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Term
Definition
You can add numbers in a sum in any order
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
3+4+5=5+4+3
You can multiply numbers in a product
in any order
(2 + 3)(4 + 5) = (4 + 5)(2 +3)
Changing the grouping of numbers will not
change their sum
(2 + 3) + 4 = 2 + (3 + 4)
Associative Property of Multiplication
Changing the grouping of numbers will not
change their product
(2 • 3)4 = 2(3 • 4)
The sum of a number and 0 is the number
Additive Identity Property
8+0=8
The product of a number and 1 is the number
Multiplicative Identity Property
Additive Inverse Property
10 • 1 = 10
1 4  4
 
2 4  8
The sum of a number and its opposite
(additive inverse) is 0

–5 + 5 = 0
7 + (–7) = 0
The product of a number and its multiplicative
inverse is 1
Multiplicative Inverse Property
4•
1
1
4
2 3
• 1
3 2
To multiply a sum or difference, the outside
number says, “Hi” to everyone inside.


Distributive Property
3(2x + 2) = 6x + 6
4(100 + 5) = 400 + 20
6x + 6y = 6(x + y)
5x – 5y = 5(x – y)