Question

Divide reciprocal of $\frac{2}{5}\times \frac{-10}{3}$ by $(\frac{1}{2}-\frac{1}{3})$.

Answer 1

Now,

$\frac{2}{5}\times \frac{-10}{3}=\frac{-4}{3}$

Therefore, reciprocal of $\frac{-4}{3}$ is $\frac{-3}{4}$

Also,

$(\frac{1}{2}-\frac{1}{3})=\frac{3-2}{6}=\frac{1}{6}$ [LCM of $2$ and $3$ is $6$].

Hence, ATQ,

$\Rightarrow \frac{-3}{4}÷\frac{1}{6}$

$=\frac{-3}{4}\times 6$

$=\frac{-9}{2}$

$=-4\frac{1}{2}$

Hence, reciprocal of $\frac{2}{5}\times \frac{-10}{3}$ divided by $(\frac{1}{2}-\frac{1}{3})=-4\frac{1}{2}$.