Question

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

(v) $4\text{and}\frac{-3}{5}$

Answer 1

Given: $4\text{and}\frac{-3}{5}$

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

$\therefore 4+\frac{-3}{5}=\frac{4}{1}+\frac{-3}{5}$
$=\frac{4\times 5}{1\times 5}+\frac{-3}{5}$
$=\frac{20}{5}+\frac{-3}{5}$
$=\frac{20-3}{5}$
$=\frac{17}{5}$

and $\frac{-3}{5}+4=\frac{-3}{5}+\frac{4}{1}$
$=\frac{-3}{5}+\frac{4\times 5}{1\times 5}$
$=\frac{-3}{5}+\frac{20}{5}$
$=\frac{-3+20}{5}$
$=\frac{17}{5}$

Thus, $4+\frac{-3}{5}=\frac{-3}{5}+4$

Hence, commutativity of addition is verified.