Question

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

(ii) $\frac{5}{9}and\frac{5}{-12}$

Answer 1

Solving $\frac{5}{9}+\frac{5}{-12}$

$\frac{5}{9}+\frac{5}{-12}=\frac{5\times 4}{9\times 4}+\frac{5\times 3}{-12\times 3}$

(LCM of 9 and 12 is 36)

$=\frac{20}{36}-\frac{15}{36}$

$=\frac{20-15}{36}$

$=\frac{5}{36}$ (equation 1)

Solving $\frac{5}{-12}+\frac{5}{9}$

$\frac{5}{-12}+\frac{5}{9}=\frac{5\times 3}{-12\times 3}+\frac{5\times 4}{9\times 4}$

(LCM of 12 and 9 is 36)

$=\frac{-15}{36}+\frac{20}{36}$

$=\frac{-15+20}{36}$

$=\frac{5}{36}$ (equation 2)

From (1) and (2), $\frac{5}{9}+\frac{5}{-12}=\frac{5}{-12}+\frac{5}{9}$

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