Question
Simplify: $\frac{\frac{1}{4}+\frac{1}{5}}{1-\frac{3}{8}\times\frac{3}{5}}$
✓
Answer
Given, $\frac{\frac{1}{4}+\frac{1}{5}}{1-\frac{3}{8}\times\frac{3}{5}}$
$=\frac{\frac{5+4}{20}}{1-\frac{9}{40}}$
$=\frac{\frac{9}{20}}{\frac{40-9}{40}}$
$=\frac{\frac{9}{20}}{\frac{40-9}{40}}$ $$
$=\frac{\frac{9}{20}}{\frac{31}{40}}=\frac{9}{20}\times\frac{40}{31}$ $\big[\because\text{reciprocal of}\ \frac{31}{40}=\frac{40}{31}\big]$
$=\frac{18}{31}$
$=\frac{\frac{5+4}{20}}{1-\frac{9}{40}}$
$=\frac{\frac{9}{20}}{\frac{40-9}{40}}$
$=\frac{\frac{9}{20}}{\frac{40-9}{40}}$ $$
$=\frac{\frac{9}{20}}{\frac{31}{40}}=\frac{9}{20}\times\frac{40}{31}$ $\big[\because\text{reciprocal of}\ \frac{31}{40}=\frac{40}{31}\big]$
$=\frac{18}{31}$
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