Question

Add the following rational numbers:​

(iv) $\frac{-7}{27}\text{and}\frac{11}{8}$

Answer 1

Given :$\frac{-7}{27}\text{and}\frac{11}{8}$

$\therefore$ LCM of denominators $27$ and $18=54$
Expressing each of the given rational number with $54$ as common denominator
$\Rightarrow \frac{-7}{27}=\frac{-7\times 2}{27\times 2}=\frac{-14}{54}$

and $\frac{11}{18}=\frac{11\times 3}{18\times 3}=\frac{33}{54}$


Now, $\frac{-7}{27}+\frac{11}{18}=\frac{-14}{54}+\frac{33}{54}$

$=\frac{-14+33}{54}$
$=\frac{19}{54}$

Hence, the sum of $\frac{-7}{27}\text{and}\frac{11}{8}$ is $\frac{19}{54}$