Definition. The commutative law of multiplication says that it doesn't matter what order you multiply variables or numbers. Let's see if this is true.

Multiply a five by a two and then vice versa by a two by a five.

5 × 2 = 10

2 × 5 = 10

In both cases you get the same result, so you can put an equal sign between the expressions 5 × 2 and 2 × 5 because they are equal to the same value:

5 × 2 = 2 × 5

10 = 10

Let's write down the commutative law of multiplication using variables:

a × b = b × a

It is not necessary to use the letters a and b to write laws as variables. Any other letters can be used, e.g. c and d or x and y. The same commutative law of multiplication can be written as follows:

x × y = y × x

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