UPSKILL MATH PLUS

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### Theory:

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:

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

$\frac{a}{b}-\frac{c}{d}\phantom{\rule{0.147em}{0ex}}\ne \phantom{\rule{0.147em}{0ex}}\frac{c}{d}-\frac{a}{b}$.
Example:
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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.

$\frac{a}{b}×\frac{c}{d}=\frac{c}{d}×\frac{a}{b}$.
Example:
iv) Division:
Changing the order of operands in the division of rational numbers changes the result. Hence, rational numbers under division are not commutative.

$\frac{a}{b}÷\frac{c}{d}\phantom{\rule{0.147em}{0ex}}\ne \phantom{\rule{0.147em}{0ex}}\frac{c}{d}÷\frac{a}{b}$.
Example:
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Important!
Therefore for rational number addition, and multiplication operations only satisfy the commutative property, not the subtraction and division operations.