,800 70.

A. 4

B. 41

C. 40

D. 410

9
(over Lesson 9-2)

Divide 810 90.

A. 90

B. 9

C. 99

D. 81

9
(over Lesson 9-3)

Solve. Use the Guess and Check strategy. A
unicycle has one wheel and a bicycle has two.
Steve walks into Hanson’s Cycling Shop and
counts 19 unicycles and bicycles and 27 wheels.
How many unicycles are there?

A. 8 unicycles
B. 9 unicycles
C. 10 unicycles
D. 11 unicycles

9
(over Lesson 9-4)

Estimate 161 5.

A. 30

B. 35

C. 32 R1

D. 33

9
(over Lesson 9-4)

Estimate 171 3.

A. 63 R2

B. 70

C. 56 R2

D. 60

9
(over Lesson 9-4)

Estimate 2,732 4.

A. 600

B. 700

C. 693

D. 690 R3

9
(over Lesson 9-4)

Estimate 5,543 9.

A. 615 R8

B. 700

C. 600

D. 611 R1

9
(over Lesson 9-5)

Divide 75 6. Use estimation to check.

A. 13 R2

B. 12 R3

C. 10 R5

D. 16 R4

9
(over Lesson 9-5)


A. 14 R2

B. 11 R3

C. 10 R2

D. 11 R5

9
(over Lesson 9-5)


A. 40

B. 31 R3

C. 33 R3

D. 34

9
(over Lesson 9-5)


A. 82 R2

B. 82 R1

C. 81

D. 77 R7

9
(over Lesson 9-6)

Choose the best strategy, then solve the problem.
What is the fifteenth number in the pattern:
8, 16, 24, 32, 40, …? Identify the pattern.

A. 110; Add 7

B. 40, 960; Multiply by 2

C. 120; Add 8

D. 130; Add 9

9
(over Lesson 9-7)

Divide 678 6. Check your answer.

A. 113 R2

B. 116 R4

C. 113

D. 111 R2

9
(over Lesson 9-7)


A. 125

B. 114 R1

C. 115

D. 111 R3

9
(over Lesson 9-7)


A. 171 R4

B. 178

C. 180

D. 177 R4

9
(over Lesson 9-7)


A. 136 R4

B. 142 R6

C. 137

D. 137 R4

9
(over Lesson 9-8)

Divide 525 5.

A. 150

B. 105

C. 15

D. 104

9
(over Lesson 9-8)

Divide 621 3.

A. 208

B. 27

C. 207

D. 270

9
(over Lesson 9-8)

Divide 967 9.

A. 107 R4

B. 17 R4

C. 107

D. 170 R4

9
(over Lesson 9-8)

Divide 635 6.

A. 15 R5

B. 150

C. 150 R5

D. 105 R5

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Math Gr4 Ch9

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Math Gr4 Ch9