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. [5 marks]

Answer 1

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

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

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