Question

If $I=\frac{3}{4}÷\frac{5}{6},II=3÷\left[\right(4÷5)÷6],III=[3÷(4÷5\left)\right]÷6,IV=3÷4(5÷6)$, then which of the following are equal?

• A. $I$ and $II$ are equal
• B. $I$ and $III$ are equal
• C. $I$ and $IV$ are equal
• D. All are equal

Answer 1

Answer: (C)

$I=\frac{3}{4}\times \frac{6}{5}=\frac{9}{10}$
$II=3÷[\frac{4}{5}\times \frac{1}{6}]=3÷\left[\frac{2}{15}\right]=\frac{45}{2}$
$III=[3÷\frac{4}{5}]=3\times \frac{5}{4}\times \frac{1}{6}=\frac{5}{8}$
$IV=3÷4\left(\frac{5}{6}\right)=3\times \frac{6}{20}=\frac{9}{10}$

Hence $I$ and $IV$ are equal.