Question

Find the number when the sum of $-\frac{2}{3}$ and its multiplicative inverse is divided by the difference of $-\frac{2}{3}$and its multiplicative inverse.

• A. $\frac{13}{5}$
• B. $\frac{5}{13}$
• C. $\frac{-5}{13}$
• D. $\frac{-13}{5}$

Answer 1

The correct option is D $\frac{-13}{5}$

The multiplicative inverse of $-\frac{2}{3}=-\frac{3}{2}$
Sum of these two:
$-\frac{2}{3}+(-\frac{3}{2})$
= $-\frac{2}{3}-\frac{3}{2}$
= $\left(\frac{-4-9}{6}\right)$
=$-\frac{13}{6}$
Difference of these two:
$-\frac{2}{3}-(-\frac{3}{2})$
= $-\frac{2}{3}+\frac{3}{2}$
= $\left(\frac{-4+9}{6}\right)$
=$\frac{5}{6}$
Now,
$-\frac{13}{6}÷\frac{5}{6}$
= $-\frac{13}{6}\times \frac{6}{5}$
=$-\frac{13}{5}$