Question:
Mark (✓) against the correct answer
What should be subtracted from $\frac{-2}{3}$ to get $\frac{3}{4} ?$
(a) $\frac{-11}{12}$
(b) $\frac{-13}{12}$
(c) $\frac{-5}{4}$
(d) $\frac{-17}{12}$
Solution:
(d) $\frac{-17}{12}$
Let the number be
Now,
$\frac{-2}{3}-x=\frac{3}{4}$
$\Rightarrow-1 \times\left(\frac{2}{3}+x\right)=\frac{3}{4}$
$\Rightarrow \frac{2}{3}+x=\frac{-3}{4}$
$\Rightarrow x=\frac{-3}{4}+\left(\right.$ Additive inverse of $\left.\frac{2}{3}\right)$
$\Rightarrow x=\frac{-3}{4}+\left(\frac{-2}{3}\right)$
$\Rightarrow x=\frac{-3}{4}+\frac{-2}{3} \Rightarrow$
$\Rightarrow x=\frac{-3 \times 3}{4 \times 3}+\frac{-2 \times 4}{3 \times 4}$
$\Rightarrow x \frac{-9}{12}+\frac{-8}{12}$
$\Rightarrow x=\frac{-17}{12}$