Question
Fill in the blanks: $6\frac{1}{6}-5\frac{1}{5}=\ ....$
✓
Answer
Given, $6\frac{1}{6}-5\frac{1}{5}=\ ....$ Let the value in the blank be $x.$
$6\frac{1}{6}-5\frac{1}{5}=\text{x}$
$\Rightarrow\text{x}=\frac{6\times6+1}{6}-\frac{5\times5+1}{5}$
$\Rightarrow\text{x}=\frac{37}{6}-\frac{26}{5}$
$\Rightarrow\text{x}=\frac{37\times5}{6\times5}-\frac{26\times6}{5\times6}$
(because $LCM$ of $6$ and $5$ is $30$)
$\Rightarrow\text{x}=\frac{185}{30}-\frac{156}{30}$
$\Rightarrow\text{x}=\frac{185-156}{30}$
$\text{x}=\frac{29}{30}$
$6\frac{1}{6}-5\frac{1}{5}=\text{x}$
$\Rightarrow\text{x}=\frac{6\times6+1}{6}-\frac{5\times5+1}{5}$
$\Rightarrow\text{x}=\frac{37}{6}-\frac{26}{5}$
$\Rightarrow\text{x}=\frac{37\times5}{6\times5}-\frac{26\times6}{5\times6}$
(because $LCM$ of $6$ and $5$ is $30$)
$\Rightarrow\text{x}=\frac{185}{30}-\frac{156}{30}$
$\Rightarrow\text{x}=\frac{185-156}{30}$
$\text{x}=\frac{29}{30}$
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