Question

Verify whether commutative property is satisfied for addition, subtraction, multiplication and division of the following pairs of rational numbers.
(i) $4$ and $\frac{2}{5}$
(ii) $\frac{-3}{7}$ and $\frac{-2}{7}$

Answer 1

(i)Addition

$4+\frac{2}{5}=\frac{20+2}{5}=\frac{22}{5}$

$\frac{2}{5}+4=\frac{2+20}{5}=\frac{22}{5}$

Commutative property is satisfied.

Subtraction

$4-\frac{2}{5}=\frac{20-2}{5}=\frac{18}{5}$

$\frac{2}{5}-4=\frac{2-20}{5}=\frac{-18}{5}$

Commutative property is not satisfied.

Multiplication

$\frac{2}{5}\times 4=\frac{8}{5}$

$4\times \frac{2}{5}=\frac{8}{5}$

Commutative property is satisfied.

Division

$4÷\frac{2}{5}=4\times \frac{5}{2}=\frac{20}{2}$

$\frac{2}{5}÷4=\frac{2}{5}\times \frac{1}{4}=\frac{2}{20}$

Commutative property is not satisfied.

(ii)Addition

$\frac{-3}{7}+\left(\frac{-2}{7}\right)=\frac{-3-2}{7}=\frac{-5}{7}$

$\frac{-2}{7}+\left(\frac{-3}{7}\right)=\frac{-2-3}{7}=\frac{-5}{7}$

Commutative property is satisfied.

Subtraction

$\frac{-3}{7}-\left(\frac{-2}{7}\right)=\frac{-3+2}{7}=\frac{-1}{7}$

$\frac{-2}{7}-\left(\frac{-3}{7}\right)=\frac{-2+3}{7}=\frac{1}{7}$

Commutative property is not satisfied.

Multiplication

$\frac{-2}{7}\times \frac{-3}{7}=\frac{6}{7}$

$\frac{-3}{7}\times \frac{-2}{7}=\frac{6}{7}$

Commutative property is satisfied.

Division

$\frac{-3}{7}÷\frac{-2}{7}=\frac{-3}{7}\times \frac{7}{-2}=\frac{3}{2}$

$\frac{-2}{7}÷\frac{-3}{7}=\frac{-2}{7}\times \frac{7}{-3}=\frac{2}{3}$

Commutative property is not satisfied.