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.) $\frac{4}{5} \div \frac{2}{3}$.

Solution

We get the reciprocal of $\frac{2}{3}$  and multiply it to $\frac{4}{5}$. The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. So,

$\displaystyle \frac{4}{5} \times \frac{3}{2} = \frac{12}{10}$

(you can use cancellation to do this quickly). Reducing to lowest terms  by dividing both the numerator and denominator by 2 results to $\frac{6}{5}$. Converting this improper fraction to mixed form, we get $1 \frac{1}{5}$.

Answer: $1 \frac{1}{5}$.

2.) $\frac{2}{7} \div \frac{5}{21}$

Solution

The division $\frac{2}{7} \div \frac{5}{21}$ is the same as

$\displaystyle \frac{2}{7} \times \frac{21}{5} =\frac{42}{35}$.

Reducing to lowest terms by dividing both the numerator and the denominator of the preceding fraction by $7$, we get $\frac{6}{5}$ or $1 \frac{1}{5}$.

Answer: $1 \frac{1}{5}$

3.) $8 \div \frac{4}{5}$

Solution

Any whole number in multiplication has a denominator $1$, so

$\displaystyle \frac{8}{1} \times \frac{5}{4} = \frac{40}{4} = 10$.

Answer: $10$

4.) $\frac{3}{5} \div 12$

The reciprocal of $12$ is $\frac{1}{12}$. Now, we multiply:

$\displaystyle \frac{3}{5} \times \frac{1}{12} = \frac{3}{60}$.

Dividing both the numerator and denominator by $3$, gives $\frac{1}{20}$ as the lowest term.

Answer: $\frac{1}{20}$

5.) $15 \div \frac{2}{3}$

We get the reciprocal of $\frac{2}{3}$,  we multiply:

$\displaystyle \frac{15}{1} \times \frac{3}{2} = \frac{45}{2}$.

Converting the improper fraction to mixed fraction gives us $22 \frac{1}{2}$.

Answer: $22 \frac{1}{2}$

6.) $3 \frac{2}{5} \div \frac{3}{4}$

First we convert the mixed fraction to improper fraction, then multiply it to the reciprocal of $\frac{3}{4}$.  If we convert $3 \frac{2}{5}$ to mixed fraction, we have $\frac{17}{5}$.

We now multiply:

$\displaystyle\frac{17}{5} \times \frac{4}{3} = \frac{68}{15}$.

Converting $\frac{68}{15}$ to mixed form gives us $4 \frac{8}{15}$.

Answer: $4 \frac{8}{15}$

7.) $\frac{3}{4} \div 2 \frac{1}{9}$.

Converting $2 \frac{1}{9}$ to mixed fractions gives us $\frac{19}{9}$. Now, multiplying $\frac{3}{4}$ to the reciprocal of $\frac{19}{9}$.

$\frac{3}{4} \times \frac{9}{19} = \frac{27}{76}$

Answer: $\frac{27}{76}$

8.)$7\frac{2}{3} \div 7\frac{1}{2}$

Converting $7 \frac{2}{3}$ to improper fraction gives us $\frac{23}{3}$. Now, converting $7 \frac{1}{2}$ to improper gives us $\frac{15}{2}$. Now, multiplying $\frac{23}{3}$ to the reciprocal of $\frac{15}{2}$, we have

$\displaystyle \frac{23}{3} \times \frac{2}{15} = \frac{46}{45} = 1 \frac{1}{45}$.

9.) $\displaystyle \frac{2\frac{3}{5}}{4}$

The given above is the same as $2 \frac{3}{5} \div 4$. Now, converting $2 \frac{3}{5}$ to improper fraction results to $\frac{13}{2}$. Now, we multiply this result to the reciprocal of $4$ which is $\frac{1}{4}$.

$\displaystyle \frac{13}{5} \times \frac{1}{4} = \frac{13}{20}$

Answer: $\frac{13}{20}$.

10.) $\displaystyle \frac{2 \frac{1}{2}}{\frac{8}{3}}$

The fraction $2 \frac{1}{2}$ in improper form is $\frac{5}{2}$. We multiply it to the reciprocal of $\frac{8}{3}$.

$\displaystyle \frac{5}{2} \times \frac{3}{8} = \frac{15}{16}$

Answer: $\frac{15}{16}$.

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