Question

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

i ) $\frac{2}{5}+\frac{7}{3}+\frac{-4}{5}+\frac{-1}{3}$

Answer 1

Given: $\frac{2}{5}+\frac{7}{3}+\frac{-4}{5}+\frac{-1}{3}$
Grouping the given rational numbers with the same denominators together,
$\therefore \frac{2}{5}+\frac{7}{3}+\frac{-4}{5}+\frac{-1}{3}=(\frac{2}{5}+\frac{-4}{5})+(\frac{7}{3}+\frac{-1}{3})$
$=\left(\frac{2-4}{5}\right)+\left(\frac{7-1}{3}\right)$
$=\frac{-2}{5}+\frac{6}{3}$
$=\frac{-2\times 3}{5\times 3}+\frac{6\times 5}{3\times 5}$
$=\frac{-6}{15}+\frac{30}{15}$
$=\frac{-6+30}{15}$
$=\frac{24}{15}$
$=\frac{8}{5}$

Hence, $\frac{2}{5}+\frac{7}{3}+\frac{-4}{5}+\frac{-1}{3}=\frac{8}{5}$