Question

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

(ii) $\frac{4}{9}\text{and}\frac{7}{-12}$

Answer 1

Given: $\frac{4}{9}\text{and}\frac{7}{-12}$

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

$\therefore \frac{4}{9}+\frac{7}{-12}=\frac{4}{9}+\frac{-7}{12}$
$=\frac{4\times 4}{9\times 4}+\frac{-7\times 3}{12\times 3}$
$=\frac{16}{36}+\frac{-21}{36}$
$=\frac{16-21}{36}$
$=\frac{-5}{36}$
and

$\therefore \frac{7}{-12}+\frac{4}{9}=\frac{-7\times 3}{12\times 3}+\frac{4\times 4}{9\times 4}$
$=\frac{-21}{36}+\frac{16}{36}$
$=\frac{-21+16}{36}$
$=\frac{-5}{36}$

Thus,$\frac{4}{9}+\frac{7}{-12}=\frac{7}{-12}+\frac{4}{9}$

Hence, commutativity of addition is verified.