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Chapter 15Divide by One-Digit Numbers

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Lesson 15-1 Divide Multiples of 10, 100, and 1,000

Lesson 15-2 Estimate Quotients

Lesson 15-3 Two-Digit Quotients

Lesson 15-4 Problem-Solving Strategy: Work Backwards

Lesson 15-5 Three-Digit Quotients

Lesson 15-6 Problem-Solving Investigation: Choose the Best Strategy

Lesson 15-7 Divide Money

15Divide by One-Digit Numbers



Five-Minute Check (over Chapter 14)

Main Idea

California Standards

Example 1: Use Models to Divide

Example 2: Divide Multiples

Example 3: Divide Multiples

15-1 Divide Multiples of 10, 100, and 1,000



• I will learn to divide multiples of 10, 100, and 1,000.



Standard 3NS2.5 Solve division problems in which a multi-digit number is evenly divided by a one-digit number (135 ÷ 5 = ___ ).


Step 1 Show 600 as 60 tens.

Find 600 ÷ 3.



Step 2 Divide the 60 tens into 3 equal groups.


200 200 200

Answer: 600 ÷ 3 = 200



Find 800 ÷ 2.

A. 250

B. 400

C. 300

D. 500


The stadium has 1,800 seats divided equally into 6 sections. How many seats are in each section?

Find 1,800 ÷ 6. Use basic facts and patterns.

Answer: So, there are 300 seats in each section.


18 ÷ 6 = 3

180 ÷ 6 = 30

1,800 ÷ 6 = 300

18 ones ÷ 6 = 3 ones

18 tens ÷ 6 = 3 tens

18 hundreds ÷ 6 = 3 hundreds



A class split up into 3 teams and had a bake sale which made $600. How much did each team earn if the money was split evenly between the teams?

A. $200

B. $300

C. $150

D. $100


How many seats are in each section if 4,200 seats are divided equally into 7 sections?


Answer: So, there are 600 seats in each section.

42 ÷ 7 = 6

420 ÷ 7 = 60

4,200 ÷ 7 = 600

Use the basic fact.

Use the pattern of zeros.

Find 4,200 ÷ 7.



Find 2,500 ÷ 5.

A. 350

B. 400

C. 500

D. 600


Five-Minute Check (over Lesson 15-1)

Main Idea


Example 1: Estimate by Rounding

Example 2: Real-World Example

15-2 Estimate Quotients



• I will estimate quotients.




Standard 3MR2.1 Use estimation to verify the reasonableness of calculated results.


There are 238 children in the school. If there are 8 classrooms, about how many students are there in each class?


You need to estimate 238 ÷ 8 or 8 238.

Step 1 Round 238 to the nearest ten that has a basic fact you can use.

238 ÷ 8 240 ÷ 8


Step 2 Write the basic fact you will use to divide.


24 ÷ 8 = 3

Step 3 Use the basic fact and patterns to divide.

24 ÷ 8 = 3 240 ÷ 8 = 30

Answer: So, 238 ÷ 8 is about 30. About 30 students are in each class.



A community center wants to break up its 103 members into teams of 5 for a basketball tournament. About how many teams will the tournament have?

A. about 20 teams

B. about 30 teams

C. about 15 teams

D. about 25 teams



A theater sold 1,113 tickets for 4 shows. About how many tickets were sold for each show?

You need to estimate 1,113 ÷ 4 or 4 1,113.

Step 1 Round 1,113 to the nearest hundred that has a basic fact you can use.

1,113 ÷ 4 1,200 ÷ 4



Step 2 Write the basic fact you will use to divide.

12 ÷ 4 = 3

Step 3 Use the basic fact and patterns to divide.

12 ÷ 4 = 3 1,200 ÷ 4 = 300

Answer: So, 1,113 ÷ 4 is about 300. About 300 tickets were sold for each show.



A fundraiser generated $1,212 from 6 local churches. About how much money did each church give to the fundraiser?

A. about $100

B. about $200

C. about $250

D. about $300



Main Idea




15-3 Two-Digit Quotients

Division



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




Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results.


A total of 95 students signed up for basketball. How many 5-person teams will there be?


Step 1 Model 95. Show 5 groups.

5 95quotientdividend

divisor


Step 2 Divide the tens.


5 951 ten in each group

5 tens used

1

– 54 4 tens left


Step 3 Regroup and divide the ones.


9 ones in each group5 95

1

– 54

45 ones used

9

5– 45

0 0 ones left

19Answer: So, 95 ÷ 5 = 19 or 5 95.



A total of 200 kids signed on for after-school softball. If there are 10 players to a team, how many teams will be formed?

A. 25 teams

B. 21 teams

C. 20 teams

D. 30 teams


Rami wants to read an 84-page book in 6 days. How many pages should he read per day?


Find 84 ÷ 6.

Step 1 Decide if there are enough tens to divide.

6 84 8 > 6 There are enough tens.




6 841

6 –2

Divide 8 tens by 6 groups.Write 1 in the tens place.Multiply. 1 × 6 tens = 6 tensSubtract 6 tens from 8 tens.Compare. 2 < 6


Step 3 Divide the ones.


6 841

6 –2

Divide 24 ones by 6 groups.Write 4 in the ones place.

Multiply. 4 × 6 ones = 24 onesSubtract 24 ones from 24 onesCompare. 0 < 6

4

4

240

Answer: So, Rami should read 14 pages each day.

–


Check Multiply the quotient by the divisor.


14× 6

4

2

8

The answer is correct.

quotientdivisordividend



Shelley makes $5 a day babysitting. She wants to buy an outfit that costs $65. How many days will Shelley have to baby-sit to earn enough money to buy the outfit?

A. 13 days

B. 15 days

C. 17 days

D. 12 days



Main Idea


Example 1: Problem-Solving Strategy

15-4 Problem-Solving Strategy: Work Backwards



• I will work backward to solve problems.



Standard 3MR1.2 Determine when and how to break a problem into simpler parts. Standard 3NS2.1 Solve division problems in which a multi-digit number is evenly divided by a one-digit number (135 ÷ 5 = ___ ).


Frannie put some money in the bank to start a savings account. Last month she put in enough money to double that amount. Today, she put in more money and the total amount doubled, again. Now she has $20. How much money did Frannie start with?



Understand

What facts do you know?

• The money doubled two times.

• The total amount at the end is $20.

What do you need to find?

• The amount of money Frannie started with.



Plan

Work backward from what you know, $20, to find the amount Frannie started with.



Solve

Start with $20.

Answer: So, the amount of money Frannie started with was $5.


Find the number that was doubled.

Since the amount was doubled two times, find half of $10.

$20

Half of $20 is $10

$10

Half of $10 is $5

$5


Check


Look back at the problem. When you double $5, the result is $5 × 2 or $10. When you double $10, the result is $10 × 2 or $20.

So, the answer is correct.



Main Idea




15-5 Three-Digit Quotients



• I will divide three-digit numbers by one-digit numbers.




Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results.


Hugan read a 572-page book in 4 weeks. How many pages did he read each week?


Find 572 ÷ 4.

Step 1 Divide the hundreds. 5 > 4, so there are enough hundreds.

4 5721

Multiply. 4 × 1 = 44 –Subtract. 5 – 4 = 11 Compare. 1 < 4

Divide. 5 ÷ 4



Step 2 Regroup. Regroup the remaining 1 hundred as 10 tens. Bring down the 7 tens.

4 5721

4 –1 7



Step 3 Divide the tens. Regroup the remaining ten as 10 ones. Bring down the ones.

Multiply. 4 × 4 = 16Subtract. 17 – 16 = 1Compare. 1 < 4

Divide. 17 ÷ 4

4 5721

4 –1 7

4

16–12




Multiply. 4 × 3 = 12Subtract. 12 – 12 = 0Compare. 0 < 4

Divide. 12 ÷ 4 = 3

4 5721

4 –1 7

4

16–12

– 12

3

0

Answer: So, Hugan read 143 pages each week.



A group of 500 people will be split into 4 groups. How many people will be in each group?

A. 150 people

B. 130 people

C. 120 people

D. 125 people


Akina is putting 115 books on 5 shelves. How many books will go on each shelf?


Find 115 ÷ 5.


Step 1 Divide the hundreds.


5 115 There are not enough hundreds to divide. Regroup the 1 hundred as 10 tens.

5 115 11 > 5 Place the first digit in the tens place.




5 115Divide. 11 ÷ 5 = 2Multiply. 5 × 2 = 10

2

10–1

Subtract. 11 – 10 = 1Compare. 1 < 5




Bring down the ones.

Divide. 15 ÷ 5 = 3

5 1152

10–1

Multiply. 5 × 3 = 15Subtract. 15 – 15 = 0

–0

3

5

Compare. 0 < 5

15

Answer: So, Akina put 23 books on each shelf.



Check Multiply to check.

23× 5

5

1

11

The answer is correct.

quotientdivisordividend



Tony wants to buy a mountain bike that costs $450. If he plans to buy it in 3 months, how much money will Tony have to save each month?

A. $175

B. $100

C. $150

D. $130



Main Idea


Example 1: Problem-Solving Investigation

15-6 Problem-Solving Investigation: Choose the Best Strategy



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



Standard 3MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.


MING: A community pool is in the shape of a circle. It measures 80 feet across. A square fence is going to be placed around the pool.

YOUR MISSION: Find if 340 feet of fencing is enough to go around the pool.



Understand

What facts do you know?

• The pool is a circle.

• It measures 80 feet across.

• A square fence will be put around the pool.

• You have 340 feet of fencing.



Understand

What do you need to find?

• You need to know if 340 feet of fencing is enough.



Plan

Divide 340 by 4 to find the length of each side of the fence. Use make a drawing strategy to compare the length of the fence to the pool.



Solve


4 3408

32–2

–0

5

020


Solve

340 feet of fence is enough to make a square that is 85 feet on each side. 80 feet is smaller than 85 feet.


Answer: So, 340 feet of fencing is enough to go around the pool.


Check

Look back at the problem. Check the answer by multiplying.



85 × 4 = 340



Main Idea


Example 1: Real-World ExampleExample 2: Quotients Less Than $1.00Example 3: Find Unit Cost

15-7 Divide Money


15-7 Divide Money

• I will divide amounts of money.


15-7 Divide Money

Standard 3NS3.3 Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors.


15-7 Divide Money

Standard 3NS2.7 Determine the unit cost when given the total cost and number of units.


Brian and 3 friends earned $9.68 for washing cars. How much will each boy receive after they share the money equally?

15-7 Divide Money

Find $9.68 ÷ 4.

Estimate $9.68 ÷ 4 $10 ÷ 4 = $2.50


Step 1 Divide the dollars.

15-7 Divide Money

4 $9.682

Divide. 9 ÷ 48– Multiply. 4 × 2 dollars1 Subtract. 9 – 8 = 1

Compare. 1 < 4


Step 2 Divide the dimes.

15-7 Divide Money

Divide. 16 ÷ 4Multiply. 4 × 4 dimes

4 $9.682

8–1

Subtract. 16 – 16 = 0Compare. 0 < 4

4

61 6–

0


Step 3 Divide the pennies.

15-7 Divide Money

Place the decimal point and dollar sign directly above.

Divide. 8 ÷ 4 = 2Multiply. 4 × 2 penniesSubtract. 8 – 8 = 0

4 $9.68$2.

8–1

4

61 6–

0

2

8–0

Compare. 0 < 4

8

Answer: So, each boy will receive $2.42.


Check for Reasonableness

15-7 Divide Money

$2.42 is close to the estimate of $2.50.

So, the answer is reasonable.

Since $2.42 × 4 = $9.68, the answer is correct.


15-7 Divide Money

Angie and 3 friends pay $25 for tickets to see a movie. How much did each of them pay for a movie ticket?

A. $6.25

B. $5.25

C. $7.25

D. $5.50


Divide $4.35 ÷ 5.

15-7 Divide Money

Estimate $4.35 ÷ 5 $4.00 ÷ 5 = $0.80

Step 1 Decide if there are enough dollars to divide.

5 $4.35 4 < 5 There are not enough.


15-7 Divide Money

Step 2 Divide the dollars as 40 dimes.

5 $4.358

4 0–35


15-7 Divide Money

Step 3 Divide the pennies.

5 $4.35$0.8

4 0– 35

7

– 350

Add the dollar sign and decimal point. Add a zero to show 0 dollars.

Answer: So, $4.35 ÷ 5 = $0.87.


15-7 Divide Money

Check for Reasonableness

The estimate $0.80 is close to $0.87. So, the answer is correct.


15-7 Divide Money

Find $3.80 ÷ 4.

A. $0.87

B. $0.95

C. $0.75

D. $0.89


Freda paid $6.84 for 6 bags of marbles. How much did each bag cost?

15-7 Divide Money

Find the unit cost. Divide $6.84 ÷ 6.


15-7 Divide Money

6 $6.84$1.

6–0

1

8 6–2

4

24–0

4

Answer: So, $6.84 ÷ 6 = $1.14. Each bag costs $1.14.

Check

$1.14× 6$6.84

2



15-7 Divide Money

Chris paid $7.25 for 5 gallons of fruit punch. How much did Chris pay for each gallon of fruit punch?

A. $1.85

B. $1.75

C. $1.55

D. $1.45




Five-Minute Checks

Math Tool Chest

Image Bank

Division


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Lesson 15-1 (over Chapter 14)

Lesson 15-2 (over Lesson 15-1)







(over Chapter 14)

Multiply.

A. $21.68

B. $4.48

C. $6.68

D. $22.68

$3.24 × 7


(over Chapter 14)

Multiply.

A. $76.08

B. $79.06

C. $74.56

D. $72.08

8 × $9.51


(over Chapter 14)

At Dora’s diner, burgers are $3.13 and drinks are $1.29. How much are 3 burgers and 1 drink?

A. $10.24

B. $10.68

C. $8.60

D. $6.60


(over Chapter 14)

At Dora’s diner, burgers are $3.13 and drinks are $1.29. What is the cost of 2 burgers and 2 drinks?

A. $8.84

B. $6.68

C. $4.60

D. $5.60


(over Lesson 15-1)

Divide. Use patterns.

A. 60

B. 18

C. 32

D. 40

320 ÷ 8


(over Lesson 15-1)


A. 220

B. 90

C. 900

D. 22

4,500 ÷ 5


(over Lesson 15-1)


A. 80

B. 36

C. 32

D. 322

720 ÷ 9


There are 6 boxes and 240 crayons. How many crayons are in each box?

A. 40 crayons

B. 32 crayons

C. 30 crayons

D. 42 crayons

(over Lesson 15-1)


(over Lesson 15-2)

Estimate by rounding.

A. 270 ÷ 3 = 90

B. 260 ÷ 3 = 90

C. 290 ÷ 3 = 97

D. 240 ÷ 3 = 80

269 ÷ 3



A. 4,100 ÷ 7 = 600

B. 4,200 ÷ 7 = 600

C. 4,200 ÷ 7 = 700

D. 4,900 ÷ 7 = 700

(over Lesson 15-2)

4,179 ÷ 7



A. 60 ÷ 6 = 12

B. 61 ÷ 6 = 11

C. 60 ÷ 6 = 10

D. 68 ÷ 6 = 8

(over Lesson 15-2)

61 ÷ 6



A. 400 ÷ 5 = 80

B. 390 ÷ 5 = 88

C. 400 ÷ 5 = 40

D. 350 ÷ 5 = 50

(over Lesson 15-2)

390 ÷ 5


(over Lesson 15-3)

Divide 68 ÷ 4. Use models if needed. Check your answer.

A. 22

B. 24

C. 12

D. 17



A. 16

B. 12

C. 14

D. 15

(over Lesson 15-3)



A. 14

B. 13

C. 10

D. 8

(over Lesson 15-3)


Jaha has 96 beads for making bracelets. She uses 6 beads for each bracelet. How many bracelets can she make?

A. 90 bracelets

B. 14 bracelets

C. 16 bracelets

D. 88 bracelets

(over Lesson 15-3)


(over Lesson 15-4)

Use the work backward strategy to solve. Julio is saving money for a new guitar. He doubled his money last year by babysitting his brother. Then he tripled that amount by working for his dad. Now he has $90. How much did he start with?

A. $22

B. $14

C. $24

D. $15


(over Lesson 15-5)

Divide 745 ÷ 5. Check your answer.

A. 155

B. 135

C. 322

D. 149


Divide 288 ÷ 6. Check your answers.

A. 48

B. 24

C. 34

D. 84

(over Lesson 15-5)


Divide 824 ÷ 2. Check your answers.

A. 411

B. 128

C. 244

D. 412

(over Lesson 15-5)


(over Lesson 15-5)

There is a total of 784 pencils. There are 7 pencils in each box. How many boxes of pencils are there?

A. 110 boxes

B. 144 boxes

C. 112 boxes

D. 122 boxes


(over Lesson 15-6)

Choose any strategy to solve the problem. Tia sold 9 baskets at the flea market for $138. She sold some baskets for $12 and some for $18 each. How many of each basket did she sell?

A. five $12 baskets and five $18 baskets

B. four $12 baskets and five $18 baskets

C. three $12 baskets and seven $18 baskets

D. four $12 baskets and four $18 baskets

This slide is intentionally blank.

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