Question

Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers:

(iii) $\frac{-3}{5}\text{and}\frac{-2}{-15}$

Answer 1

Given: $\frac{-3}{5}\text{and}\frac{-2}{-15}$

Commutativity of addition: Addition of two rational numbers $\frac{a}{b}$ and $\frac{c}{d}$ is commutative if $\frac{a}{b}+\frac{c}{d}=\frac{c}{d}+\frac{a}{b}$

$\therefore \frac{-3}{5}+\frac{-2}{-15}=\frac{-3}{5}+\frac{2}{15}$
$=\frac{-3\times 3}{5\times 3}+\frac{-2}{15}$
$=\frac{-9}{15}+\frac{2}{15}$
$=\frac{-9+2}{15}$
$=\frac{-7}{15}$

and $\frac{-2}{-15}+\frac{-3}{5}=\frac{2}{15}+\frac{-3\times 3}{5\times 3}$
$=\frac{2}{15}+\frac{-9}{15}$
$=\frac{2-9}{15}$
$=\frac{-7}{15}$
Thus,$\frac{-3}{5}+\frac{-2}{-15}=\frac{-2}{-15}+\frac{-3}{5}$

Hence, commutativity of addition is verified.