Question

The value of $\frac{3}{5}+\frac{-7}{6}+\frac{2}{5}+\frac{-5}{6}$ is_____________.

• A. $14$
• B. $0$
• C. $2$
• D. $-1$

Answer 1

The correct option is D $-1$

When we rearrange and group the numbers in pairs in such a way that each group contains a pair of rational numbers with the same denominators, we get

$\frac{3}{5}+\frac{-7}{6}+\frac{2}{5}+\frac{-5}{6}$
$=(\frac{3}{5}+\frac{2}{5})+(\frac{-7}{6}+\frac{-5}{6})$ [addition of rational numbers is commutative]

$=\left(\frac{3+2}{5}\right)+\left(\frac{-7+(-5)}{6}\right)$
$=\left(\frac{5}{5}\right)+\left(\frac{-7-5}{6}\right)$
$=1+\frac{-12}{6}$
$=1+(-2)$
$=1-2$
$=-1$