Question

Simplify $\frac{2}{5}+\frac{3}{7}+\left(\frac{-6}{5}\right)+\left(\frac{-13}{7}\right)$

Answer 1

Rearrange the given fractions keeping similar fractions together.

$\frac{2}{5}+\frac{3}{7}+\left(\frac{-6}{5}\right)+\left(\frac{-13}{7}\right)$

$=\frac{2}{5}+\frac{3}{7}-\frac{6}{5}-\frac{13}{7}$

$=(\frac{2}{5}-\frac{6}{5})+(\frac{3}{7}-\frac{13}{7})$ (by commutative law of addition)

$=\frac{2-6}{5}+\frac{3-13}{7}$

$=\frac{-4}{5}+\frac{-10}{7}$

$=\frac{-4}{5}-\frac{10}{7}$

$=\frac{-4\times 7-10\times 5}{35}$ [L.C.M of $5$ and $7$ is $35$]

$=\frac{-28-50}{35}$

$=\frac{-78}{35}$

$=-2\frac{8}{35}$