Question

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

(iii) $\frac{-7}{9},\frac{2}{-3}and\frac{-5}{18}$

Answer 1

Solving $\frac{-7}{9}+(\frac{2}{-3}+\frac{-5}{18})$

$-\frac{7}{9}+(\frac{2}{-3}+\frac{-5}{18})=-\frac{7}{9}+(\frac{2\times 6}{-3\times 6}+\frac{-5}{18})$

(LCM of 3 and 18 is 18)

$=-\frac{7}{9}+(\frac{-12}{18}-\frac{5}{18})$

$=-\frac{7}{9}+\frac{-12-5}{18}$

$=-\frac{7}{9}-\frac{17}{18}$

$=-\frac{7\times 2}{9\times 2}-\frac{17}{18}$

(LCM of 9 and 18 is 18)

$=-\frac{14}{18}-\frac{17}{18}$

$=\frac{-14-17}{18}$

$=-\frac{-31}{18}$ (equation 1)

Solving $(\frac{-7}{9}+\frac{2}{-3})+\frac{-5}{18}$

$(\frac{-7}{9}+\frac{2}{-3})+\frac{-5}{18}=(\frac{-7}{9}-\frac{2\times 3}{3\times 3})+\frac{-5}{18}$

(LCM of 9 and 3 is 3)

$=(-\frac{7}{9}-\frac{6}{9})-\frac{5}{18}$

$=\frac{-7-6}{9}-\frac{5}{18}$

$=\frac{-13}{9}-\frac{5}{18}$

$=-\frac{13\times 2}{9\times 2}-\frac{5}{18}$

(LCM of 9 and 18 is 18)

$=-\frac{26}{18}-\frac{5}{18}$

$=\frac{-26-5}{18}$

$=-\frac{31}{18}$ (equation 2)

From (1) and (2), $-\frac{7}{9}+(\frac{2}{-3}+\frac{-5}{18})=(\frac{-7}{9}+\frac{2}{-3})+\frac{-5}{18}$


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