Question

What rational number should be subtracted from $\frac{5}{8}$ to get $\frac{8}{5}$.

Answer 1

Step : Finding the other number
Let, the required number be $x$.
According to question $x$ should be subtracted
from $\frac{5}{8}$ to get $\frac{8}{5}$.
$\frac{5}{8}-x=\frac{8}{5}$
$\Rightarrow \frac{5}{8}-\frac{8}{5}=x$
$\Rightarrow x=\frac{5\times 5}{8\times 5}-\frac{8\times 8}{5\times 8}[\because \text{LCM of 5 and 8 is 40}]$
$=\frac{25}{40}-\frac{64}{40}$
$=\frac{25-64}{40}=\frac{-39}{40}$

Hence, $\frac{-39}{40}$should be subtracted from $\frac{5}{8}$ to get $\frac{8}{5}$.