Lesson 6 Introduction Divide hole Numbers - PC\|MAC

Lesson 6

Introduction

Divide Whole Numbers

5.NBT.6

Use What You Know

In the last lesson, you learned how to find products of two- and three-digit factors.

Now you will learn how to divide with two-digit divisors.

There are 345 fifth graders enrolled at Wilson Middle School and 15 fifth-grade

classrooms. How many students are in each class if each class has the same number

of students?

a. What multiplication equation can you use to solve 345 4 15?

b. Multiply 15 by multiples of 10. Fill in the blanks.

15 3 10 5 ???

15 3 20 5 ???

15 3 30 5 ???

c. Now estimate the quotient. The quotient will be between which two tens?

d. If 15 3 20 5 300, what number is left after you subtract this product from 345?

e. Divide what is left by 15. ??? 4 15 5 ???

f. Use the information above to find 345 4 15. Explain your thinking.









42

Lesson 6 Divide Whole Numbers

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Find Out More

On the previous page, you used the relationship between multiplication and division

along with properties of operations to divide.

You can also use an area model to show division. It is similar to an area model for

multiplication. You can think of division as finding a missing factor. The dividend is the

product, the divisor is the known factor, and the quotient is the unknown factor.

The area model shows 345 4 15.

20

?

(15 3 20 5 300)

15

345

15

1

3

5 23

(15 3 3 5 45)

345

2 300

45

2 45

45

0

Start with the greatest place and find the quotient place by place. On the previous page,

you estimated the quotient to be between 20 and 30. So, 20 is the greatest ten that can

be in the quotient.

? Start by multiplying 15 by 20.

? Subtract the product from the dividend, 345.

? Write the difference, 45, in the next section of the model.

? Think: 15 3 ? 5 45. Multiply 15 by 3 and subtract this product from 45.

? The difference is 0, so there is nothing left to divide.

Reflect

1 How is dividing with an area model similar to multiplying with an area model?

How is it different?







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Lesson 6 Divide Whole Numbers

43

Lesson 6

Modeled and Guided Instruction

Dividing by Two-Digit Numbers

Learn About

Read the problem below. Then explore different ways to divide by a two-digit divisor.

A grocery store only sells eggs by the dozen. There are 12 eggs in 1 dozen eggs.

If there are 624 eggs in stock, how many dozens of eggs are there?

Model It

You can use the relationship between multiplication and division to

estimate the quotient in a division problem with a two-digit divisor.

624 4 12 5 ? and 12 3 ? 5 624

Multiply 12 by multiples of 10. Make a table.

Number of dozens

10

20

30

40

50

60

Number of eggs

120

240

360

480

600

720

Since 624 is between 600 and 720, the quotient is between 50 and 60.

Model It

You can use an area model to solve a division problem with a

two-digit divisor.

?

50

(12 3 50 5 600)

12

44

624

Lesson 6 Divide Whole Numbers

12

624

2 600

24

1

2

5 52

(12 3 2 5 24)

24

2 24

0

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Connect It

Now you will record the calculations from the model as

partial quotients.

2 How many hundreds are in the dividend? ???

How many groups of 12 are in 600? ???

This partial quotient is written above the bar.

What equation in the area model shows this?

???????????????

3 Why is 600 subtracted from 624?

52

2

50

12?q¡¤¡¤¡¤¡¤

624??

2 600

24

2 24

0

quotient

partial quotient

partial quotient



4 How does the area model relate to finding the second partial quotient?





5 Explain how to use the partial quotients to find 624 4 12.



6 Describe how to divide using partial quotients.

Try It

Use what you just learned about dividing by a two-digit divisor to solve

these problems. Show your work on a separate sheet of paper.

7 An elementary school has 1,134 seeds. The seeds will be planted in 27 rows.

Each row will have the same number of seeds. How many seeds will be planted

in each row? ???????????????

8 Nathan writes an essay with a total of 583 words. Every line of his essay has 11 words.

How many lines long is Nathan¡¯s essay?

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Lesson 6 Divide Whole Numbers

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Lesson 6

Practice

Guided Practice

Dividing Whole Numbers

Study the example below. Then solve problems 9¨C11.

Example

Each package has 21 pieces of chalk. How many packages can be

made with 1,701 pieces of chalk?

Look at how you could show your work using partial quotients.

81

1

80

21?q¡¤¡¤¡¤¡¤¡¤¡¤

1,701??

2 1,680

21

2 21

21 3 80

Why is 80 a good

number to use as a

first partial quotient?

Pair/Share

21 3 1

0

81 packages

Solution

How can you use

multiplication to

check that the quotient

is correct?

9 A water cooler holds 1,284 ounces of water. How many more 6-ounce

glasses than 12-ounce glasses can be filled from a full cooler?

Show your work.

You can first estimate

how many glasses of

each size can be filled.

Pair/Share

Solution

46

Lesson 6 Divide Whole Numbers

Explain how you found

your estimate.

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