Question : What is the value of $\frac{7}{8}+\frac{8}{11}$ of $[\frac{33}{16}-\frac{5}{12}+(\frac{6}{11}-\frac{5}{12}+\frac{7}{22})] ?$
Option 1: $\frac{6871}{3605}$
Option 2: $\frac{6805}{2987}$
Option 3: $\frac{6907}{3971}$
Option 4: $\frac{6961}{2904}$
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Correct Answer: $\frac{6961}{2904}$
Solution : $\frac{7}{8}+\frac{8}{11}$ of $[\frac{33}{16}-\frac{5}{12}+(\frac{6}{11}-\frac{5}{12}+\frac{7}{22})]$ $=\frac{7}{8}+\frac{8}{11}\times[\frac{33}{16}-\frac{5}{12}+\frac{59}{132}] $ $=\frac{7}{8}+\frac{8}{11} \times\frac{1105}{528} $ $=\frac{7}{8}+\frac{1105}{726} $ $= \frac{6961}{2904} $ Hence, the correct answer is $\frac{6961}{2904}$.
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