Question

Tick (✓) the correct answer
What should be added to $\frac{-5}{7}\mathrm{to}\mathrm{get}\frac{-2}{3}?$
(a) $\frac{-29}{21}$
(b) $\frac{29}{21}$
(c) $\frac{1}{21}$
(d) $\frac{-1}{21}$

Answer 1

(c) $\frac{1}{21}$
Let the required number be x.

Now,

$\frac{-5}{7}+x=\frac{-2}{3}$
$$\begin{gathered} \Rightarrow x=\frac{-2}{3}+\left(\mathrm{Additive}\mathrm{inverse}\mathrm{of}\frac{-5}{7}\right) \\ \Rightarrow x=\left(\frac{-2}{3}+\frac{5}{7}\right) \end{gathered}$$
$$\begin{gathered} =\frac{\left(-14\right)+15}{21} \\ =\frac{1}{21} \end{gathered}$$