How to add complex fractions - SAT Math

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Question

Add: $\frac{\frac{9}{8}}{7}+\frac{7}{\frac{1}{7}}$

Answer

To add $\frac{\frac{9}{8}}{7}+\frac{7}{\frac{1}{7}}$ , first simply each term by rewriting the terms using a division sign.

$\frac{9}{8}\div7 + 7 \div \frac{1}{7}$

Take the reciprocal of the terms after the division sign, and change the division sign to a multiplication sign. Simplify.

$\frac{9}{8}\times \frac{1}{7}+ 7 \times 7 = \frac{9}{56} + 49= 49\frac{9}{56}$

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Question

Add: $\frac{1}{\frac{3}{2}}+ \frac{\frac{4}{1}}{\frac{1}{5}}$

Answer

The terms shown are complex fractions. We first need to simplify each and find the least common denominator before solving.

Rewrite the complex fraction using a division sign.

$\frac{1}{\frac{3}{2}} = 1\div\frac{3}{2}$

Change the division sign to a multiplication sign, and take the reciprocal of the second term.

$1\div\frac{3}{2} = 1\times \frac{2}{3} = \frac{2}{3}$

Repeat this step for the second term.

$\frac{\frac{4}{1}}{\frac{1}{5}} = \frac{4}{1} \div \frac{1}{5} = \frac{4}{1} \times \frac{5}{1}=20$

Add the two terms together.

The answer is: $20\frac{2}{3}$

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