Question : What is the value of $\frac{6}{13}[\frac{29}{12}+\frac{4}{18}(\frac{16}{12}+\frac{18}{9})–\frac{46}{15} \div \frac{23}{45}]$?
Option 1: $\frac{–312}{137}$
Option 2: $\frac{–307}{234}$
Option 3: $\frac{–294}{117}$
Option 4: $\frac{–207}{119}$
Correct Answer: $\frac{–307}{234}$
Solution :
$\frac{6}{13}[\frac{29}{12}+\frac{4}{18}(\frac{16}{12}+\frac{18}{9})–\frac{46}{15} \div \frac{23}{45}]$
$=\frac{6}{13}[\frac{29}{12}+\frac{4}{18}\times(\frac{48+72}{36})–\frac{46}{15} \div \frac{23}{45}]$
$=\frac{6}{13}[\frac{29}{12}+\frac{20}{27}–\frac{46}{15} \div \frac{23}{45}]$
$=\frac{6}{13}[\frac{29}{12}+\frac{20}{27}–6]$
$=\frac{6}{13}\times[\frac{261+80–648}{108}]$
$=\frac{6}{13}\times\frac{–307}{108}$
$=\frac{–307}{13\times18}$
$=\frac{–307}{234}$
Hence, the correct answer is $\frac{–307}{234}$.
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