Question

A is the additive inverse of $\frac{5}{7}$ and B is the multiplicative inverse of $\frac{-8}{9}$. Find the multiplicative inverse of A + B.

Answer 1

Additive inverse of A = $-\left(\frac{5}{7}\right)=\frac{-5}{7}$
Multiplicative inverse of B = $\frac{1}{\left(\frac{-8}{9}\right)}=\frac{-9}{8}$

$A+B=\frac{-5}{7}+\left(\frac{-9}{8}\right)=\frac{(-5\times 8)+(-9\times 7)}{7\times 8}=\frac{-40-63}{56}=\frac{-103}{56}$

Multiplicative inverse of A + B is $\frac{1}{\left(\frac{-103}{56}\right)}=\frac{-56}{103}$