Commutative property — lesson. Mathematics State Board, Class 8.

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A set of numbers is said to be commutative for a specific mathematical operation if the result obtained when changing the order of the operands does not change the result.

Rational Numbers:

i) Addition:

Changing the order of operands in addition to rational numbers, does not change the result. Hence, rational numbers under addition are commutative.

\frac{a}{b} + \frac{c}{d} = \frac{c}{d} + \frac{a}{b}

Example:

\frac{8}{5} + \frac{(- 2)}{5} = \frac{(- 2)}{5} + \frac{8}{5}

ii) Subtraction:

Changing the order of operands in the subtraction of rational numbers changes the result. Hence, rational numbers under subtraction are not commutative.

\frac{a}{b} - \frac{c}{d} \neq \frac{c}{d} - \frac{a}{b}

Example:

\frac{8}{5} - \frac{(- 2)}{5} \neq \frac{(- 2)}{5} - \frac{8}{5}

iii) Multiplication:

Changing the order of operands in the multiplication of rational numbers does not change the result. Hence, rational numbers under multiplication are commutative.

\frac{a}{b} \times \frac{c}{d} = \frac{c}{d} \times \frac{a}{b}

Example:

\frac{8}{5} \times \frac{(- 2)}{5} = \frac{(- 2)}{5} \times \frac{8}{5}

iv) Division:

Changing the order of operands in the division of rational numbers changes the result. Hence, rational numbers under division are not commutative.

\frac{a}{b} \div \frac{c}{d} \neq \frac{c}{d} \div \frac{a}{b}

Example:

\frac{4}{3} \div \frac{(- 2)}{7} \neq \frac{(- 2)}{7} \div \frac{4}{3}

Important!

Therefore for rational number addition, and multiplication operations only satisfy the commutative property, not the subtraction and division operations.

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3. Commutative property

Theory: