Question

What number, when added to the numerator and to the denominator of $\frac{5}{8},$ results in a fraction whose value is $0.4$?

Answer 1

Solve for the required value:

Given fraction is $\frac{5}{8}$

Let the number added be $\mathrm{x}$.

Then according to question, we get;

$\frac{5+\mathrm{x}}{8+\mathrm{x}}=0.4$

$\Rightarrow$ $5+\mathrm{x}=0.4\left(8+\mathrm{x}\right)$

$\Rightarrow$ $5+\mathrm{x}=3.2+0.4\mathrm{x}$

$\Rightarrow$$\mathrm{x}-0.4\mathrm{x}=3.2-5$

$\Rightarrow$ $0.6\mathrm{x}=-1.8$

$\Rightarrow$ $\mathrm{x}=\frac{-1.8}{0.6}$

$\Rightarrow$ $\mathrm{x}=-3$

Hence, the required number is $-3$.