Commutative Property:
Change Order – The order doesn’t matter; you will get the same answer.
Commutative of Addition: 4 + 5 = 5+4
Commutative of Multiplication: (6)(7) = (7)(6)
Associative Property:
Grouping Changes – The parenthesis will move but you will get the same answer
Associative of Addition: (4 + 6) + 5 = 4+ (6 + 5)
Associative of Multiplication: (4 x 2) x 3 = 4 x (2 x 3)
Additive Identity Property:
Any # plus 0 equals the original number.
Example: -5 + 0 = -5
Multiplicative Identity Property:
Any number multiplied by 1 equals the original number
Example: 7 x 1 = 7
Multiplicative Inverse:
Any number multiplied by its reciprocal equals 1.
Example: 2 x ½ = 1
Additive Inverse Property:
Any number plus its opposite equals 0.
Example: -5 + 5 = 0
Multiplicative Property of Zero:
Any number multiplied by 0 equals 0
Example: -23 x 0 = 0
Extra Credit Problems:
Identify the property shown by each example.
1. 4 + 5 + 6 = 6 + 4 + 5
2. a(0) = 0
3. 2 (½) = 1
4. (a)(d)=(d)(a)
5. (8+2)+4 = 8+(2+4)
6. 8(1) = 8
7. 42 – 6a = 6(7-a)
8. a + 0 = a
Change Order – The order doesn’t matter; you will get the same answer.
Commutative of Addition: 4 + 5 = 5+4
Commutative of Multiplication: (6)(7) = (7)(6)
Associative Property:
Grouping Changes – The parenthesis will move but you will get the same answer
Associative of Addition: (4 + 6) + 5 = 4+ (6 + 5)
Associative of Multiplication: (4 x 2) x 3 = 4 x (2 x 3)
Additive Identity Property:
Any # plus 0 equals the original number.
Example: -5 + 0 = -5
Multiplicative Identity Property:
Any number multiplied by 1 equals the original number
Example: 7 x 1 = 7
Multiplicative Inverse:
Any number multiplied by its reciprocal equals 1.
Example: 2 x ½ = 1
Additive Inverse Property:
Any number plus its opposite equals 0.
Example: -5 + 5 = 0
Multiplicative Property of Zero:
Any number multiplied by 0 equals 0
Example: -23 x 0 = 0
Extra Credit Problems:
Identify the property shown by each example.
1. 4 + 5 + 6 = 6 + 4 + 5
2. a(0) = 0
3. 2 (½) = 1
4. (a)(d)=(d)(a)
5. (8+2)+4 = 8+(2+4)
6. 8(1) = 8
7. 42 – 6a = 6(7-a)
8. a + 0 = a