Properties of Operations

You probably use properties of operations every day without even giving them a thought. You may have noticed that 3 x 4 and 4 x 3 are both 12. That”s an example of the commutative property of multiplication. The ideas are probably familiar – you just need to brush up on the vocabulary.





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The associative and commutative properties hold for both addition and multiplication.

Associative property of addition – when three or more numbers are added, the way the numbers are grouped does not change the sum.

(2 + 3) + 4 = 2 + (3 + 4)
5 + 4 = 2 + 7
9=9

Associative property of multiplication – when three or more numbers are multiplied, the way the numbers are grouped does not change the product.

(2 x 3) x 4 = 2 x (3 x 4)
6 x 4 = 2 x 12
24 = 24

Commutative property of addition – When two or more numbers are added, the order of the numbers does not change the sum.

2 + 5 = 5 + 2
7 = 7

Commutative property of multiplication – When two or more numbers are multiplied, the order of the numbers does not change the product.

2 x 5 = 5 x 2
10 = 10

Distributive property of multiplication over addition
The product of a number and a sum may be expressed as the sum of two products

3 x (1 + 4) = (3 x 1) + (3 x 4)
3 x 5 = 3 + 12
15 = 15

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