Question

Add the following rational numbers:

viii. $\frac{7}{-18}\text{and}\frac{8}{27}$

Answer 1

Given: $\frac{7}{-18}\text{and}\frac{8}{27}$

$\therefore \frac{7}{-18}+\frac{8}{27}=\frac{-7}{18}+\frac{8}{27}$

$\text{LCM of denominators 18 and 27}=54$

Expressing each ofthe given rational number with $54$ as comon denominator

$\Rightarrow \frac{-7}{18}=\frac{-7\times 3}{18\times 3}=\frac{-21}{54}$

$\text{and}\frac{8}{27}=\frac{8\times 2}{27\times 2}=\frac{16}{54}$

$\text{Now},\frac{-7}{18}+\frac{8}{27}=\frac{-21}{54}+\frac{16}{54}$

$=\frac{-21+16}{54}$

$=\frac{-5}{54}$

Hence, the sum of $\frac{7}{-18}\text{and}\frac{8}{27}\text{is}\frac{-5}{54}$.