Question : Simplify the following expression:
$[\frac{85}{34}×\frac{1}{18}–${${{(\frac{46}{69}÷\frac{27}{135})}}–(\frac{86}{129}×\frac{91}{14})$} of $\frac{112}{36}]$
Option 1: $3 \frac{1}{5}$
Option 2: $3 \frac{3}{4}$
Option 3: $3 \frac{1}{2}$
Option 4: $3 \frac{1}{4}$
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Correct Answer: $3 \frac{1}{4}$
Solution :
Given: $[\frac{85}{34}×\frac{1}{18}–${${{(\frac{46}{69}÷\frac{27}{135})}}–(\frac{86}{129}×\frac{91}{14})$} of $\frac{112}{36}]$
$=[\frac{85}{34}×\frac{1}{18}–${${{(\frac{46}{69}×\frac{135}{27})}}–(\frac{86}{129}×\frac{91}{14})$} of $\frac{112}{36}]$
$=[\frac{5}{2}×\frac{1}{18}–${${{(\frac{2}{3}×\frac{5}{1})}}–(\frac{1}{3}×\frac{13}{1})$} of $\frac{28}{9}]$
$=[\frac{5}{36}–${${{\frac{10}{3}}}–\frac{13}{3}$} ×$\frac{28}{9}]$
$=[\frac{5}{36}+{\frac{3}{3}}×\frac{28}{9}]$
$=[\frac{5}{36}+\frac{28}{9}]$
$=[\frac{5+112}{36}]$
$=\frac{117}{36} = 3 \frac{1}{4}$
Hence, the correct answer is $3 \frac{1}{4}$.
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