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SSAT Upper Level Math : How to find a complex fraction

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #1 : How To Find A Complex Fraction

Simplify:

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

Possible Answers:

$\frac{3}{10}$

$\frac{3}{7}$

$\frac{52}{75}$

$\frac{1}{5}$

$\frac{13}{12}$

Correct answer:

$\frac{13}{12}$

Explanation:

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

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

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

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

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

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

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Example Question #131 : Number Concepts And Operations

Simplify:

$\frac{\frac{1}{3} + \frac{3}{10}}{\frac{9}{10}}$

Possible Answers:

$\frac{19}{27}$

$\frac{1}{27}$

$\frac{57}{100}$

$\frac{2}{3}$

$\frac{40}{117}$

Correct answer:

$\frac{19}{27}$

Explanation:

Simplify the sum in the numerator, then divide by the denominator:

$\frac{\frac{1}{3} + \frac{3}{10}}{\frac{9}{10}}$

$=\frac{\frac{1\cdot 10}{3 \cdot 10} + \frac{3 \cdot 3}{10 \cdot 3}}{\frac{9}{10}}$

$=\frac{\frac{10}{30} + \frac{9}{30}}{\frac{9}{10}}$

$=\frac{\frac{10+9}{30} }{\frac{9}{10}} = \frac{\frac{19}{30} }{\frac{9}{10}}$

$\frac{19}{30} \div \frac{9}{10} = \frac{19}{30}\times \frac{10}{9} = \frac{19}{3}\times \frac{1}{9} = \frac{19}{27}$

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Example Question #132 : Number Concepts And Operations

Simplify:

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

Possible Answers:

$\frac{2}{5}$

$\frac{4}{15}$

$\frac{3}{5}$

$\frac{5}{18}$

$\frac{1}{4}$

Correct answer:

$\frac{5}{18}$

Explanation:

Rewrite this as a division problem, then solve:

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

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Example Question #2 : How To Find A Complex Fraction

Simplify:

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

Possible Answers:

$3 \frac{3}{4}$

$4 \frac{1}{2}$

$6\frac{1}{4}$

Correct answer:

Explanation:

Rewrite this as a division problem, then solve:

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

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Example Question #31 : Complex Fractions

Simplify:

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

Possible Answers:

$\frac{3}{4}$

$\frac{2}{3}$

$\frac{7}{10}$

$\frac{5}{9}$

$\frac{5}{8}$

Correct answer:

$\frac{2}{3}$

Explanation:

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

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

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

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

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

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

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

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Example Question #5 : How To Find A Complex Fraction

Simplify:

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

Possible Answers:

The correct answer is not given among the other responses.

$\frac{7}{25}$

$\frac{5}{19}$

$\frac{27}{100}$

$\frac{9}{23}$

Correct answer:

The correct answer is not given among the other responses.

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.

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Example Question #81 : Rational Numbers

Simplify:

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

Possible Answers:

$1\frac{3}{5}$

$1\frac{2}{5}$

$1\frac{1}{4}$

$1\frac{1}{6}$

$1\frac{1}{5}$

Correct answer:

$1\frac{1}{5}$

Explanation:

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

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

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

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

$= \frac{57}{10} \times \frac{4}{19}$

$= \frac{3}{5} \times \frac{2}{1}$

$= \frac{6}{5} = 1\frac{1}{5}$

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Example Question #5 : How To Find A Complex Fraction

Simplify, writing as a proper fraction.

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

Possible Answers:

$\frac{7}{12}$

$\frac{3}{10}$

$\frac{2}{5}$

$\frac{5}{9}$

$\frac{5}{12}$

Correct answer:

$\frac{5}{12}$

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.

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

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SSAT Upper Level Math : How to find a complex fraction

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Find A Complex Fraction

Example Question #131 : Number Concepts And Operations

Example Question #132 : Number Concepts And Operations

Example Question #2 : How To Find A Complex Fraction

Example Question #31 : Complex Fractions

Example Question #5 : How To Find A Complex Fraction

Example Question #81 : Rational Numbers

Example Question #5 : How To Find A Complex Fraction

All SSAT Upper Level Math Resources

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