Properties of Operations

1. Properties of Operations Mrs. Rauch

2. Four Properties of Operations • Commutative Property • Associative Property • Identity Property • Distributive Property

3. The Commutative Property • Background • The word commutative comes from the verb “to commute.” • Definition on dictionary.com • Commuting means changing, replacing, or exchanging • People who travel back and forth to work are called commuters. • Traffic Reports given during rush hours are also called commuter reports.

4. Here are two families of commuters. Commuter B Commuter A Commuter A & Commuter Bchangedlanes. Remember… commute means to change. Commuter A Commuter B

5. Here is another example…

6. Think of this situation: Every day you ride your bike to school. The distance from home to school is 2 miles. The distance from school to home is also 2 miles.

7. Home School The distance from Home to School is the same as the distance from school to home. Home + School = School + Home H + S = S + H A + B = B + A

8. The Commutative Property A + B = B + A

9. The Commutative Property • The order of the numbers being added can be changed and the outcome will be the same

10. Four Properties of Operations • Commutative • Associative • Identity • Distributive

11. The Associative Property • Background • The word associative comes from the verb “to associate.” • Definition on dictionary.com • Associate means connected, joined, or related • People who work together are called associates. • They are joined together by business, and they do talk to one another.

12. Let’s look at another hypothetical situation Three people work together. Associate B needs to call Associates A and C to share some news. Does it matter who he calls first?

13. A C B Here are three associates. B calls A first He calls C last If he called C first, then called A, would it have made a difference? NO!

14. (The Role of Parentheses) • In math, we use parentheses to show groups. • In the order of operations, the numbers and operations in parentheses are done first. (PEMDAS) So….

15. A C B A C B The Associative Property The parentheses identify which two associates talked first. (A + B) + C = A + (B + C) THEN THEN

16. The Associative Property • When three or more numbers are being added, you can regroup and have the same outcome • Ex: (2 + 8) + 4 = 2 + (8 + 4)

17. 4 Properties of Operations • Commutative • Associative • Identity • Distributive

18. The Identity Property of Addition I am me! You cannot change My identity!

19. Zero is the only number you can add to something and see no change.

20. Identity Property of Addition A + 0 = A + 0 =

21. Identity Property of Multiplication One is the only number that you can multiply by something and see no change

22. Identity Property of Multiplication • 1 = A • 1 = A

23. Let’s practice ! Look at the problem. Identify which property it represents.

24. (9 + 8) + 7 = 9 + (8 + 7) The Associative Property of Addition It is the only addition property that has parentheses.

25. 12 + 0 = 12 The Identity Property of Addition It is the only addition property that has two addends and one of them is a zero.

26. 9 + 7 = 7 + 9 The Commutative Property of Addition It is the only addition property that has numbers that change places.

27. 4 + 6 = 6 + 4 The Commutative Property of Addition Numbers change places.

28. 3 + 0 = 3 The Identity Property of Addition See the zero?

29. (4 + 3) + 2 = 4 + (3 + 2) The Associative Property of Addition It has parentheses!

30. a + 0 = a The Identity Property of Addition Zero!

31. a + b = b + a The Commutative Property of Addition Moving numbers!

32. A C B (a + b) + c = a + (b + c) The Associative Property of Addition Parentheses!