Question : If $A=\frac{2}{3} \div \frac{4}{9}, B=\frac{6}{11} \times\frac{33}{12}$ and $C=\frac{1}{3} \times \frac{9}{2}$, then what is the value of $A \times B-C$?
Option 1: $\frac{3}{8}$
Option 2: $\frac{3}{2}$
Option 3: $\frac{3}{4}$
Option 4: $\frac{3}{16}$
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Correct Answer: $\frac{3}{4}$
Solution : $A=\frac{2}{3} \div \frac{4}{9}=\frac{2}{3} \times \frac{9}{4}=\frac{3}{2}$ $B=\frac{6}{11} \times\frac{33}{12}=\frac{3}{2}$ $C=\frac{1}{3} \times \frac{9}{2}=\frac{3}{2}$ $\therefore A \times B-C$ $=\frac{3}{2}\times\frac{3}{2}-\frac{3}{2}$ $=\frac{9}{4}-\frac{3}{2}$ $=\frac{9-6}{4}$ $=\frac{3}{4}$ Hence, the correct answer is $\frac{3}{4}$.
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