2. Properties A property is something that is true for all situations.

3. Why Should you Learn about the Properties of Multiplication?  It helps you solve problems without working them out.  It helps with mental math.  It makes understanding math easier.

4. Four Properties 1.Distributive 2.Commutative 3.Associative 4.Identity properties of one and zero 5.Zero Property

5. Commutative Property

6. We commute when we go back and forth from school to home.

7. Algebra terms commute when they trade places

8. Commutative Property of addition and multiplication Changing the order of the numbers in addition or multiplication will not change the result.  Commutative Property of Addition states: a + b = b + a For Example: 2 + 3 = 3 + 2  Commutative Property of Multiplication states: ab = ba For Example: 4 5 = 5 4

9. Commutative Property Brainpop

10. Associative Property

11. To associate with someone means that we like to be with them.

12. The tiger and the panther are associating with each other. They are leaving the lion out. ( )

13. In algebra:

14. The panther has decided to befriend the lion. The tiger is left out. ( )

15. In algebra:

16. This is a statement of the Associative Property: The variables do not change their order.

17. Associative Property of multiplication and Addition Associative Property or Multiplication  (a · b) · c = a · (b · c) Example: (6 · 4) · 3 = 6 · (4 · 3) Associative Property of Addition  (a + b) + c = a + (b + c) Example: (6 + 4) + 3 = 6 + (4 + 3) Changing the grouping of the numbers in addition or multiplication will not change the result.

18. Associative Property Brainpop

19. Distributive Property

20. We have already used the distributive property. Sometimes I ask for help in distributing papers.

21. The distributive property only has one form. Not one for addition...and one for multiplication...because both operations are used in one property.

22. Distributive Property Multiplication distributes over addition.

23. Distributive Property Brainpop

24. Zero Property

25. Zero Property When any number is multiplied with zero, the answer is zero.  98,756,432 X 0 = 0

26. Identity Property

27. The identity property makes me think about my identity.

28. The identity property for addition asks, “What can I add to myself to get myself back again?

29. Identity Properties Additive Identity Property: If you add 0 to any number, the number stays the same. a + 0 = a or 5 + 0 = 5 Multiplicative Identify Property: If you multiply any number times 1, the number stays the same. a x 1 = a or 5 x 1 = 5

30. Let’s play “Name that property!”

31. State the property or properties that justify the following. 3 + 2 = 2 + 3 Commutative Property

32. State the property or properties that justify the following. 3(x – 10) = 3x – 30 Distributive Property

33. State the property or properties that justify the following. 3 + (4 + 5) = (3 + 4) + 5 Associative Property

34. 6 4 = 4 6 Commutative Property of Multiplication 5.

35. State the property or properties that justify the following. (5 + 2) + 9 = (2 + 5) + 9 Commutative Property

36. 3 + 7 = 7 + 3 Commutative Property of Addition 2.

37. (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition 1.

38. 3(2 + 5) = 32 + 35 Distributive Property 9.

39. Test Yourself 1.9 X 3 = 3 X w 2. 3 X (4 X 2 ) = (n X 4) X 2 3. 56 X p = 11 X 56 Rewrite each equation with the correct answer, and write the name of the property.

40. Test Yourself Answers 1.9 X 3 = 3 X 9 Commutative 2.3 X (4 X 2) = (3 X 4) X 2 Associative 3.56 X 11 = 11 X 56 Commutative 4.4 X 8 = 8 X 4 Commutative 5.5 X (7 X 2) = (5 X 7) X 2 Associative 6.4 X 509 = (4 X 500) + (4 X 9) Distributive 7.6 X 310 = (6 X 300) + (6 X 10) Distributive 10. (2 X 8) X 5 = 2 X (8 X 5) Associative 11. 195 X 5 = (200 X 5) – (5 X 5) Distributive 12. 5 X 9 = 9 X 5 Commutative 13. 5 X 205 = (5 X 200) + (5 X 5) Distributive 14. 4 X (1 X 7) = (4 X 1) X 7 Associative