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

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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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Question

Simplify:

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

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Answer

$$\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.

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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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Question

Simplify:

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

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Answer

$$\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.

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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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Question

Simplify:

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

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Answer

$$\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.

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Question

Simplify:

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

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Answer

$$\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}$$

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Question

Simplify:

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

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Answer

$$\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}$$

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