Divide the sum of $\frac{65}{12}$ and $\frac{12}{7}$ by their difference.

To do:

We have to divide the sum of $\frac{65}{12}$ and $\frac{12}{7}$ by their difference.

Solution:

Sum of $\frac{65}{12}$ and $\frac{12}{7}$ is,

$\frac{65}{12}+\frac{12}{7}=\frac{65\times7+12\times12}{84}$         (LCM of 12 and 7 is 84)

$=\frac{455+144}{84}$

$=\frac{599}{84}$

Difference of $\frac{65}{12}$ and $\frac{12}{7}$ is,

$\frac{65}{12}-\frac{12}{7}=\frac{65\times7-12\times12}{84}$         (LCM of 12 and 7 is 84)

$=\frac{455-144}{84}$

$=\frac{311}{84}$

Therefore,

$\frac{599}{84}\div\frac{311}{84}=\frac{599}{84}\times\frac{84}{311}$

$=\frac{599\times84}{84\times311}$

$=\frac{599}{311}$ 

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Updated on: 10-Oct-2022

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