Associative Property

1. Associative Property

2. The Associative Propertyis like two people getting married. First, they are each counted separately, then after they are married they are counted as one, even though they are still separate people.

3. Before a couple are married they are considered as two separate people.

4. After the marriage they are considered as one. ( )

5. These numbers are all separate. • 4 + 5 + 9 + 3 = • 6 x 3 x 8 x 4 =

6. The numbers with parentheses around them are counted as one number. • (4 + 5) + 9 + 3 = • 6 x 3 x (8 x 4) =

7. Therefore, the operations inside the parentheses must be done first. • (4 + 5) + 9 + 3 = • 6 x 3 x (8 x 4) =

8. Definition Associative Property – the way addends are grouped does not change a sum (4 + 3) + 9 = 16 4 + (3 + 9) = 16

9. Order of Operations The operations within parentheses must be done first before the other operations. (4 + 3) + 9 = 16 7 + 9 = 16

10. Associative Property Solve these problems • (76 – 13) + 20 = • 60 – (45 - 23) = • (329 + 200) – 125 = • 75 – (25 -13) = • 88 + (55 – 13) = 83 38 404 63 130

11. Check Did you remember to do the operations in the parentheses () first?

12. Associative Property Solve these problemsLet n = 5 • (16 – n) + 4 = • n – (3 + 1) = • (n + n) – 8 = • 24 – (n +7) = • 14 + (n + 13) = 15 1 2 12 32

13. Check Did you remember to do the operations in the parentheses () first?

14. Insert parentheses to make each equation true • 11 – 5 + 1 = 5 • 15 - 10 – 8 = 13 • 8 – 2 + 7 = 13 • 9 + 3 – 2 = 10 • 11 – (5 + 1) = 5 • 15 – (10 – 8) = 13 • (8 – 2) +7 = 13 • (9 + 3) – 2 = 10

15. IdentityProperty

16. i·den·ti·ty –noun, plural -ties. the state or fact of remaining the same one or ones, as under varying aspects or conditions: The identity of the fingerprints on the gun with those on file provided evidence that he was the killer. 2. the condition of being oneself or itself, and not another: He doubted his own identity. 3. condition or character as to who a person or what a thing is: a case of mistaken identity. 4. the state or fact of being the same one as described. 5. exact likeness in nature or qualities: an identity of interests. 6. an instance or point of sameness or likeness

17. What is an Identity Card? Any document which may be used to verify aspects of a person's personal identity.

18. Identity Property The sum of any addend and zero equals the addend.

19. Identity Property Solve these problems • 9 + 0 = • 6,458 + 0 = • 0 + 12.567 = • .0098 + 0 = • 0 + 7,987,402 = 9 6,458 12.567 .0098 7,987,402

20. CommutativeProperty

21. What do these pictures have in common?

22. They are all pictures of people going back and forth to work. What is the name for a person who travelsback & forthto work? Commuter

23. Many people commute to work. They get up at home in the morning, dress, eat breakfast, brush their teeth, then drive or take the train or a bus to work. In other words, they change places. In the afternoon they change places again and drive or ride home. So we call them commuters. The commutative property means " to change places."

24. Commutative Property The order of addends does not change a sum. a+b is the same as b+a They are both commuting. That's the commutative property.

25. Commutative Property – The order of addends does not change a sum.

26. Commutative Property Show the commutative property and then solve. 7 + 9 = 16 • 9 + 7 = • a + x = • 8.2 + 1.8 = • 6.4 + 3.6= • 5.75 + 4.25 x + a 1.8 + 8.2 = 10 3.6 + 6.4 = 10 4.25 + 5.75 = 10

28. Properties of Addition

29. Which Property?

30. Which Property? (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition

31. Which Property? 3 + 7 = 7 + 3 Commutative Property of Addition

32. Which Property? 8 + 0 = 8 Identity Property of Addition

33. Which Property? (x + c) + b = x + (c + b) Associative Property of Addition

34. Which Property? 4.87 + 0 = 4.87 Identity Property of Addition

35. Which Property? .004 + .05 = .05 + .004 Commutative Property of Addition