# Dividing Fractions

**Key Words:
**Fraction

Division

Dividend

Divisor

Quotient

Multiplicative

inverse

Reciprocal

**Learning
Objectives:
**• Writing whole

numbers as

fractions with

denominators of 1

• Dividing whole

numbers, mixed

numbers, and

proper fractions

• Using trial and

error to find an

unknown divisor

when the

dividend and

quotient are given

• Using trial and

error to find an

unknown dividend

when the divisor

and quotient are

given

## Solving Missing Value Problems when Dividing Fractions

**As you work through the tutorial, complete the
following questions.**

1. What unit of measure is used especially to define an amount of

firewood? ______________________

2. The improper fraction 5/4 is the reciprocal of __________ .

3. What is the product of 5/4 and its multiplicative inverse? ________________

4.Write 5 as a fraction with a denominator of 1. ________________________

5. What math statement is used to check the answer for ? __________

6. In Dijit’s problem of what is the
multiplicative inverse of the

divisor? ________________________________________________________

7. __________

8. If then __________ ÷ __________ = __________ .

9. __________

10. Division is the inverse of which math operation ? ______________________

11. Summarize the two helpful hints suggested for dividing fractions.

a. ______________________________________________________________

______________________________________________________________

b. ______________________________________________________________

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**Your Turn**

1. Rewrite 17 as a fraction with a denominator of 1. ____________________

2. Find Show your work. Check your answer.
__________________

________________________________________________________________

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3. Chip uses cups of water to make 5
portions of his special stew. How

many cups would he use for just one portion? ________________________

4. Dijit changes the stew recipe so that he uses
cups of water to make

6 portions. How many cups of water does the changed recipe use per

single portion? __________________________________________________

5. What is the missing divisor in the following equation ?

8 ÷ __________ = 5

6. What is the missing dividend in the following equation?

__________

7. What is the missing divisor in the following equation?

9 ÷ __________ = 4

8. Show how you can check your work in Question 7. __________________

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**Unit Review**

**Estimating Quotients of Fractions**

1. Rewrite 4/5 as an equivalent fraction with a denominator of 10.

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2. Round the following fractions to the nearest whole numbers.

3. To prepare condensed soup for a crowd, Sophie mixes 2/3 cup of milk with

each can of condensed soup. She uses a total of 4 cups of milk. How

many cans of soup will she need? Show your work.

________________________________________________________________

________________________________________________________________

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**Using Multiplicative Inverses**

4. Rewrite the following mixed numbers as improper fractions.

5. Using multiplicative inverses, rewrite these division problems as

multiplication problems. If necessary, convert mixed numbers to improper

fractions.

6. To make a fruit punch, Dijit needs to mix 1/2 cup of the fruit punch powder

with 1 quart of water. The fruit punch container holds 4 cups of powder.

How many quarts of water does Dijit need to mix with one whole

container of the powder? ________________________________________

**Solving Missing Value Problems when Dividing Fractions**

7. For a summer job, you mow lawns. Your lawn mower uses 2/3 gallon of

fuel an hour. If you used 6 gallons of fuel one day, how many hours did

you spend mowing grass that day? Show your steps and check your

answer. ________________________________________________________

8. Sophie spends hours on a shopping trip for
her clients. She spends

the same amount of time, hours, at each store
she visits. How many

stores does she visit? Show the steps you use to solve the problem.

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**Putting It All Together**

9. The net weight of bolts in a keg is pounds.
The weight of one bolt

is ounces. How many bolts are there in the
keg? (Remember to

convert pounds to ounces.) ________________________________________

10. Chip builds a fence that is yards long,
with a post at each end. He

has a total of 14 fence posts, including the two at each end. How far

apart should he place his posts? Make a drawing and show your work.

________________________________________________________________

**Unit Assessment**

1. Your friend wants your help to solve the problem
Write words

and steps that explain how to find this quotient. ______________________

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2. a. Place a point on the number line to show
to the nearest whole

number.

b. Is closer to 2 or 3?
______________________

3.Write a problem with a divisor that is a whole number, a dividend that is

a mixed number, and a quotient that is a proper fraction in lowest terms .

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4. Find the multiplicative inverse of ________________________________

5. Can the reciprocal of a proper fraction always be written as a mixed

number? __________ Explain. ____________________________________

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6. Chip has 3/4 of a pizza that he wants to divide equally between himself

and two of his friends. What fraction of the pizza will Chip get?

Show your work. ________________________________________________

__________________________________________________________________

7. Sophie is designing a decorator item using colored yarn. She needs 35

pieces of yarn that are 1/4 yard each to complete the project. She has

yards of yarn. Will Sophie have enough yarn to complete her design?

__________ Explain your answer. __________________________________

__________________________________________________________________

__________________________________________________________________

8.Will the reciprocal of a whole number (other than 1) be a proper fraction or

an improper fraction? Explain. ____________________________________

__________________________________________________________________

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