Question

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

vi. $-4\text{and}\frac{4}{-7}$

Answer 1

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

Commutativity of addition : Addition of two rational numbers $\frac{a}{b}\text{and}\frac{c}{d}$ is commutative if $\frac{a}{b}+\frac{c}{d}=\frac{c}{d}+\frac{a}{b}$
$\therefore -4+\frac{4}{-7}=\frac{-4}{1}+\frac{-4}{7}$
$=\frac{-4\times 7}{1\times 7}+\frac{-4}{7}$
$=\frac{-28}{7}+\frac{-4}{7}$
$=\frac{-28-4}{7}$
$=\frac{-32}{7}$

and $\frac{4}{-7}+(-4)=\frac{-4}{7}+\frac{-4}{1}$
$=\frac{-4}{7}+\frac{-4\times 7}{1\times 7}$
$=\frac{-4}{7}+\frac{-28}{7}$
$=\frac{-28-4}{7}$
$=\frac{-32}{7}$
Thus, $-4+\frac{4}{-7}=\frac{4}{-7}+(-4)$

Hence, commutativity of addition is verified.