How to divide complex fractions

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SSAT Upper Level Quantitative › How to divide complex fractions

Questions 1 - 10

1

$\frac{\frac{2}{3}}{\frac{4}{5}}=?$

$\frac{5}{6}$

$\frac{6}{5}$

$\frac{8}{15}$

$\frac{4}{5}$

Explanation

Keep in mind that the main fraction line just means "divide."

So then,

$\frac{\frac{2}{3}}{\frac{4}{5}}=\frac{2}{3}\div\frac{4}{5}$

Now, divide this like any other fraction.

$\frac{2}{3}\div\frac{4}{5}=\frac{2}{3}\times\frac{5}{4}=\frac{10}{12}=\frac{5}{6}$

2

$\frac{\frac{4}{3}}{6}=?$

$\frac{2}{9}$

$\frac{1}{8}$

$\frac{3}{4}$

$\frac{7}{8}$

Explanation

Remember that the main line in the fraction means "divide."

Then,

$\frac{\frac{4}{3}}{6}=\frac{4}{3}\div6$

Now, divide this like you would divide any other fraction.

$\frac{4}{3}\div6=\frac{4}{3}\times\frac{1}{6}=\frac{4}{18}=\frac{2}{9}$

3

$\frac{\frac{9}{10}}{\frac{5}{2}}=?$

$\frac{9}{25}$

$\frac{11}{15}$

$\frac{25}{9}$

$\frac{4}{5}$

Explanation

Remember that the main line in the fraction means "divide."

Now,

$\frac{\frac{9}{10}}{\frac{5}{2}}=\frac{9}{10}\div\frac{5}{2}$

Divide these two fractions.

$\frac{9}{10}\div\frac{5}{2}=\frac{9}{10}\times\frac{2}{5}=\frac{18}{50}=\frac{9}{25}$

4

$\frac{\frac{8}{9}}{\frac{1}{2}}=?$

$\frac{16}{9}$

$\frac{9}{16}$

$\frac{10}{9}$

$\frac{13}{9}$

Explanation

The main fraction line means "divide."

Rewrite the complex fraction:

$\frac{\frac{8}{9}}{\frac{1}{2}}=\frac{8}{9}\div\frac{1}{2}$

Divide these fractions.

$\frac{8}{9}\div\frac{1}{2}=\frac{8}{9}\times\frac{2}{1}=\frac{16}{9}$

5

$\frac{\frac{12}{13}}{\frac{1}{4}}=?$

$\frac{48}{13}$

$\frac{37}{13}$

$\frac{13}{48}$

$\frac{12}{5}$

Explanation

The main fraction line means "divide."

Rewrite the complex fractions as thus:

$\frac{\frac{12}{13}}{\frac{1}{4}}=\frac{12}{13}\div\frac{1}{4}$

Now, divide these two fractions.

$\frac{12}{13}\div\frac{1}{4}=\frac{12}{13}\times\frac{4}{1}=\frac{48}{13}$

6

$\frac{\frac{7}{8}}{\frac{5}{4}}=?$

$\frac{7}{10}$

$\frac{4}{5}$

$\frac{10}{7}$

$\frac{4}{7}$

Explanation

The main fraction line means "divide." Rewrite the complex fraction as thus:

$\frac{\frac{7}{8}}{\frac{5}{4}}=\frac{7}{8}\div\frac{5}{4}$

Divide these two fractions.

$\frac{7}{8}\div\frac{5}{4}=\frac{7}{8}\times\frac{4}{5}=\frac{28}{40}=\frac{7}{10}$

7

$\frac{\frac{12}{11}}{\frac{5}{2}}=?$

$\frac{24}{55}$

$\frac{55}{24}$

$\frac{5}{11}$

$\frac{11}{5}$

Explanation

The main line in a fraction means "divide." Rewrite the complex fraction as thus:

$\frac{\frac{12}{11}}{\frac{5}{2}}=\frac{12}{11}\div\frac{5}{2}$

Now, divide the fractions.

$\frac{12}{11}\div\frac{5}{2}=\frac{12}{11}\times\frac{2}{5}=\frac{24}{55}$

8

$\frac{\frac{3}{2}}{\frac{5}{4}}=?$

$\frac{6}{5}$

$\frac{5}{6}$

$\frac{12}{7}$

$\frac{5}{9}$

Explanation

The main line in a fraction means "divide." Rewrite the complex fraction as thus:

$\frac{\frac{3}{2}}{\frac{5}{4}}=\frac{3}{2}\div\frac{5}{4}$

Now, divide the fractions.

$\frac{3}{2}\div\frac{5}{4}=\frac{3}{2}\times\frac{4}{5}=\frac{12}{10}=\frac{6}{5}$

9

Simplify: $\frac{\frac{1}{2}}{2}+\frac{2}{\frac{1}{2}}$

$\frac{17}{4}$

$\frac{5}{4}$

Explanation

Rewrite the expression using a division sign.

$\frac{\frac{1}{2}}{2}+\frac{2}{\frac{1}{2}}=\frac{1}{2}\div2+2 \div \frac{1}{2}$

Take the reciprocal of the term after the division signs and convert the division sign to a multiplication sign.

$\frac{1}{2}\times\frac{1}{2}+2 \times2=\frac{1}{4}+4=4\frac{1}{4}=\frac{17}{4}$

10

$\frac{\frac{1}{8}}{\frac{7}{8}}=?$

$\frac{1}{7}$

$\frac{3}{5}$

$\frac{9}{56}$

Explanation

The main line in a fraction means "divide." Rewrite the complex fraction as thus:

$\frac{\frac{1}{8}}{\frac{7}{8}}=\frac{1}{8}\div\frac{7}{8}$

Now, divide these fractions.

$\frac{1}{8}\div\frac{7}{8}=\frac{1}{8}\times\frac{8}{7}=\frac{8}{56}=\frac{1}{7}$

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