Different Types of Properties
Associative Property
Definition - Changing the grouping of factors or addends in an equation does not change the outcome.
Examples - (a + b) + c = a + (b + c)
(3 + 4) + 2 = 3 + (4 + 2)
7 + 2 = 3 + 6
9 = 9
(3 x 4) x 2 = 3 x (4 x 2)
12 x 2 = 3 x 8
24 = 24
The outcome is the same on both sides of the equal sign.
Commutative Property
Definition - Changing the order of factors or addends in an equation does not change the outcome.
Example - a + b = b + a
a x b = b x a
3 + 4 = 4 + 3
7 = 7
3 x 4 = 4 x 3
12 = 12
Distributive Property
Definition - When a number is multiplied by the total of two other numbers, the first number can be multiplied by each number in the parentheses separately.
Example - a x (b + c) = (a x b) + (a x c)
5 x (2 + 3) = (5 x 2) + (5 x 3)
5 x 5 = 10 + 15
25 = 25
2 x (4 + 7) = (2 x 4) + (2 x 7)
2 x 11 = 8 + 14
22 = 22
The outcome is always the same on both sides of the equal sign.
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