When multiplying two numbers, reversing the order of the numbers in the equation results in the same product. This is known as the commutative property of multiplication and is quite similar to the associative property of addition. For example, multiplying three by six equals six times three (3 x 6 = 6 x 3 = 18). Expressed in algebraic terms, the commutative property is a x b = b x a, or simply ab = ba.
The associative property of multiplication may be viewed as an extension of the commutative property of multiplication and parallels the associative property of addition. When multiplying more than two numbers, changing the order in which the numbers are multiplied, or how they are grouped results in the same product. For instance, (3 x 4) x 2 = 12 x 2 = 24. Changing the order of multiplication to 3 x (4 x 2) produces 3 x 8 = 24. In algebraic terms, the associative property may be described as (a + b) + c = a + (b + c).
It may be helpful to remember the associative and commutative properties of addition in reference to the associative and commutative properties of multiplication. According to the commutative property of addition, two numbers added together results in the same sum whether they're added forwards or backwards. In other words, two plus six equals eight and six plus two also equals eight (2 + 6 = 6 + 2 = 8) and is reminiscent of the commutative property of multiplication. Again, this may be expressed algebraically as a + b = b + a.
In the associative property of addition, the order which more than three or more sets of numbers are added together does not change the sum of the numbers. Thus, (1 + 2) + 3 = 3 + 3 = 6. Just as in the associative property of multiplication, changing the order does not change the result since 1 + (2 + 3) = 1 + 5 = 6. Algebraically, the associative property of addition is (a + b) + c = a + (b + c).