How to find a solution to a compound fraction

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

Questions 1 - 6

1

Simplify:

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

The correct answer is not given among the other responses.

$\frac{1}{50}$

$\frac{1}{2}$

Explanation

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

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

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

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

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

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

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

This answer is not among the given choices.

2

Simplify:

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

$57 \frac{1}{6}$

$54\frac{6}{7}$

$55\frac{1}{49}$

$54\frac{48}{49}$

$55\frac{1}{7}$

Explanation

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

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

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

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

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

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

$= \frac{343}{6}$

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

3

Simplify:

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

$\frac{7}{22}$

$\frac{77}{200}$

$\frac{5}{72}$

$\frac{147}{200}$

$\frac{7}{38}$

Explanation

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

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

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

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

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

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

$= \frac{7}{22}$

4

Simplify:

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

$\frac{6}{7}$

$\frac{21}{32}$

$\frac{1}{2}$

$\frac{7}{8}$

$\frac{8}{9}$

Explanation

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

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

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

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

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

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

$= \frac{6}{7}$

5

Simplify:

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

$1 \frac{17}{32}$

$1\frac{1}{28}$

$1\frac{27}{28}$

None of the other responses gives the correct answer.

Explanation

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

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

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

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

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

$= \frac{49}{32}$

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

6

Simplify:

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

$\frac{17} {22}$

$\frac{1}{2}$

$\frac{5}{8}$

$\frac{374}{225}$

$\frac{2}{9}$

Explanation

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

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

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

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

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

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

$= \frac{17} {22}$

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