What number should be added to $\frac{−5}{7}$ to get $\frac{−2}{3}$?

Given :

The given numbers are $\frac{-5}{7}$ and $\frac{-2}{3}$.

To do :

We have to find the number that should be added to $\frac{-5}{7}$ to get $\frac{-2}{3}$.

Solution :

Let the number to be added to $\frac{-5}{7}$ to get $\frac{-2}{3}$ be $x$.

This implies,

$\frac{-5}{7}+x=\frac{-2}{3}$

$x =\frac{-2}{3} - (\frac{-5}{7})$

$x =\frac{-2}{3} + \frac{5}{7}$

$x = \frac{[-2(7)+5(3)]}{21}$

$x = \frac{(-14+15)}{21}$

$x = \frac{1}{21}$.

The number to be added to $\frac{-5}{7}$ to get $\frac{-2}{3}$ is $\frac{1}{21}$.    

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Updated on: 10-Oct-2022

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