Question

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

(iii) $\frac{-4}{5}and\frac{-13}{-15}$

Answer 1

Solving $\frac{-4}{5}+\frac{-13}{-15}$

$\frac{-4}{5}+\frac{-13}{-15}=\frac{-4\times 3}{5\times 3}+\frac{-13}{-15}$

(LCM of 5 and 15 is 15)

$=\frac{-12}{15}+\frac{13}{15}$

$=\frac{-12+13}{15}$

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

Solving $\frac{-13}{-15}+\frac{-4}{5}$

$\frac{13}{15}+\frac{-4}{5}=\frac{-13}{-15}+\frac{-4\times 3}{5\times 3}$

(LCM of 15 and 5 is 15)

$=\frac{-13}{-15}-\frac{12}{15}$

$=\frac{13-12}{15}$

$=\frac{1}{15}$ (equation 2)

From (1) and (2) , $\frac{-4}{5}+\frac{-13}{-15}=\frac{-13}{-15}+\frac{-4}{5}$

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