1. Warm Up Problem A football team has a win to loss ratio of 8 : 7. What is their ratio of wins to games played? A. 7 : 8 B. 7 : 15 C. 8 : 15 D. 15 : 8

2. LESSON 6-5 Algebra: Properties

3. Objectives I can use properties to simplify expressions. I can define the commutative, associative, and identity properties.

4. Vocabulary

5. Vocabulary Continued Commutative Properties – in + and x the order does not change the sum or product a + b = b + a a b = b a Associative Properties – in + x the way numbers are grouped does not change the sum or product a + (b + c) = (a + b) + c a (b c) = (a b) c Identity Properties – a number + zero or x 1 equals itself

6. Example 1 - Notes Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why. 1) 15 + (5 + 8) and (15 + 5) + 8 They are equivalent by the Associative Property. 15 + (5 + 8) = (15 + 5) + 8

7. Example 2 - Notes

8. Example 3 - Notes Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why. 3) 34 + 0 and 34 The expressions are equivalent by the Identity Property. 34 + 0 = 34

9. Example 4 - Notes

10. Example 1-4 – Guided Practice

11. Example 5 - Notes In a recent season, the Kansas Jayhawks had 15 guards, 4 forwards, and 3 centers on their roster. Write two equivalent expressions using the Associative Property that can be used to find the total number of players on their roster. 15 + (4 + 3) = (15 + 4) + 3

12. Example 5 – Guided Practice 5) Milo earned $7 babysitting and $12 cleaning out the garage. Write two equivalent expressions using the Commutative Property that can be used to find the total amount he earned.

13. Example 6 - Notes 15 ft. 12 ft.

14. Example 6 - Guided Practice