Question:
Tick (✓) the correct answer
What should be added to $\frac{-5}{7}$ to get $\frac{-2}{3} ?$
(a) $\frac{-29}{21}$
(b) $\frac{29}{21}$
(c) $\frac{1}{21}$
(d) $\frac{-1}{21}$
Solution:
(c) $\frac{1}{21}$
Let the required number be x.
Now,
$\frac{-5}{7}+x=\frac{-2}{3}$
$\Rightarrow x=\frac{-2}{3}+\left(\right.$ Additive inverse of $\left.\frac{-5}{7}\right)$
$\Rightarrow x=\left(\frac{-2}{3}+\frac{5}{7}\right)$
$=\frac{(-14)+15}{21}$
$=\frac{1}{21}$