Question

Add the following rational numbers:​

(ii) $\frac{5}{-9}\text{and}\frac{7}{3}$

Answer 1

Given : $\frac{5}{-9}\text{and}\frac{7}{3}$

$\therefore \frac{5}{-9}+\frac{7}{3}=\frac{-5}{9}+\frac{7}{3}$
LCM of denominators $9\text{and}3=9$
Expressing each of the given rational number with $9$ as common denominator

$\Rightarrow \frac{7}{3}=\frac{7\times 3}{3\times 3}=\frac{21}{9}$
Now, $\frac{-5}{9}+\frac{7}{3}=\frac{-5}{9}+\frac{21}{9}$
$=\frac{-5+21}{9}$
$=\frac{16}{9}$

Hence, the sum of $\frac{5}{-9}\text{and}\frac{7}{3}$ is $\frac{16}{9}$.