Divide by a. One-Digit Divisor

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102

CHAPTER

The The

BIG Idea

Division

Lesson 1

Divide by a

One-Digit

Divisor.

gg

Make this Foldable

to help organize

information about

division.

How can I accurately

divide by one-digit

numbers when the

division problem is

shown in various ways?

3

Divide by a

One-Digit Divisor

Key Vocabulary

Review Vocabulary

English

Español

quotient cociente dividend dividendo divisor divisor × ÷

Fact Family familia de operaciones A group

of related facts using the same numbers. 3 × 5 = 15 5 × 3 = 15 15 ÷ 5 = 3 15 ÷ 3 = 5 0102_0104_C03CO_101808.indd 102 0102_0104_C03CO_101808.indd 102 12/3/09 3:57 PM12/3/09 3:57 PM

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Divide by a One-Digit Divisor 103

When Will I Use This?

You will solve this problem in the chapter.

hi

Your Turn!

err

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Are You Ready

Text Option

Take the Quick Check below.

104 Divide by a One-Digit Divisor

Are You Ready

for the Chapter?

Online Option

Take the Online Readiness Quiz.

Multiply.

1. 12 × 7 2. 42 × 8 3. 51 × 9

4. 7 × 18 5. 3 × $75 6. 3 × $89

7. Turner’s bookshelf has 6 shelves. Each shelf has 17 books.

How many books are on the bookshelf?

Round each number to its greatest place value.

8. 36 9. $451 10. 7,499

11. $33,103 12. $271 13. $5,001

14. There are 7,209 students at the amusement park.

Approximately how many students are at the park?

Divide.

15. 8 ÷ 2 16. 15 ÷ 5 17. 27 ÷ 3

18. 28 ÷ 4 19. 48 ÷ 6 20. 54 ÷ 9

21. Three people spent a total of $24 for lunch.

If they divide the total cost evenly, how much does each person pay?

Item Cost Pizza $12 Salads $6 Drinks $6

You have two options for checking

Prerequisite Skills for this chapter.

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Get ConnectED

Multi-Part Lesson

1

Lesson 1A Divide by a One-Digit Divisor 105

PART

_A

B C D E

Main Idea I will understand how division and multiplication are related. Vocabulary fact family V f

A fact family is a group of related facts that use the same numbers. You can use fact families to relate multiplication and division.

Relate Division

to Multiplication

Divide by a One-Digit Divisor

BASKETBALL Sheryl is putting away 20 basketballs after practice.

She places the balls on a rack that has 5 shelves. How many basketballs can she put on each shelf?

Use a fact family.

5 × 4 = 20

4 × 5 = 20

20 ÷ 5 = 4

20 ÷ 4 = 5

So, 20 ÷ 5 = 4.

Sheryl can put 4 basketballs on each shelf.

B

2

×

÷

Write a Fact Family

Write a fact family for the counters shown.

There are 5 rows, 9 columns, and a total of 45 counters.

45÷ 9= 5 45÷ 5 =9 9 _× 5 ₌ 45 5 _×9 ₌ 45

W

GLE 0506.2.3 Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. SPI 0506.2.4 Solve problems

involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers.

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You can also use mental math to help you divide basic facts.

Write a fact family for each set. See Examples 1 and 2 1.

3. 9, 8, 72

2.

4. 6, 7, 42

Divide. Use a related multiplication fact. See Example 3

5. 48 ÷

= 6 6. 40 ÷ 5 =

7. 18 ÷ 3 =

8. 12 ÷ 6 =

9.

÷ 7 = 3 10. 63 ÷ 9 =

11. There are 3 students playing a board game. The game contains

18 game pieces. If each student receives the same number of game pieces, how many pieces should each student receive?

12.

E

TALK MATH Explain how multiplication facts can help you divide.

Write a fact family for each set See Examples 1 and 2

Use Related Facts

GIFT BAGS Ellie is creating gift

bags for her party guests. She bought a total of 56 pencils that she wants to divide equally among the 7 gift bags. How many pencils will go in each bag?

Find 56 ÷ 7. You can use a related multiplication fact to help you divide.

56 ÷ 7 =

Think What number times 7 is 56?

7 ×

= 56 Write a related multiplication fact.

7 × 8 = 56

So, Ellie will put 8 pencils in each gift bag. Check for

reasonableness by comparing your answer

to what was asked in the question.

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Lesson 1A Divide by a One-Digit Divisor 107

Write a fact family for each set. See Examples 1 and 2 13.

15. 9, 4, 36

14.

16. 6, 6, 36

Divide. Use a related multiplication fact. See Example 3

17. 64 ÷ 8 =

18. 45 ÷ 9 =

19.

÷ 9 = 9 20.

÷ 8 = 4 21. 40 ÷

= 8 22. 63 ÷

= 7 W it f t f il f h t

02!#4)#%

PRACTICE

EXTRA

Begins on page EP2.

Orange blossoms have 5 petals and are some of the most fragrant flowers.

23. How many petals would there be in a

group of 7 orange blossoms?

24. If you count 40 petals in all, what is the

number of orange blossoms?

25. How many petals would there be in a

group of 11 orange blossoms?

26. OPEN ENDED Write a real-world division problem that can be solved by using fact families.

27. REASONING Can the number 12 be part of more than one fact family? Explain.

28. WHICH ONE DOESN’T BELONG? Identify the equation that does not belong with the other three. Explain.

54 ÷

9 =

6

54 ÷

6 =

9

9 ×

3 =

27

6 ×

9 =

54

29.

E

WRITE MATH Describe how you would find 42 ÷ 7.

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Get ConnectED

Divide by a One-Digit Divisor

Multi-Part

Lesson

1

PART

A

_B

C D E

Main Idea

I will explore division using models.

Materials base-ten blocks

Division Models

You can use base-ten blocks to help you divide.

In art class, three students share 48 markers evenly. How many markers will each student have?

Find 48 ÷ 3.

Step 1

Model 48 using base-ten blocks.

Step 2

Divide the tens into 3 equal groups.

Step 3

Regroup the remaining tens block into 10 ones. You now have 18 ones.

Step 4

Divide the ones.

There are 16 in each group. So, 48 ÷ 3 = 16. Use multiplication to check your answer. 16 × 3 = 48

GLE 0506.2.3 Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE 0506.2.5 Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals.

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Lesson 1B Divide by a One-Digit Divisor 109

and Apply It

Find each quotient using models. Tell how many are left over.

1. 44 ÷ 4 2. 39 ÷ 3 3. 54 ÷ 3 4. 63 ÷ 3

5. 32

÷

5 6. 57

÷

8 7. 64

÷

5 8. 45

÷

8

9. Kendrick has 42 craft sticks to make 3 identical crafts. How many sticks will he use for

each craft?

10.

E

WRITE MATH Will 32 ÷ 3 have any left over? Explain.

Find 56 ÷ 5.

Step 1

Step 2

Divide the tens into 5 equal groups.

Step 3

Divide the ones.

When you divide 56 into 5 groups, there are 11 in each group with one left over.

There is one left over.

Model Remainders

M

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Get ConnectED

Divide by a One-Digit Divisor

PART

1

A B

C

D E

Main Idea

I will carry out division with and without remainders. Vocabulary dividend divisor quotient remainder

V In division, the dividend is the number that is being divided.

The divisor tells you how many groups. dividend

36÷3 3 36

divisor

The result of the division problem is called the quotient .

Divide a Two-Digit Dividend

by a One-Digit Divisor

BABYSITTING Mindy babysat on the weekend for 3 hours. If she made $36, how much did she make each hour?

Find 36 ÷ 3.

Step 1 Model 36.

Step 2 Divide the tens.

Step 3 Divide the ones.

So, 36 ÷ 3 = 12. Mindy made $12 every hour she babysat. 3 36 1 3 36 −−− -₃ 0 1 ten in each group. 12 3 36 −−−− - 3 06 −−− -₆ 0 2 ones in each group. GLE 0506.2.3 Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE 0506.2.5 Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI 0506.2.4 Solve

problems involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers. Also addresses

GLE 0506.1.1.

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Lesson 1C Divide by a One-Digit Divisor 111

A remainder is the number, or part left, after you divide. We use R to represent the remainder.

Divide

Fill in each

with the correct number to find 85 ÷ 5.

7 5 8 5 ₋₋₋₋- 5

5 −−−−− -

0 1 7 5 85 ₋₋₋₋-₅ 35 −−−− - ₃₅ 0 Divide: 8 ÷ 5 = 1 Subtract: 8 - 5 = 3 Multiply: 7 × 5 = 35 So, 85 ÷ 5 = 17.

BASEBALL Caleb is putting his baseball cards in an album. He has 57 cards and can put 4 cards on each page.

How many full pages will Caleb have? Will there be any cards left?

You need to find 57 ÷ 4.

Step 1 Rewrite as 4 57 . Then divide the tens.

Bring down the ones. Divide. 17 ÷ 4 = 4

Put 4 in the quotient over the ones place. Multiply. 4 × 4 = 16 Subtract. 17 - 16 = 1 Compare. 1 < 4 The remainder is 1. 14 4 57 ₋₋₋₋- 4 17 −−−− - ₁₆ 1 R1 57 ÷ 4 = 14 R1

So, there will be 14 full pages and 1 card will be left over. Check for Reasonableness 14 × 4 = 56 and 56 + 1 = 57.

1 4 57 −−−− - 4 1 Divide. 5 ÷ 4 = 1

Put 1 in the quotient over the tens place. Multiply. 4 × 1 = 4

Subtract. 5 - 4 = 1 Compare. 1 < 4

Divide with Remainders

Write 57 ÷ 4 as 4 57 to find the quotient.

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Divide. Use multiplication to check your answer. See Examples 1–3

1. 2. 3. 4.

5. 3 63 6. 7 96 7. 68 ÷ 5 8. 39 ÷ 2

9. Five students volunteered to carry boxes. There are 62 boxes. Is it

possible for each student to carry the same number of boxes and have all the boxes carried? Explain.

10.

E

TALK MATH Why is the remainder always less than the divisor?

Divide. Use multiplication to check your answer. See Examples 1–3

11. 12. 13. 14.

15. 2 28 16. 5 65 17. 60 ÷ 4 18. 51 ÷ 3

19. 7 85 20. 3 41 21. 64 ÷ 5 22. 70 ÷ 6

23. Maranda practiced a total of 52 hours

in 4 weeks to prepare for a piano recital. If she practiced the same number of hours each week, how many hours did she practice each week? 24. Lance is putting 75 photos in a scrapbook. If he puts 5 photos on each page, how

many pages will he need? ng ng

5 6 5 ₋₋₋₋- 5

5 −−−−− -

0

5 3 4 5 ₋₋₋₋₋-

5 ₋₋₋₋₋- 1

0 R 6 7 4 −−−−− -₆ −−−− - 1

2

1 R 4 5 5 −−−−− -

−−−−− -

Di id U lti li ti t h k

02!#4)#%

PRACTICE

EXTRA

Begins on page EP2.

3 4 2 ₋₋₋₋- 3

2 −−−−− -

0

7 4 6 8 ₋₋₋₋₋-

8 ₋₋₋₋₋- 2

0 R 2 3 3 −−−−− -₂ −−−− - 1

1

1 R 5 7 7 −−−−− -

−−−−− -

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Lesson 1C Divide by a One-Digit Divisor 113

25.

HIKING

Alberto and Darcy are hiking in the Great Smoky Mountain National Park. One trail is about 68 miles long. Alberto and Darcy split the trip into 4 days of hiking. How many miles will they walk each day?

26. OPEN ENDED A two-digit dividend is divided by a one-digit divisor. The remainder is 2. Find possible values for the dividend and divisor.

27. NUMBER SENSE Use the digits 3, 6, and 9 one time each to write a division problem that contains a two-digit dividend. Write the division problem with the greatest quotient.

28. REASONING The following fact families show the relationship between multiplication and division.

18 ÷ 3 = 6 3 × 6 = 18

18 ÷ 0 = ? 0 × ? = 18

Explain why it is not possible to divide by zero.

29.

E

WRITE MATH Explain the meaning of a remainder in a division problem.

30. A box of granola bars has 26 bars. If

7 friends split the bars evenly, how many bars will be left?

A. 3 C. 5

B. 4 D. 6

31. An airplane that can hold

63 passengers is separated into 3 sections. Each section holds the same number of passengers. Which division sentence correctly describes the situation? F. 63 ÷ 21 = 3 H. 63 ÷ 21 = 5 G. 63 ÷ 3 = 21 I. 21 ÷ 3 = 7

Test Practice

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Get ConnectED

Divide by a One-Digit Divisor

PART

1

A B C

D

E

Main Idea I will use basic facts and patterns to divide multiples of 10, 100, and 1,000 mentally.

You can use basic facts and patterns to divide by multiples of 10.

Division Patterns

BUTTERFLIES A monarch butterfly can fly 240 miles in 3 days.

Suppose it flies the same distance each day. How many miles

can it fly each day?

Since 240 is a multiple of 10, use the basic fact and continue the pattern. 24 ÷ 3 = 8 basic fact

240 ÷ 3 = 80 24 tens divided by 3 equals 8 tens

2,400 ÷ 3 = 800 24 hundreds divided by 3 equals 8 hundreds

24,000 ÷ 3 = 8,000 24 thousands divided by 3 equals 8 thousands

So, the butterfly can fly 80 miles each day.

B c

Divide Multiples

of 10

Divide Multiples of 10

Find 600 ÷ 3 mentally.

Since 600 is a multiple of 10, you can use the basic fact and continue the pattern.

6 ÷ 3 = 2 6 ones divided by 3 equals 2 ones.

60 ÷ 3 = 20 6 tens divided by 3 equals 2 tens.

600÷ 3 = 200 6 hundreds divided by 3 equals 2 hundreds.

So, 600 ÷ 3 = 200. GLE 0506.2.3

Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE 0506.2.5 Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI 0506.2.4 Solve

GLE 0506.1.5.

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Lesson 1D Divide by a One-Digit Divisor 115

Divide mentally. See Examples 1–3

1. 500 ÷ 5 2. 320 ÷ 8 3. 200 ÷ 10

4. 420 ÷ 70 5. 800 ÷ 2 6. 150 ÷ 30

7. 270 ÷ 90 8. 5,600 ÷ 70 9. 2,100 ÷ 30

10. A sailfish grabbed a fishing line and

dragged it 300 feet in just 3 seconds. On average, how many feet did the fish drag the line each second?

11. Explain how you know that the quotients 48 ÷ 6 and 480 ÷ 60 are equal without doing any computation.

E

TALK MATH

Divide mentally See Examples 1 3

MEASUREMENT A cow eats 900 pounds of hay over a period of 30 days. How many pounds of hay would the cow eat each day at this rate?

You need to find 900 ÷ 30.

Use the fact family of 3, 3, and 9 to help represent the problem.

3 × 3 = 9 9 ÷ 3 = 3

30 × 3 = 90 90 ÷ 30 = 3 30 × 30 = 900 900 ÷ 30 = 30

This pattern suggests that you can cross out the same number of zeros in the dividend and the divisor to make division easier. 900/ ÷ 30/ Cross out the same number of zeros in both the

dividend and divisor.

90 ÷ 3 = 30 Divide. THINK: 9 tens ÷ 3 = 3 tens.

So, 900 ÷ 30 = 30.

The cow eats 30 pounds of hay each day. In multiplication, count

the number of zeros in each factor. Write the

zeros to the right of the product of the

basic fact.

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Divide mentally. See Examples 1–3

12. 800 ÷ 2 13. 900 ÷ 3 14. 150 ÷ 5

15. 140 ÷ 7 16. 450 ÷ 9 17. 280 ÷ 4

18. 180 ÷ 60 19. 240 ÷ 30 20. 4,200 ÷ 70

21. 1,800 ÷ 30 22. 2,000 ÷ 400 23. 2,400 ÷ 300

24. A group of 10 people bought tickets to a reptile exhibit and paid a

total of $130. What was the price of one ticket?

25.

Measurement

The fastest team in a wheelbarrow race traveled 100 meters in about 20 seconds. On average, how many meters did the team travel each second?

26.

Measurement

Daniela has a 160-ounce bag of potting soil. She puts an equal amount of soil in each pot shown. How much soil will she put in each pot?

27. A video store took in $450 in DVD rentals during one day.

If DVDs rent for $9 each, how many DVDs were rented?

Di id ll

02!#4)#%

PRACTICE

EXTRA

Begins on page EP2.

28. OPEN ENDED Write a real-world division problem that can be solved by using basic facts or patterns.

29. NUMBER SENSE Write two different division problems that both have a quotient of 50.

30. FIND THE ERROR Sonia is finding 5,400 ÷ 90 mentally. Find her mistake and correct it.

31.

E

WRITE MATH Describe how placing zeros at the end of basic division facts helps you divide mentally. Write an example.

5,40

/

0 /

÷

90 /

54 ÷

9 =

6

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Lesson 1D Divide by a One-Digit Divisor 117

Divide. Use multiplication to check your answer. (Lesson 1C)

36. 3 45 37. 4 72 38. 6 72 39. 5 69

40. A fisherman caught 42 fish over 3 days. If he caught

the same number of fish each day, how many fish did he catch in one day? (Lesson 1C)

Write a fact family for each set of numbers. (Lesson 1A)

41. 9, 6, 54 42. 28, 4, 7 43. 18, 6, 3 44. 56, 7, 8 32. An elementary school has 320 students.

All of the students are going on a field trip. If 40 students can ride a bus, how many buses are needed?

SchoolBus School Bus S SchhoollBBus School Bus A. 5 C. 7 B. 6 D. 8

34. There are 560 people in the

auditorium. There are 70 rows of seats. Which number sentence describes the number of seats in each row?

A. 56 × 7 = 392

B. 560 ÷ 70 = 8

C. 560 ÷ 8 = 70

D. 560 ÷ 70 = 80

33. Petra and 5 of her friends have to

hand out the number of fliers shown for the school play. If each person passes out the same number of fliers, how many fliers will Petra hand out?

F. 15 H. 90

G. 20 I. 540

35. SHORT RESPONSE Write two

division sentences using the numbers below.

4, 17, 68

Test Practice

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1

GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution. GLE 0506.2.3 Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division.

A B C

U

_nderstand

_{What facts do you know?}

•

• Bactrian camels have two humps.

•

• Dromedary camels have one hump.

•

• There are 20 camels with 28 humps.

What do you need to find? •

• How many camels of each type are there?

P

_lan

_{You can use the guess, check, and revise strategy to solve the problem.} Use combinations of 20 total camels to guess.

S

_olve

_Guess: _{10 Bactrian camels and 10 Dromedary camels}

Check: 10 × 2 = 20 humps 20 humps + 10 humps = 30 humps

10 × 1 = 10 humps Too high.

Revise: Try fewer Bactrian camels and more Dromedary camels.

Guess: 7 Bactrian camels and 13 Dromedary camels

13 × 1 = 13 humps Too low.

Revise: Try more Bactrian camels and less Dromedary camels.

Guess: 8 Bactrian camels and 12 Dromedary camels

12 × 1 = 12 humps This guess is correct. So, there are 8 Bactrian camels and 12 Dromedary camels.

C

_heck

_{Look back at the problem. 8}₊₁₂₌_{20 camels and 16}₊₁₂₌_{28 humps.} So, the answer is correct.

The Bactrian camel has two humps, while the Dromedary camel has just one. Toby counted 20 camels with a total of 28 humps. How many camels of each type are there?

Main idea I will solve problems by using the guess, check, and revise strategy.

P

_roblem-

S

_olving

S

_trategy:

_{Guess, Check, and Revise}

E

D

PART

Divide by a One-Digit Divisor

1

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119

Refer to the problem on the previous page. 1. Are there any other combinations of

each type of camel that Toby could have seen? Explain your reasoning.

2. Suppose you saw 18 camels with a

total of 22 humps. How many of each type did you see?

3. Explain how the guess, check, and revise method helped you solve this

problem.

4. Explain why you should record your

guesses and their results in the solve step of the problem-solving plan.

Solve. Use the guess, check, and revise strategy. 5. Ruben sees 14 wheels on a total of

6 bicycles and tricycles. How many bicycles and tricycles are there?

6. Conner spent $66 on rookie cards and

Hall of Famer cards. How many of each type of card did he buy?

Baseball Card Cost

Rookie 4 for $6 Hall of Famer 2 for $9

7. A teacher is having three students take

care of 28 goldfish during the summer. He gave some of them to Alaina. Then he gave twice as many to Miguel. He gave twice as many to Kira as he gave to Miguel. How many fish did each student get?

8.

Measurement

Bike path A is 4 miles long. Bike path B is 7 miles long. If April biked a total of 37 miles, how many times did she bike each path?

9. Jerome bought 2 postcards and

received $1.35 in change in quarters and dimes. If he got 6 coins back, how many of each coin did he get?

10. The sum of two numbers is 30. Their

product is 176. What are the two numbers?

11. A tour director collected $258 for tour

packages. Tour package A costs $18 and tour package B costs $22. How many of each tour package were sold?

12. Ticket prices for a science museum

are shown in the table. If $162 is collected from a group of 12 people, how many adults and students are in the group?

13.

E

WRITE MATH Refer to Exercise 10. How did you use the guess, check, and

revise strategy to find the numbers?

02!#4)#%

PRACTICE

EXTRA

Begins on page EP2.

To assess mastery of SPI0506.2.8, see your Tennessee Assessment Book.

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All players find their quotients. The player with the greatest quotient earns one point. In case of a tie, each of those players earn one point.

The first person to earn 5 points wins.

Get Ready!

Players: 2, 3, or 4 players

Get Set!

Each player makes a game sheet like the one shown at the right.

Make a spinner as shown.

Go!

The first person spins the spinner. Each player writes the number in one of the blanks on his or her game sheet. A zero cannot be placed as the divisor. The next person spins, and

each player writes that number in a blank. The next player

spins and each player fills in their game sheet. A player loses if he or she cannot use all the numbers.

You will need: spinner, index cards

Mission: Division

Dividing Whole Numbers

1 2 3 0 4 9 5 8 6 7 dex cards Game Sheet ÷ isor n spins, and tes that tes that nk. 0120_C03GT_101808.indd 120 0120_C03GT_101808.indd 120 11/16/09 3:35 PM11/16/09 3:35 PM

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Mid-Chapter

Check

Mid-Chapter Check 121

Divide. Use a related multiplication fact. (Lesson 1A)

1. 36 ÷= 9 2. 42 ÷ 6 =

3. 54 ÷ 9 = 4. 18 ÷ 3 =

5. ÷ 6 = 6 6. ÷ 9 = 8

7.

Measurement

The length of a rectangle can be found by dividing the area by the width. Find the length of the rectangle below. (Lesson 1C)

3 cm area = 39 sq cm

8.

MULTIPLE CHOICE

Suki received $87 for working 3 days. If she made the same amount each day, how much did Suki earn each day? (Lesson 1C)

A. $20 C. $25 B. $29 D. $30 Divide. (Lesson 1C) 9. 2 48 10. 5 85 11. 4 63 12. 7 81 13. 78 ÷ 5 14. 96 ÷ 4

15.

Measurement

The table shows the heights of the three tallest cacti. Find the height of each cactus in yards. (Hint: 1 yard = 3 feet) (Lesson 1C)

Cactus Height

Saguaro 75 ft Organ-pipe 48 ft Opuntia 33 ft

Divide mentally. (Lesson 1D)

16. 400 ÷ 2 17. 240 ÷ 6

18. 3,500 ÷ 5 19. 420 ÷ 60

20. 4,800 ÷ 800 21. 1,200 ÷ 300

22.

MULTIPLE CHOICE

A total of 180 students went on a field trip. There were 3 buses. If each bus had the same number of students on it, how many students were on each bus? (Lesson 1D)

F. 6 G. 36 H. 54 I. 60

Solve. Use the guess, check, and revise strategy. (Lesson 1E)

23. The sum of two numbers is 70. Their

quotient is 13. What are the two numbers?

24. Rory has $1.30 in coins. If there is a

total of 15 coins, how many quarters, dimes, nickels, and pennies does he have?

25.

E

WRITE MATH Can the remainder in a division problem ever equal the divisor? Explain.

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Get ConnectED

PART

Divide Three- and Four-Digit Dividends

2

C D

Estimate Quotients

To estimate a quotient, you can use compatible numbers , or numbers that are easy to divide mentally. Look for numbers that are part of fact families.

Use a Compatible

Dividend

DOGS A dog’s heart beats 365 times in 3 minutes. About how many times does a dog’s heart beat in 1 minute?

365 ÷ 3 Change 365 to 360 because 360 and 3 are compatible numbers.

360÷ 3 = 120 Divide.

So, a dog’s heart beats about 120 times a minute. Check for Reasonableness 120 × 3 = 360.

Find a Compatible Divisor

Estimate 3,200 ÷ 9.

3,200 ÷ 9

3,200 ÷ 8 Change 9 to 8 because

32 and 8 are compatible numbers.

3,200 ÷ 8 = 400 Divide mentally.

So, 3,200 ÷ 9 is about 400.

Check for Reasonableness 8 × 400 = 3,200.

E Main Idea I will estimate quotients using rounding and compatible numbers. Vocabulary compatible numbers V E F

A

B GLE 0506.2.3 Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE 0506.2.5 Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI 0506.2.4 Solve

GLE 0506.1.2.

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Lesson 2A Divide Three- and Four-Digit Dividends 123

DOGS Six dogs equally share a 45-pound bag of dog food each week. About how much does each dog eat each week?

One Way:

Use 45 and 5.

Another Way:

Use 48 and 6.

45 ÷

6

45 ÷

5 =

9

45 ÷

6

48 ÷

6 =

8

So, each dog eats about 8 or 9 pounds of dog food each week.

Use Rounding and Compatible Numbers

Estimate 208 ÷ 8.

Step 1 Round the dividend to the nearest ten.

Step 2 Change the divisor to a number that is compatible with 210. Notice it is easy to divide 210 by 7.

Step 3 Divide mentally. So, 208 ÷ 8 is about 30. E 208 ÷ 8 210 ÷ 8 210 ÷ 8 210 ÷7 210 ÷ 7 = 30

Estimate. Show your work. See Examples 1–4

1. 850 ÷ 9 2. 635 ÷ 8 3. 545 ÷ 5 4. 431 ÷ 2

5. 374 ÷ 9 6. 541 ÷ 6 7. 120 ÷ 5 8. 610 ÷ 7

9. An E-mail contained 250 characters.

The 4-line E-mail contained the same number of characters on each line. About how many characters were on each line? Show how you estimated.

10. Explain how you could use compatible numbers to estimate 272 ÷ 4.

E

TALK MATH

Estimate Show your work See Examples 1 4

To round 208 to the nearest ten, look at the

number to the right of the tens place. Since 8

is 5 or greater, round up. 208 210

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Estimate. Show your work. See Examples 1–4

11. 397 ÷ 4 12. 432 ÷ 7 13. 753 ÷ 9 14. 253 ÷ 5

15. 554 ÷ 6 16. 360 ÷ 7 17. 791 ÷ 2 18. 151 ÷ 3

19. 289 ÷ 9 20. 477 ÷ 9 21. 230 ÷ 7 22. 244 ÷ 8

23. 660 ÷ 7 24. 860 ÷ 3 25. 639 ÷ 7 26. 486 ÷ 6

Solve. Show your work.

27. A grocery store employee puts 8 bagels in each bag. If she has

385 bagels, about how many bags does she need?

28.

Measurement

Jani drives 240 miles in 4 hours. About how many miles does she drive each hour?

29. There were 317 marbles divided equally among 8 bowls.

About how many marbles were in each bowl?

30.

Measurement

Emilio has 5 bags of birdseed. Each bag has about 28 ounces of birdseed. If he divides the birdseed equally into 3 containers, about how much birdseed will he put in each container?

31. The table shows how much each fifth grade

room earned from a bake sale. The money is going to be given to 6 different charities. If each charity is given an equal amount, about how much will each charity receive? Show how you estimated.

E ti t Sh k l

02!#4)#%

PRACTICE

EXTRA

Begins on page EP2.

32. OPEN ENDED Write a division problem and show two different ways that you can estimate the quotient using compatible numbers.

33. NUMBER SENSE Without calculating, predict whether 617 ÷ 7 is greater than or less than 100. Explain your reasoning.

34.

E

WRITE MATH Write a real-life problem in which you estimate the quotient of two numbers.

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Lesson 2A Divide Three- and Four-Digit Dividends 125

Solve. Use the guess, check, and revise strategy. (Lesson 1E) 38. Stacie counts 26 legs in a barnyard with horses and chickens.

If there are 8 animals, how many are horses?

Divide mentally. (Lesson 1D)

39. 400 ÷ 2 40. 180 ÷ 3 41. 630 ÷ 70 42. 2,500 ÷ 500

Divide. Use estimation to check. (Lesson 1C)

43. Miss Carbone read a book to her class. The book contained

54 pages and she read the same number of pages each day. If it took her 3 days to read the book, how many pages did she read each day?

44. BAR DIAGRAM Frankie paid $18 to rent a paddleboat. If the cost of renting is $6 per hour, for how many hours did Frankie rent the paddleboat?

Divide. Use a related multiplication fact. (Lesson 1A)

45. 24 ÷ 4 46. 32 ÷ 8 47. 56 ÷ 8

48. Samuel swam a total of 48 laps over 4 days. He swam

the same number of laps each day. How many laps did Samuel swim each day? (Lesson 1A)

C04 005A 105939A

35. Which of the following is the most

reasonable estimate for the number of Calories in one serving of milk?

Servings of Milk Calories 5 430 A. between 8 and 9 B. less than 80 C. between 80 and 90 D. more than 90

36. A train traveled 300 miles in

5 hours. How far did the train travel each hour on average?

F. 60 mi

G. 150 mi

H. 600 mi

I. 1,500 mi

37. SHORT RESPONSE Mrs. Chong

bought 480 bookmarks. If each box contains 60 bookmarks, how many boxes did she buy? Explain your reasoning.

Test Practice

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MP-Title

Get ConnectED

PART

2

A

_B

C D

Division Models with

Greater Numbers

You can also use base-ten blocks to divide greater numbers.

E

Main Idea

I will explore division using models. Materials base-ten blocks

T

i

t

tl

t

l

e

--

T

Divide Three- and Four-Digit Dividends

F

At the fair, you need tickets to ride the rides. Three friends share 336 tickets equally. How many tickets will each friend receive? Find 336 ÷ 3.

Step 1

Step 2

Divide the hundreds into 3 groups.

Step 3

Divide the tens blocks into 3 groups.

Step 4

Divide the ones blocks into 3 groups.

So, 336 ÷ 3 = 112.

Use multiplication to check your answer. 112 × 3 = 336

GLE 0506.2.3 Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. Also addresses GLE 0506.1.4.

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Lesson 2B Divide Three- and Four-Digit Dividends 127

Find 319 ÷ 2.

Step 1

Step 2

Divide the hundreds into 2 groups.

Step 3

Divide the remaining ten and the ones into 2 groups.

When you divide 319 into 2 groups, there are 159 in each group with one left over. So, 319 ÷ 2 = 159 R1.

Use multiplication to check your answer. 159 × 2 = 318 + 1 = 319

F

Model Remainders

There is one left over.

and Apply It

Use models to find each quotient.

1. 344 ÷ 2 2. 469 ÷ 7 3. 255 ÷ 5 4. 364 ÷ 4

5. 373 ÷ 4 6. 567 ÷ 5 7. 383 ÷ 3 8. 582 ÷ 4

9.

E

WRITE MATH If you are dividing a three-digit even number by two, will you ever have a remainder? Explain.

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MP-Title

Get ConnectED

PART

2

A B

_C

D

Distributive Property

and Partial Quotients

The Distributive Property allows you to divide each place-value position by the same factor.

E

Main Idea

I will divide using the distributive property and partial quotients. Vocabulary partial quotients V

T

i

t

tl

t

l

e

--

T

Divide Three- and Four-Digit Dividends

F

Jesse has 369 beads to be split evenly among 3 necklaces. How many beads can Jesse put on each necklace?

Find 369 ÷ 3 using the

Distributive Property and a bar diagram.

Step 1

Model 369 as (300 + 60 + 9).

300 60 9

Step 2

Divide each section by 3.

Write each quotient above the bar.

300 60 9

3

100 20 3

Step 3

Add the quotients.

100 + 20 + 3 = 123

So, 369 ÷ 3 = 123.

Jesse can put 123 beads on each necklace. Check 123 × 3 = 369.

J

GLE 0506.2.3 Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division.

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Lesson 2C Divide Three- and Four-Digit Dividends 129

and Apply It

Divide. Use the Distributive Property.

1. 248 ÷ 2 2. 488 ÷ 4 3. 963 ÷ 3

Divide. Use partial quotients.

4. 654 ÷ 6 5. 352 ÷ 4 6. 176 ÷ 8

7.

E

WRITE MATH Suppose you are finding 296 ÷ 4 using partial quotients. Is 50 or 70 a more reasonable partial quotient? Explain.

Partial quotients is a method of dividing where you break the

dividend into sections that are easy to divide.

Use Partial Quotients

There are 738 students in Manuel’s school. There are 6 grade levels in his school, with each grade having the same number of students. How many students are in the fifth grade?

Find 738 ÷ 6 by using partial quotients.

Step 1

Divide the hundreds. Since 6 × 100 is 600, and 600 is close to 738, divide 600 by 6. 100 is a partial quotient. Subtract.

Step 2

Divide the tens. Since 6 × 20= 120, and 120 is close to 138, divide 120

by 6. 20 is a partial quotient. Subtract.

Step 3

Divide the ones. There are only 18 left and 6 × 3 =18. 3 is a partial quotient.

Step 4

Add the partial quotients.

100+ 20+ 3 =123

So, 738 ÷ 6 = 123.

There are 123 students in the fifth grade. Check 123 × 6 = 738. 6 738 −−−− - 600 138 −−−− -120 18 −−−− -₁₈ 0 100 20 3 0128_0129_C03L02_101808.indd 129 0128_0129_C03L02_101808.indd 129 12/3/09 5:54 PM12/3/09 5:54 PM

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Get ConnectED

PART

Multi-Part

Lesson

2 Divide Three- and Four-Digit Dividends

A E

RIDES In a 4-hour period, 852 people rode the Thunder

Canyon ride. If the same

number of people rode the ride each hour, how many people rode the ride in the first hour?

Find 852 ÷ 4.

Estimate 852 ÷ 4 900 ÷ 4 = 225

Step 1 Divide the hundreds. Step 2 Divide the tens.

So, 213 people rode Thunder Canyon in the first hour. Check 213 × 4 = 852. der 2 4 852 −−− -₈ 0 2 1 4 852 −−− -₈ 05 −−− -₄ 1 Divide: 8 ÷ 4 Multiply: 2 × 4 Subtract: 8 - 8 Compare: 0 < 4 Divide: 5 ÷ 4 Multiply: 1 × 4 Subtract: 5 - 4 Compare: 1 < 4

To divide a greater dividend by a one-digit divisor, use the same process as dividing a two-digit dividend by a one-digit divisor.

Divide Three- and

Four-Digit Dividends

B C

_D

Main Idea I will divide up to a four-digit number by a one-digit number. F 213 4 852 ₋₋₋- 8 05 −−− -₄ 12 −−−− - ₁₂ 0 Divide: 12 ÷ 4 Multiply: 3 × 4 Subtract: 12 - 12 Compare: 0 < 4 GLE 0506.2.3 Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. SPI 0506.2.4 Solve problems

involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers.

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Lesson 2D Divide Three- and Four-Digit Dividends 131

Divide by a One-Digit Number

Find 2 856 . Estimate 900 ÷ 2 = 450

Step 1

Divide the hundreds. 4 2 856 −−− - ₈ 0 Step 2

Divide the tens. 4 2 2 856 −−−− -₈ 05 −−− -₄ 1 Step 3

Divide the ones. 428 2 856 −−−− -₈ 05 −−−− -₄ 16 −−−− -₁₆ 0

The quotient is 428. Compare to the estimate.

8 ÷ 2 4 ×2 8 - 8 0 < 2 5 ÷ 2 2 ×2 5 - 4 1 < 2 16 ÷ 2 8 ×2 16 - 16 0 < 2

Divide a Four-Digit Number

Find 7,946 ÷ 6.

Step 1 Divide the thousands. Step 2 Divide the hundreds. 1 6 _7,946 −−− -₆ 1 13 6 _7,946 −−− -₆ 19 −−−− -₁₈ 1

Step 3 Divide the tens. Step 4 Divide the ones. 132 6 _7,946 −−− -₆ 19 −−−− -₁₈ 14 −−−− - ₁₂ 2 1,324 R2 6 7,946 ₋₋₋- 6 1 9 −−−− -_{1 8} 14 −−−− -₁₂ 26 −−−− -24 2 The quotient is 1,324 R2. 7 ÷ 6 1 × 6 7 - 6 1 < 6 19 ÷ 6 3 × 6 19 - 18 1 < 6 14 ÷ 6 2 × 6 14 - 12 2 < 6 26 ÷ 6 4 × 6 26 - 24 2 < 6

To check division with a remainder, first

multiply the quotient and the divisor. Then

add the remainder. 1,324 −−−− × 6 7,944 7,944 ₋₋₋₋ + 2 7,946 0130_0133_C03L02_101808.indd 131 0130_0133_C03L02_101808.indd 131 12/3/09 5:58 PM12/3/09 5:58 PM

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Divide. See Examples 1–3

1. 2 268 2. 5 595 3. 4 625 4. 3 410

5. 516 ÷ 3 6. 932 ÷ 6 7. 5,816 ÷ 5 8. 9,982 ÷ 7

9. Three adult kangaroos weigh 435 pounds. If each adult weighs

the same, how much would one adult kangaroo weigh?

10. Does the quotient of 945 and 8 have two or three digits? Explain how you know without solving.

Divide. See Examples 1–3

11. 5 755 12. 2 648 13. 3 493 14. 4 8,469

15. 3 945 16. 5 630 17. 4 97 18. 2 87

19. 515 ÷ 5 20. 595 ÷ 4 21. 766 ÷ 6 22. 969 ÷ 8

23. 428 ÷ 3 24. 590 ÷ 4 25. 9,350 ÷ 7 26. 6,418 ÷ 3

27. BAR DIAGRAM A state park has cable cars that

travel about 864 yards in 4 minutes. How many yards do the cars travel per minute?

28. Three new video game systems cost $645. If all

the game systems cost the same, what is the cost of each game system?

29. On Monday, a concession stand manager ordered

985 popcorn bags. She splits the bags evenly among 5 concession stands. How many popcorn bags will each concession stand receive?

30. Mr. Harris wants to divide his 36 students into

equal groups of 3 students each. How many groups of 3 students can he make? How many students will not be in a group of 3?

Divide See Examples 1 3

E

TALK MATH

i id

02!#4)#%

PRACTICE

EXTRA

Begins on page EP2.

1 min 1 min 1 min 1 min

? yd

864 yards

0130_0133_C03L02_101808.indd 132

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Lesson 2D Divide Three- and Four-Digit Dividends 133

31. OPEN ENDED Write a real-world division problem with a divisor of 4 that has no remainder. Then write a real-world division problem with a divisor of 4 that has a remainder.

32. NUMBER SENSE Place the digits 2, 4, 7, and 8 in

÷

to create a division problem with the greatest quotient.

33.

E

WRITE MATH Explain how estimation is useful when solving division problems.

34. Use the table below to make a true

statement.

Weight of Whales Mammal Weight Blue whale 144 tons Gray whale 36 tons

A blue whale is about ________ heavier than a gray whale.

A. 3 times C. 6 times

B. 4 times D. 8 times

35. Lauren poured an equal amount of

the solution below in each of 4 test tubes. How much solution is in each test tube?

F. 30 mL H. 105 mL

G. 100 mL I. 110 mL

Divide. Use the partial quotients method. (Lesson 2C)

36. 368 ÷ 4 37. 725 ÷ 5

38. Enrique has 685 trading cards that he wants to place into

5 different albums. If each album will hold the same number of cards, how many cards will fit in each album? (Lesson 2C)

39. There are 520 baseballs that will be shipped to nine sports stores.

Estimate the number of baseballs each store is to receive if they each receive about the same number. (Lesson 2A)

Divide. Use a related multiplication fact. (Lesson 1A)

40. 63 ÷ 7 41. 25 ÷ 5 42. 40 ÷ 8 43. 18 ÷ 6

Test Practice

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Get ConnectED

PART

Multi-Part

Lesson

2 Divide Three- and Four-Digit Dividends

A

_E

Sometimes you may have a three-digit dividend, but there are not enough hundreds to divide. If so, the quotient should start at the next place value position.

Place the First Digit

B C D

Main Idea

I will understand how to place the first digit in a quotient.

F

Raven received 135 E-mails over 3 weeks. If she received the same number of E-mails each week, how many E-mails did she receive in the first week?

Find 135 ÷ 3.

Step 1 Divide the hundreds. 3 135

There are not enough hundreds to divide into three groups. So, regroup the hundreds block into 10 tens.

Step 2 Divide the tens. 4 3 135 −−−− -₁₂ 15

The first digit of the quotient is in the tens place.

Step 3 Divide the ones. 45 3 135 −−−− -₁₂ 15 −−−− -₁₅ 0

So, 135 ÷ 3 = 45. Raven received 45 e-mails in the first week. Check 45 × 3 = 135.

R 3

GLE 0506.2.3 Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE 0506.2.5 Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI 0506.2.4 Solve problems

involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers. Also addresses GLE

0506.1.7.

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Lesson 2E Divide Three- and Four-Digit Dividends 135

Divide

Find 7 684 . Estimate 700 ÷ 7 = 100

Step 1

Divide the hundreds.

7 684

Step 2

Divide the tens. 9 7 684 −−−− -₆₃ 5 Step 3

Divide the ones. 9 7 R5 7 684 −−−− - 63 54 −−−− -₄₉ 5 So, 684 ÷ 7 = 97 R5.

Compare to the estimate. 97 R5≈ 100

The symbol ≈ means about or almost equal to. Since 7 > 6, look at

the tens. 7 < 68. The first digit is in the tens place.

Divide. Check your answer using multiplication. See Examples 1 and 2 1. 5 4 3 5 −−−−− - −−−−− -

2. 4 2 5 6 −−−−− - −−−−− -

3.

R 8 6 2 9 −−−−− - −−−−− -

4. 6 576 5. 5 385 6. 6 427 7. 4 217 8. 282 ÷ 3 9. 108 ÷ 9 10. 274 ÷ 4 11. 312 ÷ 4

12. There are 594 people standing in line to see a movie premiere. The

movie is playing in 6 theaters. If the same number of people will see the movie in each theater, how many people will be in one theater?

13. If the first digit in the dividend is less than the number in the divisor, where will you begin writing your quotient?

Divide Check your answer using multiplication See Examples 1 and 2

E

TALK MATH First estimate your

answer by rounding or using compatible numbers. 687 ÷ 7 700÷ 7 = 100 So, 687 ÷ 7 is about 100. 0134_0136_C03L02_103031.indd 135 0134_0136_C03L02_103031.indd 135 2/26/10 8:50 AM2/26/10 8:50 AM

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Divide. Check your answer using multiplication. See Examples 1 and 2 14. 6 4 9 8 −−−−− - −−−−− -

15. 7 3 1 5 −−−−− - −−−−− -

16.

R 3 2 8 6 −−−−− - −−−−− -

17. 6 486 18. 9 738 19. 7 662 20. 6 392 21. 117 ÷ 9 22. 237 ÷ 3 23. 485 ÷ 5 24. 567 ÷ 9 25. 178 ÷ 6 26. 472 ÷ 7 27. 382 ÷ 5 28. 518 ÷ 6

29. There are 624 envelopes to be sorted into 8 different mail bags.

If the same number of envelopes will be in each bag, how many envelopes will be in one bag?

Use the information to solve the problem.

30. How much food does one manatee eat in a day if the three

manatees eat the same amount?

i id Ch k i l i li i

02!#4)#%

PRACTICE

EXTRA

Begins on page EP2.

31. WHICH ONE DOESN’T BELONG? Identify the expression that does not have a two-digit quotient.

519 ÷

6

915 ÷

7

439 ÷

7

812 ÷

9

32.

E

WRITE MATH Can you determine the number of digits in the quotient of 637 ÷ 7 without dividing? Explain.

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Get ConnectED

2

Lesson 2F Divide Three- and Four-Digit Dividends 137

A B C D E

_F

Sometimes quotients will contain zeros.

Quotients with Zeros

Main Idea

I will solve division problems that result in quotients that have zeros.

PART

Divide Three- and Four-Digit Dividends

ELECTRONICS Maya is saving to buy a television. The television costs $327. She plans to save money for 3 months. How much does Maya need to save each month to buy the television?

Find $327 ÷ 3.

Estimate 300 ÷ 3 = 100

Step 1 Divide the hundreds. 1 3 327 - 3 0

Step 2 Divide the tens. 10 3 327 - 3 02 - 0 2

109 3 327 - 3 02 - 0 27 - 27 0

Maya needs to save $109 each month. Compare to the estimate. $109 ≈ $100.

C011--0331A-112112057

$

₃

2

22

2

2 ₇

₇

₇₇₇

₇

Notice there are not enough tens to divide. Place a 0 in the quotient.

Regroup the two tens as twenty ones. There are now 27 ones.

GLE 0506.2.3 Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE 0506.2.5 Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI 0506.2.4 Solve problems involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers. Also addresses GLE

0506.1.7.

0137_0139_C03L03_103031.indd 137

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Divide. See Examples 1 and 2

1. 3 324 2. 2 418 3. 4 4,324

4. 840 ÷ 7 5. 842 ÷ 4 6. 420 ÷ 6

7. 613 ÷ 2 8. 692 ÷ 3 9. 9,163 ÷ 3

10. BAR DIAGRAM There are 630 minutes of music to be put on 6 CDs. If the same number of minutes fit on each CD, how many minutes of music fit on each CD?

11. Explain how to model finding the quotient 416 ÷ 4 using base-ten blocks.

E

TALK MATH

Divide See Examples 1 and 2

Quotients with Zeros

Find 523 ÷ 4.

Estimate 500 ÷ 4 = 125

Step 1 Divide the hundreds. Step 2 Divide the tens. 1 4 523 −−−−- 4 1

Step 3 Divide the ones. 13 0 4 523 −−−- 4 12 −−− -12 03 −−−− - 0 3

There are not enough ones to divide. Place 0 in the ones place. The remainder is 3.

So, 523 ÷ 4 = 130 R3.

Compare 130 R3 to the estimate. 130 R3 ≈ 125

Check using multiplication 130 × 4 = 520, 520 + 3 = 523

1 3 4 523 −−−- 4 12 −−− -12 0 Use the same strategy

to divide a three-digit number that you used

to divide a two-digit number.

0137_0139_C03L03_103031.indd 138

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139

Divide. See Examples 1 and 2

12. 2 210 13. 3 627 14. 6 782 15. 5 530

16. 4 413 17. 9 817 18. 8 856 19. 2 6,461

20. 928 ÷ 3 21. 841 ÷ 4 22. 815 ÷ 2 23. 3,213 ÷ 3

24. There are 312 fish at the aquarium in

3 different fish tanks. Each tank has the same number of fish. How many fish are in each tank?

25. Kirk has watched 120 minutes of

television in the last 4 days. He

watched the same amount of television each day. How many minutes of

television did he watch in 1 day?

Use the information to solve the problem.

26. How much does one manatee eat if the three manatees eat the

same amount?

Di id l d

02!#4)#%

PRACTICE

EXTRA

Begins on page EP2.

27. OPEN ENDED Write two division problems that have zeros in the quotient. One of the problems should have a remainder and the other should not.

28. WHICH ONE DOESN’T BELONG? Identify the division problem that does not belong with the other three. Explain.

621 ÷

6

384 ÷

3

719 ÷

7

514 ÷

5

29. NUMBER SENSE In problems like 714 ÷7, where the digit in the greatest place of the dividend is the same as the divisor, will the quotient always have a zero? If not, give an example.

30.

E

WRITE MATH Explain how to find the quotient of 936 ÷ 9.

To assess partial mastery of SPI0506.2.4, see your Tennessee Assessment Book.

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Get ConnectED

PART

Interpret the Remainder

Multi-Part

Lesson

3

C D E

B

A

Interpret the Remainder

The following activities show you how to use remainders in different kinds of problems.

Main Idea I will explore interpreting the remainder in a division problem. Materials connecting cubes

A group of fifth graders collected 46 cans of food to donate to 3 food banks. If each food bank is to get an equal number of cans, how many cans do they each receive?

Step 1

Use 46 connecting cubes to represent the cans of food. Use three paper plates to represent the food banks. Divide the cubes equally among the

three plates.

Step 2

Interpret the remainder.

Since each food bank is to get the same number of cans of food, they will each receive 15 cans. There is one can left over.

b O Di it Di i GLE 0506.2.3

Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. SPI 0506.1.3 Recognize the unit associated with the remainder in a division problem or the meaning of the fractional part of a whole given in either decimal or fraction form. SPI 0506.2.3

Select a reasonable solution to a real-world division problem in which the remainder must be considered. Also addresses

GLE 0506.1.4, GLE 0506.1.6.

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