Question

What number should be subtracted from $\frac{-2}{3}$ to get $\frac{-1}{6}$?

Answer 1

Let the required number be x.

Now,

$\frac{-2}{3}-x=\frac{-1}{6}$
$\Rightarrow \frac{-2}{3}-x+x=\frac{-1}{6}+x$ (Adding $x$ to both the sides)
$\Rightarrow \frac{-2}{3}=\frac{-1}{6}+x$
$\Rightarrow \frac{-2}{3}+\frac{1}{6}=\frac{-1}{6}+x+\frac{1}{6}$ (Adding $\frac{1}{6}$ to both the sides)
$\Rightarrow \left(\frac{-4}{6}+\frac{1}{6}\right)=x$
$\Rightarrow \left(\frac{-4+1}{6}\right)=x$
$$\begin{gathered} \Rightarrow \frac{-3}{6}=x \\ \Rightarrow \frac{-1\times 3}{2\times 3}=x \\ \Rightarrow \frac{-1}{2}=x \end{gathered}$$

Hence, the required number is$\frac{-1}{2}$.