Question

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

(i) $\frac{-11}{5}\text{and}\frac{4}{7}$

Answer 1

Given: $\frac{-11}{5}\text{and}\frac{4}{7}$

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

$\therefore \frac{-11}{5}+\frac{4}{7}=\frac{-11\times 7}{5\times 7}+\frac{4\times 5}{7\times 5}$
$=\frac{-77}{35}+\frac{20}{35}$
$=\frac{-77+20}{35}$
$=\frac{-57}{35}$
and
$\therefore \frac{4}{7}+\frac{-11}{5}=\frac{4\times 5}{7\times 5}+\frac{-11\times 7}{5\times 7}$
$=\frac{20}{35}+\frac{-77}{35}$
$=\frac{20-77}{35}$
$=\frac{-57}{35}$
Thus,$\frac{-11}{5}+\frac{4}{7}=\frac{4}{7}+\frac{-11}{5}$

Hence, commutativity of addition is verified.