Question

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

(vi) $-2and\frac{3}{-5}$

Answer 1

Solving $-2+\frac{3}{-5}$

$-2+\frac{3}{-5}=\frac{-2\times 5}{1\times 5}+\frac{3}{-5}$

(LCM of 1 and 5 is 5)

$=\frac{-10}{5}-\frac{3}{5}$

$=\frac{-10-3}{5}$

$=\frac{-13}{5}$ (equation 1)

Solving $\frac{3}{-5}+(-2)$

$\frac{3}{-5}+(-2)=\frac{3}{-5}+\frac{-2\times 5}{1\times 5}$

(LCM of 5 and 1 is 5)

$=\frac{-3}{5}+\frac{10}{5}$

$=\frac{-3-10}{5}$

$=\frac{-13}{5}$ (equation 2)

From (1) and (2), $-2+\frac{3}{-5}=\frac{3}{-5}+(-2)$

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