Question

For each pair of rational numbers, verify commutative property of addition of rational numbers:

(iv) $\frac{2}{-5}and\frac{11}{-15}$

Answer 1

Solving $\frac{2}{-5}+\frac{11}{-15}$

$\frac{2}{-5}+\frac{11}{-15}=\frac{2\times 3}{-5\times 3}+\frac{11}{-15}$

(LCM of 5 and 15 is 15)

$=\frac{-6}{15}-\frac{11}{15}$

$=\frac{-6-11}{15}$

$=\frac{-17}{15}$ (equation 1)

Solving $\frac{11}{-15}+\frac{2}{-5}$

$\frac{11}{-15}+\frac{2}{-5}=\frac{11}{-15}+\frac{-2\times 3}{-5\times 3}$

(LCM of 15 and 5 is 15)

$=-\frac{11}{15}-\frac{6}{15}$

$=\frac{-11-6}{15}$

$=\frac{-17}{15}$ (equation 2)

From (1) and (2), $\frac{2}{-5}+\frac{11}{-15}=\frac{11}{-15}+\frac{2}{-5}$

Hence, commutative property of addition of rational numbers is verified.