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Commutative property of Multiplication


$a \times b \,=\, b \times a$

The product of two quantities equals to their product in reverse order is called the commutative property of multiplication.


Let $a$ and $b$ be two operands in algebraic form and their product is written in mathematical form as $a.b$. Now, multiply them in reverse order and the product of them is expressed as $b.a$ simply. Mathematically, the two expressions in product form are equal and it is called as the commutative law of multiplication.


$4$ and $5$ are two quantities. Multiply $4$ by $5$ to obtain product of them.

$\implies$ $4 \times 5 = 20$

Similarly, multiply the number $5$ by the number $4$.

$\implies$ $5 \times 4 = 20$

$\,\,\, \therefore \,\,\,\,\,\,$ $4 \times 5$ $\,=\,$ $5 \times 4$ $\,=\,$ $20$

In this way, the commutative rule of multiplication is verified in numerical system.


Learn how to derive the commutative law of multiplication in algebraic form by geometrical approach.

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