What should be subtracted from $(\frac{3}{4}-\frac{2}{3})$ to get $\frac{−1}{6}$?

Given :

The given numbers are $(\frac{3}{4}-\frac{2}{3})$ and $\frac{-1}{6}$.

To do :

We have to find the number that should be subtracted from $(\frac{3}{4}-\frac{2}{3})$ to get $\frac{-1}{6}$.

Solution :

Let the number to be subtracted from $(\frac{3}{4}-\frac{2}{3})$ to get $\frac{-1}{6}$ be $x$.

This implies,

$(\frac{3}{4}-\frac{2}{3})-x=\frac{-1}{6}$

$x =(\frac{3}{4}-\frac{2}{3})-\frac{-1}{6}$

$x = \frac{[3(3)-4(2)]}{12}+\frac{1}{6}$

$x = \frac{(9-8)}{12}+\frac{1}{6}$

$x = \frac{1}{12}+\frac{1}{6}$

$x=\frac{1(1)+1(2)}{12}$

$x=\frac{3}{12}$

$x=\frac{1}{4}$

The number to be subtracted from $(\frac{3}{4}-\frac{2}{3})$ to get $\frac{-1}{6}$ is $\frac{1}{4}$.