How to find a complex fraction

SSAT Upper Level Quantitative · Learn by Concept

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SSAT Upper Level Quantitative › How to find a complex fraction

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Simplify:

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

$\frac{13}{12}$

CORRECT

$\frac{52}{75}$

$\frac{1}{5}$

$\frac{3}{7}$

$\frac{3}{10}$

Explanation

Add the fractions in the numerator, then divide the sum by the denominator:

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

$=\frac{\frac{2\cdot 5}{3\cdot 5} + \frac{1\cdot 3}{5\cdot 3}}{\frac{4}{5}}$

$=\frac{\frac{10}{15} + \frac{3}{15}}{\frac{4}{5}}$

$=\frac{\frac{10+3}{15} }{\frac{4}{5}} = \frac{\frac{13}{15} }{\frac{4}{5}}$

$= \frac{13}{15} \div \frac{4}{5} = \frac{13}{15} \times \frac{5}{4} = \frac{13}{3} \times \frac{1}{4} =\frac{13}{12}$

Simplify, writing as a proper fraction.

$\frac{2\tfrac{1}{4}}{5\tfrac{2}{5}}$

$\frac{5}{12}$

CORRECT

$\frac{7}{12}$

$\frac{2}{5}$

$\frac{5}{9}$

$\frac{3}{10}$

Explanation

Remember that that fraction bar is just a division symbol. Rewrite as a division, rewrite those mixed fractions as improper fractions, then rewrite as as a multiplication by the reciprocal of the second fraction.

$\frac{2\tfrac{1}{4}}{5\tfrac{2}{5}} = 2\tfrac{1}{4} \div 5\tfrac{2}{5} = \frac{9}{4} \div \frac{27}{5} = \frac{9}{4} \cdot \frac{5}{27} = \frac{1}{4} \cdot \frac{5}{3}= \frac{5}{12}$

Simplify:

$\frac{3\frac{1}{2}-2\frac{1}{5}}{4\frac{3}{4}}$

The correct answer is not given among the other responses.

CORRECT

$\frac{27}{100}$

$\frac{9}{23}$

$\frac{5}{19}$

$\frac{7}{25}$

Explanation

$\frac{3\frac{1}{2}-2\frac{1}{5}}{4\frac{3}{4}}$

$=\left ( 3\frac{1}{2}-2\frac{1}{5} \right )\div 4\frac{3}{4}}$

$= \left ( \frac{7}{2}- \frac{11}{5} \right ) \div \frac{19}{4}$

$= \left ( \frac{35}{10}- \frac{22}{10} \right ) \times \frac{4}{19}$

$= \frac{13}{10} \times \frac{4}{19}$

$= \frac{13}{5} \times \frac{2}{19}$

$= \frac{26}{95}$

This is not among the given responses.

Simplify:

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

$\frac{2}{3}$

CORRECT

$\frac{3}{4}$

$\frac{5}{8}$

$\frac{7}{10}$

$\frac{5}{9}$

Explanation

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

$=3\frac{4}{5} \div \left ( 3\frac{1}{2}+2\frac{1}{5} \right )$

$= \frac{19}{5} \div \left ( \frac{7}{2}+ \frac{11}{5} \right )$

$=\frac{19}{5} \div \left ( \frac{35}{10}+ \frac{22}{10} \right )$

$=\frac{19}{5} \div \frac{57}{10}$

$=\frac{19}{5} \times \frac{10}{57}$

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

Simplify:

$\frac{5}{1\frac{1}{4}}$

CORRECT

$3 \frac{3}{4}$

$6\frac{1}{4}$

$4 \frac{1}{2}$

Explanation

Rewrite this as a division problem, then solve:

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

Simplify:

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

$\frac{5}{18}$

CORRECT

$\frac{3}{5}$

$\frac{4}{15}$

$\frac{1}{4}$

$\frac{2}{5}$

Explanation

Rewrite this as a division problem, then solve:

$\frac{1\frac{1}{3}}{4 \frac{4}{5}} = 1\frac{1}{3} \div 4 \frac{4}{5} = \frac{4}{3} \div \frac{24}{5}= \frac{4}{3} \times \frac{5}{24}= \frac{1}{3} \times \frac{5}{6}= \frac{5}{18}$