Question

For each set of rational numbers given below, verify the associative property of addition of rational numbers:

(iv) $-1,\frac{5}{6},-\frac{-2}{3}$

Answer 1

Solving $-1+(\frac{5}{6}+\frac{-2}{3})$

$-1+(\frac{5}{6}+-\frac{-2}{3})=-1+(\frac{5}{6}-\frac{2\times 2}{3\times 2})$

(LCM of 6 and 3 is 6)

$=-1+(\frac{5}{6}-\frac{4}{6})$

$=-1+\frac{5-4}{6}$

$=-1+\frac{1}{6}$

$=-\frac{1\times 6}{1\times 6}+\frac{1}{6}$

(LCM of 1 and 6 is 6)

$=-\frac{6}{6}+\frac{1}{6}$

$=\frac{-6+1}{6}$

$=-\frac{5}{6}$ (equation 1)

Solving $(-1+\frac{5}{6})+\frac{-2}{3}$

$(-1+\frac{5}{6})+\frac{-2}{3}=(\frac{-1\times 6}{1\times 6}+\frac{5}{6})-\frac{2}{3}$

(LCM of 1 and 6 is 6)

$=(\frac{-6}{6}+\frac{5}{6})-\frac{2}{3}$

$=\frac{-6+5}{6}-\frac{2}{3}$

$=-\frac{1}{6}-\frac{2\times 2}{3\times 2}$

(LCM of 6 and 3 is 6)

$=-\frac{1}{6}-\frac{4}{6}$

$=\frac{-1-4}{6}$

$=-\frac{5}{6}$ (equation 2)

From (1) and (2),$-1+(\frac{5}{6}+\frac{-2}{3})=(-1+\frac{5}{6})+\frac{-2}{3}$

Hence, the associative property of addition of rational numbers is verified.