Question

Add and express the sum as a mixed fraction:

$\left(iii\right)$ $\frac{-31}{6}$ and $\frac{-27}{8}$

Answer 1

Given: $\frac{-31}{6}$ and $\frac{-27}{8}$

$\text{LCM}$ of denominators $6$ and $8=24$

$\therefore \frac{-31}{6}+\frac{-27}{8}=\frac{-31\times 4}{6\times 4}+\frac{-27\times 3}{8\times 3}$

$=\frac{-124}{24}+\frac{-81}{24}$

$=\frac{-124+(-81)}{24}$

$=\frac{-124-81}{24}$

$=\frac{-205}{24}$

$=-8\frac{13}{24}$

Hence, the required sum is $-8\frac{13}{24}.$