1. Bell Quiz

2. Objectives Simplify expressions using the properties of real numbers. Discuss the numeric example for each property and relate it to the general statement.

3. Properties of Addition and Multiplication The properties of real numbers are used to simplify expressions and write equivalent expressions.

4. Identity Property of Addition For every real number a, a + 0 = a Example: 5 + 0 = 5

5. Identity Property Of Multiplication For every real number a, a ∙ 1 = a Example: 5 ∙ 1 = 5

6. Commutative Property of Addition For every real number a and b, a + b = b + a Example: 5 + 2 = 2 + 5 7 = 7

7. Commutative Property of Multiplication For every real number a and b, a ∙ b = b ∙ a ab = ba Example: 5 ∙ 2 = 2 ∙ 5 10 = 10

8. Associative Property of Addition For every real number a, b and c, (a + b) + c = a + (b + c) Example: (1 + 2) + 3 = 1 + (2 + 3) 3 + 3 = 1 + 5 6 = 6

9. Associative Property of Multiplication For every real number a, b and c, (a ∙ b) ∙ c = a ∙ (b ∙ c) Example: (1 ∙ 2) ∙ 3 = 1 ∙ (2 ∙ 3) 2 ∙ 3 = 1 ∙ 6 6 = 6

10. Example 1 Identifying Properties Identify the property illustrated in each equation. a.1 ∙ 8 = 8 b.13 + 5 = 5 + 13 c.(3 ∙ 4) ∙ 7 = 3 ∙ (4 ∙ 7) d.(12 + 9) + 5 = (9 + 12) + 5

11. Lesson Practice Identify the property illustrated in each equation. a.5 + (9 + 8) = (5 + 9) + 8 b.0 + 10 = 10 c.15 ∙ 3 = 3 ∙ 15 d.17 ∙ 1 = 17

12. Example 2 Using Properties to Justify Statements Tell whether each statement is true or false. a.gh = hg b.b + 1 = b c.d + (e + f) = (d + e) + f

13. Lesson Practice Tell whether each statement is true or false. a.(ab)c = a(bc) b.m – z = z – m c.w + 0 = w

14. Example 3 Justifying Steps to Simplify an Expression Simplify each expression a.16 + 3x + 4 b.(25) ∙ y ∙ (1/25)

15. Lesson Practice Simplify each expression a.18 + 7x + 4 b.(1/3)d ∙ 3

16. Example 4 Application: Consumer Math Envelopes, pens, and correction tape can be purchased at an office supply store for the following prices respectively: $2.85, $5.35, and $2.15. Find the total cost of the supplies.

17. Lesson Practice Erasers, markers, and paper can be purchased at the school store for the following prices, respectively: $1.45, $3.35, and $2.65. Find the total cost of the supplies.