Question

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

• A. $14$
• B. $2$
• C. $0$
• D. $-1$

Answer 1

The correct option is D $-1$

Rearranging and grouping the numbers in pairs in such a way that each group contains a pair of rational numbers with same denominators, we have,
$=\frac{3}{5}+\frac{-7}{6}+\frac{2}{5}+\frac{-5}{6}$
$=\frac{3}{5}+(\frac{-7}{6}+\frac{2}{5})+\frac{-5}{6}$
$=\frac{3}{5}+(\frac{2}{5}+\frac{-7}{6})+\frac{-5}{6}$ [Since addition of rational numbers is commutative]
$=(\frac{3}{5}+\frac{2}{5})+(\frac{-7}{6}+\frac{-5}{6})$ [Since addition of rational numbers is associative]
$=\frac{3+2}{5}+\frac{(-7)+(-5)}{6}$
$=\frac{5}{5}+\frac{(-12)}{6}=1+(-2)$
$=-1$