Mark (✓) against the correct answer
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 x.

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 $\left.\frac{2}{3}\right)$

$\Rightarrow x=\frac{-3}{4}+\left(\frac{-2}{3}\right)$

$\Rightarrow x=\frac{-3}{4}+\frac{-2}{3} \Rightarrow$

$\Rightarrow x=\frac{-3 \times 3}{4 \times 3}+\frac{-2 \times 4}{3 \times 4}$

$\Rightarrow x \frac{-9}{12}+\frac{-8}{12}$

$\Rightarrow x=\frac{-17}{12}$