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Properties Statements that are true for any number of variables. Multiplicative Property of Zero What do you multiply a number by to get zero? a • 0 = 0 (If you multiply by 0, the answer is 0.) Commutative Property Commutative means that the order does not make any difference. a + b = b + a a • b = b • a Examples 4 + 5 = 5 + 4 2 • 3 = 3 • 2 The commutative property does not work for subtraction or division. Associative Property Associative means that the grouping does not make any difference. (a + b) + c = a + (b + c) (ab) c = a (bc) Examples (1 + 2) + 3 = 1 + (2 + 3) (2 • 3) • 4 = 2 • (3 • 4) The associative property does not work for subtraction or division.
**Distributive Property Identity Properties
- Additive Identity** What do you add to a number to get the same number? a + 0 = a 2) Multiplicative Identity What do you multiply a number by to get the same number? a • 1 = a **Inverse Properties
- Additive Inverse (Opposite)** a + (-a) = 0 2) Multiplicative Inverse (Reciprocal) a 1 a 1 Name the property
- 5a + (6 + 2a) = 5a + (2a + 6) commutative (switching order)
- 5a + (2a + 6) = (5a + 2a) + 6 associative (switching groups)
- 2(3 + a) = 6 + 2a distributive
Commutative Property Commutative Property of Multiplicationof Multiplication
17 + (-17) = 0 Inverse Property ofInverse Property of Addition Addition 6.6. 2(5) = 5(2) Commutative Property Commutative Property of Multiplicationof Multiplication
3(2 + 5) = 3•2 + 3• 5 Distributive Property Distributive Property 9.9.
Associative Property of Associative Property of Multiplication Multiplication 10.10. 5 • 1 = 5 Identity Property ofIdentity Property of MultiplicationMultiplication 11.11. (6 – 3)4 = 6• 4 – 3 • 4 Distributive Property Distributive Property 13.13.
Identity Property of Identity Property of Addition Addition 18.18. 3 • 7 – 3 • 4 = 3(7 – 4) Distributive Property Distributive Property 19.19. 6 + [(3 + (-2)] = (6 + 3) + (- 2) Associative Property Associative Property of Addition of Addition 20.20. 7 + (-5) = - 5 + 7 Commutative Commutative Property of Addition Property of Addition 21.21.
Distributive Property Distributive Property 22.22.
- 3(5 • 4) = (- 3 • 5) Associative Property of Associative Property of Multiplication Multiplication 23.23.
- 8(4) = 4(-8) Commutative Property Commutative Property of Multiplicationof Multiplication
[(-
2 / 3
)(5)]9 = -
2 / 3
[(5)(9)]
Associative Property of Associative Property of Multiplication Multiplication 30.30. 6(3 – 2n) = 18 – 12n Distributive Property Distributive Property
2x + 3 = 3 + 2x Commutative Property Commutative Property of Addition of Addition 32.32.
ab = ba Commutative Property Commutative Property of Multiplication of Multiplication
a + 0 = a Identity Property ofIdentity Property of Addition Addition 34.34. a(bc) = (ab)c Associative Property of Associative Property of Multiplication Multiplication
a•1 = a Identity Property ofIdentity Property of MultiplicationMultiplication 36.36.
