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: $\frac{3}{16}$
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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