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Helpful Hints to Remember Properties
Additive = Addition
Multiplicative = Multiplication
***These are NOT properties*** These SPECIFY the operation
Commutative: The ORDER changes
Example: 3 + 4 = 4 + 3 Commutative of addition
Example: 3 x 4 = 4 x 3 Commutative of multiplication
Associative: the GROUPING changes
Example: (3 + 4) + 5 = 3 + (4 + 5) Associative of addition
Example: (3 x 4) x 5 = 3 x (4 x 5) Associative of multiplication
Identity: the number is the answer
Example: 3 + 0 = 3 Additive Identity
Example: 3 x 1 = 3 Multiplicative Identity
Property of Zero: ONLY multiplication; multiplying a number by “0”
Example: 3 x 0 = 0
Reflective: the order does not change
Example: 10 + 2 + 3 = 10 + 2 + 3
Symmetric Property: If and Then
Example: If 2+5=7 then 5+2=7
Transitive: Similar to Commutative; IF, AND,THEN will be in the
problem; Should see what the answer is
Example: If 15 + 2 = 17, then 17 = 2 + 15
Substitution: a REPLACEMENT of a number occurs
Example: 56 – 34 = 56 – (22 + 12) we replaced 22+12 with 34
Distributive: MULTIPLYING a number to many numbers
Example: 10(5x+2) = 50x + 20
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