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PSAT Math : How to find a solution to a compound fraction

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Example Question #1 : How To Find A Solution To A Compound Fraction

Simplify:

$\frac{56}{1-\frac{1}{49}}$ $\displaystyle \frac{56}{1-\frac{1}{49}}$

Possible Answers:

$54\frac{48}{49}$ $\displaystyle 54\frac{48}{49}$

$57 \frac{1}{6}$ $\displaystyle 57 \frac{1}{6}$

$55\frac{1}{7}$ $\displaystyle 55\frac{1}{7}$

$54\frac{6}{7}$ $\displaystyle 54\frac{6}{7}$

$55\frac{1}{49}$ $\displaystyle 55\frac{1}{49}$

Correct answer:

$57 \frac{1}{6}$ $\displaystyle 57 \frac{1}{6}$

Explanation:

$\frac{56}{1-\frac{1}{49}}$ $\displaystyle \frac{56}{1-\frac{1}{49}}$

$= 56 \div \left ( 1-\frac{1}{49} \right )$ $\displaystyle = 56 \div \left ( 1-\frac{1}{49} \right )$

$= 56 \div \left (\frac{49}{49} -\frac{1}{49} \right )$ $\displaystyle = 56 \div \left (\frac{49}{49} -\frac{1}{49} \right )$

$= \frac{56 }{1}\div \frac{48}{49}$ $\displaystyle = \frac{56 }{1}\div \frac{48}{49}$

$= \frac{56 }{1}\cdot \frac{49}{48}$ $\displaystyle = \frac{56 }{1}\cdot \frac{49}{48}$

$= \frac{7}{1}\cdot \frac{49}{6}$ $\displaystyle = \frac{7}{1}\cdot \frac{49}{6}$

$= \frac{343}{6}$ $\displaystyle = \frac{343}{6}$

$= 57 \frac{1}{6}$ $\displaystyle = 57 \frac{1}{6}$

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Example Question #1 : How To Find A Solution To A Compound Fraction

Simplify:

$\frac{\frac{3}{4}-\frac{2}{5}}{2- \frac{9}{10}}$ $\displaystyle \frac{\frac{3}{4}-\frac{2}{5}}{2- \frac{9}{10}}$

Possible Answers:

$\frac{7}{38}$ $\displaystyle \frac{7}{38}$

$\frac{77}{200}$ $\displaystyle \frac{77}{200}$

$\frac{5}{72}$ $\displaystyle \frac{5}{72}$

$\frac{7}{22}$ $\displaystyle \frac{7}{22}$

$\frac{147}{200}$ $\displaystyle \frac{147}{200}$

Correct answer:

$\frac{7}{22}$ $\displaystyle \frac{7}{22}$

Explanation:

$\frac{\frac{3}{4}-\frac{2}{5}}{2- \frac{9}{10}}$ $\displaystyle \frac{\frac{3}{4}-\frac{2}{5}}{2- \frac{9}{10}}$

$= \left ( \frac{3}{4}-\frac{2}{5} \right ) \div \left ( 2- \frac{9}{10} \right )$ $\displaystyle = \left ( \frac{3}{4}-\frac{2}{5} \right ) \div \left ( 2- \frac{9}{10} \right )$

$= \left ( \frac{15}{20}-\frac{8}{20} \right ) \div \left ( \frac{20}{10}- \frac{9}{10} \right )$ $\displaystyle = \left ( \frac{15}{20}-\frac{8}{20} \right ) \div \left ( \frac{20}{10}- \frac{9}{10} \right )$

$= \frac{7}{20} \div \frac{11}{10}$ $\displaystyle = \frac{7}{20} \div \frac{11}{10}$

$= \frac{7}{20} \cdot \frac{10}{11}$ $\displaystyle = \frac{7}{20} \cdot \frac{10}{11}$

$= \frac{7}{2} \cdot \frac{1}{11}$ $\displaystyle = \frac{7}{2} \cdot \frac{1}{11}$

$= \frac{7}{22}$ $\displaystyle = \frac{7}{22}$

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Example Question #3 : How To Find A Solution To A Compound Fraction

Simplify:

$\frac{1-\frac{1}{4}}{1-\frac{1}{8}}$ $\displaystyle \frac{1-\frac{1}{4}}{1-\frac{1}{8}}$

Possible Answers:

$\frac{21}{32}$ $\displaystyle \frac{21}{32}$

$\frac{6}{7}$ $\displaystyle \frac{6}{7}$

$\frac{8}{9}$ $\displaystyle \frac{8}{9}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{7}{8}$ $\displaystyle \frac{7}{8}$

Correct answer:

$\frac{6}{7}$ $\displaystyle \frac{6}{7}$

Explanation:

$\frac{1-\frac{1}{4}}{1-\frac{1}{8}}$ $\displaystyle \frac{1-\frac{1}{4}}{1-\frac{1}{8}}$

$= \left (1 -\frac{1}{4} \right ) \div \left (1-\frac{1}{8} \right )$ $\displaystyle = \left (1 -\frac{1}{4} \right ) \div \left (1-\frac{1}{8} \right )$

$= \left (\frac{4}{4}-\frac{1}{4} \right ) \div \left (\frac{8}{8}-\frac{1}{8} \right )$ $\displaystyle = \left (\frac{4}{4}-\frac{1}{4} \right ) \div \left (\frac{8}{8}-\frac{1}{8} \right )$

$= \frac{3}{4} \div \frac{7}{8}$ $\displaystyle = \frac{3}{4} \div \frac{7}{8}$

$= \frac{3}{4} \cdot \frac{8}{7}$ $\displaystyle = \frac{3}{4} \cdot \frac{8}{7}$

$= \frac{3}{1} \cdot \frac{2}{7}$ $\displaystyle = \frac{3}{1} \cdot \frac{2}{7}$

$= \frac{6}{7}$ $\displaystyle = \frac{6}{7}$

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Example Question #2 : How To Find A Solution To A Compound Fraction

Simplify:

$\frac{2-\frac{1}{4}}{1+\frac{1}{7}}$ $\displaystyle \frac{2-\frac{1}{4}}{1+\frac{1}{7}}$

Possible Answers:

$1\frac{1}{28}$ $\displaystyle 1\frac{1}{28}$

None of the other responses gives the correct answer.

$1\frac{27}{28}$ $\displaystyle 1\frac{27}{28}$

$\displaystyle 2$

$1 \frac{17}{32}$ $\displaystyle 1 \frac{17}{32}$

Correct answer:

$1 \frac{17}{32}$ $\displaystyle 1 \frac{17}{32}$

Explanation:

$\frac{2-\frac{1}{4}}{1+\frac{1}{7}}$ $\displaystyle \frac{2-\frac{1}{4}}{1+\frac{1}{7}}$

$= \left ( 2-\frac{1}{4} \right ) \div \left ( 1+\frac{1}{7} \right )$ $\displaystyle = \left ( 2-\frac{1}{4} \right ) \div \left ( 1+\frac{1}{7} \right )$

$= \left (\frac{8}{4}-\frac{1}{4} \right ) \div \left ( \frac{7}{7}+\frac{1}{7} \right )$ $\displaystyle = \left (\frac{8}{4}-\frac{1}{4} \right ) \div \left ( \frac{7}{7}+\frac{1}{7} \right )$

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

$= \frac{7}{4} \cdot \frac{7}{8}$ $\displaystyle = \frac{7}{4} \cdot \frac{7}{8}$

$= \frac{49}{32}$ $\displaystyle = \frac{49}{32}$

$= 1 \frac{17}{32}$ $\displaystyle = 1 \frac{17}{32}$

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Example Question #1 : How To Find A Solution To A Compound Fraction

Simplify:

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

Possible Answers:

$\frac{2}{9}$ $\displaystyle \frac{2}{9}$

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{17} {22}$ $\displaystyle \frac{17} {22}$

$\frac{374}{225}$ $\displaystyle \frac{374}{225}$

Correct answer:

$\frac{17} {22}$ $\displaystyle \frac{17} {22}$

Explanation:

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

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

$=\left ( \frac{5}{15}+\frac{12}{15} \right ) \div\left ( \frac{10}{15}+\frac{12}{15} \right )$ $\displaystyle =\left ( \frac{5}{15}+\frac{12}{15} \right ) \div\left ( \frac{10}{15}+\frac{12}{15} \right )$

$= \frac{17}{15} \div \frac{22}{15}$ $\displaystyle = \frac{17}{15} \div \frac{22}{15}$

$= \frac{17}{15} \cdot \frac{15}{22}$ $\displaystyle = \frac{17}{15} \cdot \frac{15}{22}$

$= \frac{17}{1} \cdot \frac{1}{22}$ $\displaystyle = \frac{17}{1} \cdot \frac{1}{22}$

$= \frac{17} {22}$ $\displaystyle = \frac{17} {22}$

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Example Question #1 : How To Find A Solution To A Compound Fraction

Simplify:

$\frac{\frac{1}{2}-\frac{1}{10} }{\frac{1}{4}-\frac{1}{5} }$ $\displaystyle \frac{\frac{1}{2}-\frac{1}{10} }{\frac{1}{4}-\frac{1}{5} }$

Possible Answers:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{1}{50}$ $\displaystyle \frac{1}{50}$

The correct answer is not given among the other responses.

$\displaystyle 50$

$\displaystyle 2$

Correct answer:

The correct answer is not given among the other responses.

Explanation:

$\frac{\frac{1}{2}-\frac{1}{10} }{\frac{1}{4}-\frac{1}{5} }$ $\displaystyle \frac{\frac{1}{2}-\frac{1}{10} }{\frac{1}{4}-\frac{1}{5} }$

$= \left ( \frac{1}{2}-\frac{1}{10} \right )\div \left ( \frac{1}{4}-\frac{1}{5} \right )$ $\displaystyle = \left ( \frac{1}{2}-\frac{1}{10} \right )\div \left ( \frac{1}{4}-\frac{1}{5} \right )$

$= \left ( \frac{5}{10}-\frac{1}{10} \right )\div \left ( \frac{5}{20}-\frac{4}{20} \right )$ $\displaystyle = \left ( \frac{5}{10}-\frac{1}{10} \right )\div \left ( \frac{5}{20}-\frac{4}{20} \right )$

$= \frac{4}{10} \div \frac{1}{20}$ $\displaystyle = \frac{4}{10} \div \frac{1}{20}$

$= \frac{4}{10} \cdot \frac{20}{1}$ $\displaystyle = \frac{4}{10} \cdot \frac{20}{1}$

$= \frac{4}{1} \cdot \frac{2}{1}$ $\displaystyle = \frac{4}{1} \cdot \frac{2}{1}$

$= \frac{8}{1} = 8$ $\displaystyle = \frac{8}{1} = 8$

This answer is not among the given choices.

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PSAT Math : How to find a solution to a compound fraction

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Find A Solution To A Compound Fraction

Example Question #1 : How To Find A Solution To A Compound Fraction

Example Question #3 : How To Find A Solution To A Compound Fraction

Example Question #2 : How To Find A Solution To A Compound Fraction

Example Question #1 : How To Find A Solution To A Compound Fraction

Example Question #1 : How To Find A Solution To A Compound Fraction

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