Lesson 12 Introduction Divide Whole NumbersIf you divided 17 baseballs equally among 4 brothers, each brother would get ... Subtract 25 groups of 4. How many groups of 4 in 25? 6 Subtract

Introduction

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Use What You Know

Lesson 12 Divide Whole Numbers

Lesson 12Divide Whole Numbers

You have learned how to multiply one-digit numbers by multiples of 10, 100, and 1,000. Take a look at this problem.

a. What division equation can be used to solve this problem?

b. What is the related multiplication equation?

c. What basic multiplication fact can you use to help find the answer?

d. If you divide 30 hundreds into 5 equal groups, how many hundreds are in

each group?

e. How can the basic fact help find 3,000 4 5?

f. Explain how to find the number of miles the Chase family will drive each day.

The Chase family is driving 3,000 miles across the country. They plan on driving for 5 days, traveling the same distance each day. How many miles will the Chase family drive each day?

3,000 miles

4.NBT.2.6

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The area model below shows the numbers for the Chase family trip.

5 3,000

600

An area model shows both multiplication (5 3 600 5 3,000) and division (3,000 4 5 5 600). Here are two possible ways you could break apart the factor 600 and the total 3,000.

5 1,500 1,500

300 3001

5 500500500 500500500

100 100100 11 1 100 100100 1 1

When you look at this as a model for division, the sum of the numbers in red is the quotient, or the result of the division problem. The sum of the numbers inside the area model is the dividend, or the total you are dividing. The number at the side of the model is the divisor, or the number you are dividing by.

Sometimes numbers don’t divide evenly. The amount left over is the remainder. If you divided 17 baseballs equally among 4 brothers, each brother would get 4 baseballs and there would be 1 baseball left over. This is written as:

4 R14 q ··· 17

Reflect1 Explain how an area model shows both multiplication and division.

Modeled and Guided Instruction

Learn About


Lesson 12


Dividing Three-Digit Numbers

Read the problem below. Then explore different ways to divide three-digit numbers by one-digit numbers.

There are 150 students going on a field trip. Students are put in equal groups of 6. How many groups are there? Are there any students left over?

Model It You can use an area model to help understand the problem.

20 51

(6 3 5 5 30)(6 3 20 5 120)

302 30

1502 120

6 150

?

6

5 25

030

150 4 6 5 25

Use multiplication to check: There is no remainder.

25 3 6 5 (20 3 6) 1 (5 3 6) 5 120 1 30 5 150

There are 25 groups and 0 students left over.

Model It You can also subtract partial products to divide the numbers.

150 2 120

30 2 30

0

6 3 20

6 3 5 no remainder

Stop subtracting when you reach zero or a number less than the divisor (6). The quotient is the sum of all the numbers you multiplied by 6.

20 1 5 5 25

There are 25 groups and 0 students left over.


Connect It Now you will solve the problem from the previous page using a different area model.

2 Melinda decided to split her area model into five sections that each show 6 3 5 5 30. Draw Melinda’s area model below. Then show how to subtract the partial products to find the answer.

3 Can you use Melinda’s model to solve the problem? Why or why not?

4 Explain how an area model can help you break apart a division problem to make it

easier to solve.

Try It Use what you just learned to solve these problems. Show your work on a separate sheet of paper.

5 132 4 3 5

6 364 4 7 5

Modeled and Guided Instruction

Learn About


Lesson 12


Read the problem below. Then explore different ways to divide four-digit numbers by one-digit numbers.

A factory has 2,125 DVD players to ship to electronics stores. They ship 4 DVD players in each box. How many full boxes can they ship?

Model It You can use an area model to help understand the problem.

4 2,125

?25 611

(4 3 6 5 24)(4 3 255 100)

remainder

252 24

125

4 1252 100

500

(4 3 500 5 2,000)

125

2,1252 2,000

5 531

Model It You can also find partial quotients to divide the numbers.

Divide each place value of 2,125 by 4.

6 25

500 4 q ······ 2,125 2 2,000

125 2 100

25 2 24

1

How many groups of 4 in 2,000? 500 Subtract 500 groups of 4.

How many groups of 4 in 100? 25 Subtract 25 groups of 4.

How many groups of 4 in 25? 6 Subtract 6 groups of 4.

The partial quotients are 500, 25, and 6. The quotient, 531, is the sum of the partial quotients. The remainder is 1.

Dividing Four-Digit Numbers


Connect It Now you will explore the problem from the previous page further.

7 How many full boxes can they ship?

8 What does the remainder mean in this problem?

9 If the factory could ship partially filled boxes, how would the answer change?

10 How is the partial quotients model on the previous page like the subtracting

partial products model in the field trip problem?

11 Which division model do you like better: area models, subtracting partial products, or finding partial quotients? Explain how that model helps you divide.

Try It Use what you just learned to solve these problems. Show your work on a separate sheet of paper.

12 1,010 4 9

13 5,783 4 6

Guided Practice

Practice


Lesson 12

Dividing Whole Numbers


Pair/ShareHow else could you solve this problem?

Pair/ShareWhat does the remainder mean in this problem?

How could you use an area model to help solve the problem?

The student first multiplied 8 3 10. After subtracting 80 from 104, there were still 24 left.

Example

14 A tailor has 641 yards of material to make costumes. Each costume needs 3 yards of material. How many costumes can be made? Will there be any material left over?

Show your work.

Solution

In art class, 8 students share 104 scraps of felt. Each student gets the same number of pieces. How many scraps of felt does each student get?

Look at how you could show your work using an area model.

104

? 10 3 13

8

1 5

8 1042 80 24

242 24 0

(8 3 10 5 80) (8 3 3 5 24)

Solution

Study the example below. Then solve problems 14–16.

13 scraps of felt


Pair/ShareHow can you tell that Awan’s answer doesn’t make sense?

Pair/ShareHow else could you solve this problem?

Will there be any toys left over?

Can you use multiplication to help solve the problem?

15 The Prize Place has 252 toys to be divided equally among 6 piñatas. How many toys will go into each piñata?

Show your work.

Solution

16 There are 1,275 people trying out for a show. The director needs to put people in 5 waiting rooms. If each room has the same number of people, how many will be in each room? Circle the letter of the correct answer.

A 111

B 251

C 255

D 1,270

Awan chose D as the correct answer. How did he get that answer?

Independent Practice

Practice


Lesson 12

Dividing Whole Numbers


Solve the problems.

1 James, Micah, and Rebecca work at a restaurant. Last night there was $115 in the tip jar. They decided to divide the tips equally among them and leave any extra money in the jar. How much money did they leave in the jar?

A $1

B $2

C $38

D $39

2 Together Aiden and his sister saved 360 quarters. Aiden saved twice as many quarters as his sister. If Aiden plans to put his quarters into 3 equal piles, how many quarters will he put in each pile?

A 36

B 60

C 80

D 120

3 A group of 53 tourists visit a museum. Museum volunteers lead tours for groups of no more than 8 tourists. Draw a model to show the least number of groups that can be formed for these 53 tourists. Use circles to show the groups and choose a symbol to show each person.

What is the fewest number of tour groups that need to be formed?

Self Check


4 Tell whether each equation is True or False.

a. 8,675 4 8 5 1,084 True False

b. 493 4 7 5 73 True False

c. 3,604 4 4 5 91 True False

d. 675 4 5 5 135 True False

5 Mrs. Long is making 7 snack bags. She has 175 almonds to share evenly among the bags. How many almonds will be in each bag? How many almonds will be left over?

Show your work.

Answer There will be almonds in each bag.

There will be almonds left over.

6 Trina has a box of 1,132 beads to make necklaces. She wants to use as many of the beads as possible to make 9 necklaces. If she uses the same number of beads for each necklace, how many beads will be on each one? How many beads will be left over?

Show your work.

Answer There will be beads on each necklace.

There will be beads left over.

Go back and see what you can check off on the Self Check on page 121.

Documents

Lesson 12 Introduction Divide Whole NumbersIf you divided 17 baseballs equally among 4 brothers, each brother would get ... Subtract 25 groups of 4. How many groups of 4 in 25? 6 Subtract