Question

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

(v) $3and\frac{-2}{7}$

Answer 1

Solving $3+\frac{-2}{7}$

$3+\frac{-2}{7}=\frac{3\times 7}{1\times 7}+\frac{-2}{7}$ (LCM of 1 and 7 is 7)

$=\frac{21}{7}-\frac{2}{7}$

$=\frac{21-2}{7}$

$=\frac{19}{7}$ (equation 1)

Solving $\frac{-2}{7}+3$

$\frac{-2}{7}+3=\frac{-2}{7}+\frac{3\times 7}{1\times 7}$ (LCM of 7 and 1 is 7)

$=\frac{-2}{7}+\frac{21}{7}$

$=\frac{-2+21}{7}$

$=\frac{19}{7}$ (equation 2)

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

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