Question

Simplify:

$\frac{\frac{1}{4}+\frac{1}{5}}{1-\frac{3}{8}\times \frac{3}{5}}$

Answer 1

Given: $\frac{\frac{1}{4}+\frac{1}{5}}{1-\frac{3}{8}\times \frac{3}{5}}$

$=\frac{\frac{5+4}{20}}{1-\frac{9}{40}}$ [Since, LCM of $4$ and $5$ is $20$ and $\frac{a}{b}\times \frac{c}{d}=\frac{a\times c}{c\times d}$]

$=\frac{\frac{9}{20}}{\frac{40-9}{40}}$

$=\frac{\frac{9}{20}}{\frac{31}{40}}$

$=\frac{9}{20}\times \frac{40}{31}$ [Since, $\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$]

$=\frac{9}{1}\times \frac{2}{31}$

$=\frac{9\times 2}{1\times 31}$

$=\frac{18}{31}$

$\therefore \frac{\frac{1}{4}+\frac{1}{5}}{1-\frac{3}{8}\times \frac{3}{5}}=\frac{18}{31}$