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Simplify : ...

Question

Simplify :
$[3 \frac{1}{4} \div {1 \frac{1}{4} - \frac{1}{2} (2 \frac{1}{2} - \frac{1}{4} - \frac{1}{6})}] \div (\frac{1}{2} o f 4 \frac{1}{3})$

A

18

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B

36

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C

39

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D

78

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Solution

The correct option is C: $36$
Given expression:
$[3 \frac{1}{4} \div {1 \frac{1}{4} - \frac{1}{2} (2 \frac{1}{2} - \frac{1}{4} - \frac{1}{6})}] \div (\frac{1}{2} o f 4 \frac{1}{3})$
$= [\frac{13}{4} \div {\frac{5}{4} - \frac{1}{2} (\frac{5}{2} - \frac{2}{24})}] \div (\frac{1}{2} o f \frac{13}{3})$
$= [\frac{13}{4} \div {\frac{5}{4} - \frac{1}{2} (\frac{5}{2} - \frac{1}{12})}] \div \frac{13}{6}$
$= [\frac{13}{4} \div {\frac{5}{4} - \frac{1}{2} \times (\frac{30 - 1}{12})}] \div \frac{13}{6}$
$= [\frac{13}{4} \div {\frac{5}{4} - \frac{29}{24}}] \div \frac{13}{6}$
$= [\frac{13}{4} \div (\frac{30 - 29}{24})] \div \frac{13}{6}$
$= (\frac{13}{4} \div \frac{1}{24}) \div \frac{13}{6}$
$= \frac{13}{4} \times 24 \times \frac{6}{13}$
$= 36$

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