# Division of Fraction Practice Test Solutions and Answers

This is the complete solutions and answers to the** Practice Test on Division of Fractions**. If you are not familiar with the method, or you have forgotten how to do it, please read “**How to Divide Fractions**.“

In dividing fractions, you must **convert all mixed fractions to improper fractions** before performing the division. The division involves getting the reciprocal (multiplicative inverse) of the divisor, and then multiplying both fractions instead of dividing them.

1.) .

*Solution *

We get the reciprocal of and multiply it to . The reciprocal of is . So,

(you can use cancellation to do this quickly). Reducing to lowest terms by dividing both the numerator and denominator by 2 results to . Converting this improper fraction to mixed form, we get .

*Answer: *.

2.)

*Solution *

The division is the same as

.

**Reducing to lowest terms** by dividing both the numerator and the denominator of the preceding fraction by , we get or .

*Answer: *

3.)

*Solution *

Any whole number in multiplication has a denominator , so

.

*Answer: *

4.)

The reciprocal of is . Now, we multiply:

.

Dividing both the numerator and denominator by , gives as the lowest term.

*Answer:*

5.)

We get the reciprocal of , we multiply:

.

Converting the** improper fraction to mixed fraction **gives us .

*Answer:*

6.)

First we convert the mixed fraction to improper fraction, then multiply it to the reciprocal of . If we convert to mixed fraction, we have .

We now multiply:

.

Converting to mixed form gives us .

*Answer:*

7.) .

Converting to mixed fractions gives us . Now, multiplying to the reciprocal of .

*Answer: *

8.)

Converting to improper fraction gives us . Now, converting to improper gives us . Now, multiplying to the reciprocal of , we have

.

9.)

The given above is the same as . Now, converting to improper fraction results to . Now, we multiply this result to the reciprocal of which is .

*Answer:* .

10.)

The fraction in improper form is . We multiply it to the reciprocal of .

*Answer: *.

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