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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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