What should be added to $\frac{2}{3}+\frac{3}{5}$ to get $\frac{-2}{15}$?

Given :

The given expressions are $\frac{2}{3}+\frac{3}{5}$ and $\frac{-2}{15}$.

To do :

We have to find the number to be added to $\frac{2}{3}+\frac{3}{5}$ to get $\frac{-2}{15}$.

Solution :

Let the number to be added to$\frac{2}{3}+\frac{3}{5}$ to get $\frac{-2}{15}$ be x.

This implies,

$\frac{2}{3}+\frac{3}{5}+x=\frac{-2}{15}$

$\frac{(2\times 5+3\times 3)}{15} + x = \frac{-2}{15}$

$\frac{(10+9)}{15} + x = \frac{-2}{15}$

$\frac{19}{15} + x = \frac{-2}{15}$

$x = \frac{-2}{15} - \frac{19}{15}$

$x = \frac{(-2-19)}{15}$

$x = \frac{-21}{15}$

$x = \frac{-7}{5}$

The number to be added to $\frac{2}{3}+\frac{3}{5}$ to get $\frac{-2}{15}$ is $\frac{-7}{5}$.

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Updated on: 10-Oct-2022

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