Question
Simplify: $\frac{2\frac{1}{2}+\frac{1}{5}}{2\frac{1}{2}+\frac{1}{5}}$
✓
Answer
Given, $\frac{2\frac{1}{2}+\frac{1}{5}}{2\frac{1}{2}+\frac{1}{5}}$
$=\frac{\frac{(2\times2)+1}{2}+\frac{1}{5}}{\frac{(2\times2)+\frac{1}{5}}{2}}$
$=\frac{\frac{5}{2}+\frac{1}{5}}{\frac{5}{2}+\frac{1}{5}}$
$=\frac{\frac{25+2}{10}}{\frac{5}{2}\times5}=\frac{27}{10}$ $\big[\because\text{reciprocal of}\ \frac{1}{5}=5\big]$
$=\frac{25}{2}=\frac{27}{10}\times\frac{2}{25}$ $\big[\because\text{reciprocal of}\ \frac{25}{2}=\frac{2}{25}\big]$
$=\frac{27}{125}$
$=\frac{\frac{(2\times2)+1}{2}+\frac{1}{5}}{\frac{(2\times2)+\frac{1}{5}}{2}}$
$=\frac{\frac{5}{2}+\frac{1}{5}}{\frac{5}{2}+\frac{1}{5}}$
$=\frac{\frac{25+2}{10}}{\frac{5}{2}\times5}=\frac{27}{10}$ $\big[\because\text{reciprocal of}\ \frac{1}{5}=5\big]$
$=\frac{25}{2}=\frac{27}{10}\times\frac{2}{25}$ $\big[\because\text{reciprocal of}\ \frac{25}{2}=\frac{2}{25}\big]$
$=\frac{27}{125}$
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