Question

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

(i) $\frac{-8}{7}and\frac{5}{14}$

Answer 1

Solving $\frac{-8}{7}+\frac{5}{14}$

$\frac{-8}{7}+\frac{5}{14}=\frac{-8\times 2}{7\times 2}+\frac{5}{14}$ (LCM of 7 and 14 is 14)

$=\frac{-16}{14}+\frac{5}{14}$

$=\frac{-16+5}{14}$

$=-\frac{11}{14}$ (equation 1)

Solving $\frac{5}{14}+\frac{-8}{7}$

$\frac{5}{14}+\frac{-8}{7}=\frac{5}{14}+\frac{-8\times 2}{7\times 2}$ (LCM of 7 and 14 is 14)

$=\frac{5}{14}+\frac{-16}{14}$

$=\frac{5-16}{14}$

$=-\frac{11}{14}$ (equation 2)

From (1) and (2), $\frac{-8}{7}+\frac{5}{14}=\frac{5}{14}+\frac{-8}{7}$

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