Question

Rearrange suitable and find the sum in each of the following:

iii) $\frac{3}{5}+\frac{7}{3}+\frac{9}{5}+\frac{-13}{15}+\frac{-7}{3}$

Answer 1

Given: $\frac{3}{5}+\frac{7}{3}+\frac{9}{5}+\frac{-13}{15}+\frac{-7}{3}$

$\therefore \frac{3}{5}+\frac{7}{3}+\frac{9}{5}+\frac{-13}{15}+\frac{-7}{3}$
$=\frac{-13}{15}+(\frac{3}{5}+\frac{9}{5})+(\frac{7}{3}+\frac{-7}{3})$
$=\frac{-13}{15}+\left(\frac{3+9}{5}\right)+\left(\frac{7-7}{3}\right)$
$=\frac{-13}{15}+\left(\frac{12}{5}\right)+0$
$=\frac{-13}{15}+\frac{12\times 3}{5\times 3}$
$=\frac{-13}{15}+\frac{36}{15}$
$=\frac{-13+36}{15}$
$=\frac{23}{15}$

Hence, $\frac{3}{5}+\frac{7}{3}+\frac{9}{5}+\frac{-13}{15}+\frac{-7}{3}=\frac{23}{15}$