Properties Multiplicative Property of Zero What do you multiply a number by Statements that are true to get zero? for any number of variables. a • 0 = 0 (If you multiply by 0, the answer is 0.) Commutative Property Associative Property Commutative means that the order does not Associative means that the grouping does not make any difference. make any difference. a + b = b + a a • b = b • a (a + b) + c = a + (b + c) (ab) c = a (bc) Examples Examples 4 + 5 = 5 + 4 (1 + 2) + 3 = 1 + (2 + 3) 2 • 3 = 3 • 2 (2 • 3) • 4 = 2 • (3 • 4) The associative property does not work for The commutative property does not work for subtraction or division. subtraction or division. 1 Identity Properties 1) Additive Identity What do you add to a number to get Distributive the same number? Property a + 0 = a 2) Multiplicative Identity What do you multiply a number by to get the same number? a • 1 = a Name the property Inverse Properties 1) 5a + (6 + 2a) = 5a + (2a + 6) 1) Additive Inverse (Opposite) commutative (switching order) a + (-a) = 0 2) 5a + (2a + 6) = (5a + 2a) + 6 2) Multiplicative Inverse associative (switching groups) (Reciprocal) 1 3) 2(3 + a) = 6 + 2a a 1 a distributive 2 1. 4. 0 12 = 0 Multiplicative Prop. Of Zero 5. 6 + (-6) = 0 Additive Inverse 6. 1 m = m Multiplicative Identity (2 + 1) + 4 = 2 + (1 + 4) 7. x + 0 = x Additive Identity Associative Property 1 8. 11 1 Multiplicative Inverse 11 of Addition 2. 3. 3 + 7 = 7 + 3 8 + 0 = 8 Commutative Identity Property of Property of Addition Addition 3 5. 6. 6 • 4 = 4 • 6 17 + (-17) = 0 Commutative Property Inverse Property of of Multiplication Addition 7. 9. 2(5) = 5(2) 3(2 + 5) = 3•2 + 3•5 Commutative Property Distributive Property of Multiplication 4 10. 11. 6(7•8) = (6•7)8 5 • 1 = 5 Associative Property of Identity Property of Multiplication Multiplication 13. (6 – 3)4 = 6•4 – 3•4 Distributive Property 5 14. 15 . 1(-9) = -9 3 + (-3) = 0 Identity Property of Inverse Property of Multiplication Addition 16. 17. 1 + [-9 + 3] -3(6) = 6(-3) = [1 + (-9)] + 3 Associative Property of Commutative Property Addition of Multiplication 6 18. 19. -8 + 0 = -8 3•7 – 3•4 = 3(7 – 4) Identity Property of Distributive Property Addition 20. 20. 21. 6 + [(3 + (-2)] 7 + (-5) = -5 + 7 = (6 + 3) + (- 2) Associative Property Commutative of Addition Property of Addition 7 22. 23. (5 + 4)9 = 45 + 36 -3(5 • 4) = (-3 • 5)4 Distributive Property Associative Property of Multiplication 24. -8(4) = 4(-8) Commutative Property of Multiplication 8 25. 26. 1 1 3 6 6 3 5 /7 + 0 = 5 /7 /4 – /7 = – /7 + /4 Identity Property of Commutative Property Addition of Addition 27. 29. 2 2 2 2 1 /5 • 1 = 1 /5 -8 /5 + 0 = -8 /5 Identity Property of Identity Property of Multiplication Addition 9 30. 2 2 [(- /3)(5)]9 = - /3[(5)(9)] Associative Property of Multiplication 31. 32. 6(3 – 2n) = 18 – 12n 2x + 3 = 3 + 2x Distributive Property Commutative Property of Addition 10 33. 34. ab = ba a + 0 = a Commutative Property Identity Property of of Multiplication Addition 35. 36. a(bc) = (ab)c a•1 = a Associative Property of Identity Property of Multiplication Multiplication 11 37. 38. a +b = b + a a(b + c) = ab + ac Commutative Property Distributive Property of Addition 39. 40. a + (b + c) = (a +b) + c a + (-a) = 0 Associative Property of Inverse Property of Addition Addition 12.