How to divide complex fractions - SSAT Upper Level Quantitative

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Question

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

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Answer

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}$

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Question

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

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Answer

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}$=\frac{48}{13}$

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Question

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

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Answer

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}$

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Question

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

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Answer

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}$

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Question

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

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Answer

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}$

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Question

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

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Answer

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}$=\frac{16}{9}$

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Question

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

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Answer

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}$=\frac{24}{55}$

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Question

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

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Answer

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}$

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Question

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

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Answer

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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Question

$$\frac{\frac{3}{4}$}{$\frac{9}{10}$}=?$

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Answer

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

$\frac{\frac{3}{4}$}{$\frac{9}{10}$}=\frac{3}{4}$\div$\frac{9}{10}$

Now, divide these fractions.

$\frac{3}{4}$\div$\frac{9}{10}$=\frac{3}{4}$\times$\frac{10}{9}$=\frac{30}{36}$=\frac{5}{6}$

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Question

$$\frac{\frac{3}{5}$}{$\frac{1}{4}$}=?$

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Answer

The main line in a fraction means "divide." Rewrite the complex fraction like this:

$\frac{\frac{3}{5}$}{$\frac{1}{4}$}=\frac{3}{5}$\div$\frac{1}{4}$

Now, divide these two fractions.

$\frac{3}{5}$\div$\frac{1}{4}$=\frac{3}{5}$\times$\frac{4}{1}$=\frac{12}{5}$

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Question

$$\frac{\frac{10}{3}$}{$\frac{5}{3}$}=?$

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Answer

The main fraction line means "divide." Rewrite the complex fraction like this:

$\frac{\frac{10}{3}$}{$\frac{5}{3}$}=\frac{10}{3}$\div$\frac{5}{3}$

$$\frac{10}{3}$\div$\frac{5}{3}$=\frac{10}{3}$\times$\frac{3}{5}$=\frac{30}{15}$=2$

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Question

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

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Answer

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}$=\frac{17}{4}$

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Question

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

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Answer

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}$

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Question

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

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Answer

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}$

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Question

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

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Answer

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}$

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Question

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

Tap to reveal answer

Answer

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}$=\frac{16}{9}$

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Question

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

Tap to reveal answer

Answer

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}$=\frac{48}{13}$

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Question

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

Tap to reveal answer

Answer

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}$

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Question

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

Tap to reveal answer

Answer

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}$=\frac{24}{55}$

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