1. Chapter 1 Section 2 Part 2

2. In Algebra, certain statements or properties are true for any number.

3. Four properties for equality are listed. Property of EqualitySymbolsNumbers SubstitutionIf a = b, then a may be replaced by b. If 9 + 2 = 11, the 9 + 2 may be replaced by 11 Reflectivea = a21 = 21 SymmetricIf a = b, then b = aIf 10 = 4 + 6, then 4 + 6 = 10 TransitiveIf a = b and b = c, the a = cIf 3 + 5 = 8 and 8 = 2(4), then 3 + 5 = 2(4)

4. Example 1 Name the property of equality shown by each statement. If 9 + 3 = 12, then 12 = 9 + 3. Symmetric Property of Equality

5. Example 2 Name the property of equality shown by each statement. If z = 8, then z ÷ 4 = 8 ÷ 4. Substitution Property of Equality

6. Your Turn Name the property of equality shown by each statement. 7 – c = 7 – c Reflective

7. Your Turn Name the property of equality shown by each statement. If 10 – 3 = 4 + 3 and 4 + 3 = 7, then 10 – 3 = 7 Transitive

8. These properties of numbers help to find value of expressions. PropertyWordsSymbolsNumbers Additive IdentityWhen 0 is added to any number a, the sum is a. For any number a, a + 0 = 0 + a = a 45 + 0 = 45 0 + 6 = 6 0 is the identity Multiplicative Identity When a number a is multiplied by 1, the product is a. For any number a, a ∙ 1 = 1 ∙ a = a 12 ∙ 1 = 12 1 ∙ 5 = 5 Multiplicative Property of Zero If 0 is a factor, the product is 0. For any number a, a ∙ 0 = 0 ∙ a = 0 7 ∙ 0 = 0 0 ∙ 23 = 0

9. When two or more sets of grouping symbols are used, simplify within the innermost grouping symbols first.

10. Example 3 Find the value of 5[3 – (6 ÷ 2)] + 14. Identify the properties used. 5[3 – (6 ÷ 2)] + 14 = 5[3 – 3] + 14 = 5(0) + 14 = 0 + 14 = 14 Substitution Property of Equality Multiplication Property of Zero Additive Identity

11. Your Turn (22 – 15) ÷ 7 ∙ 9 9- Substitution Property of Equality

12. Your Turn 8 ÷ 4 ∙ 6(5 – 4) 12- Substitution Property of Equality And Multiplicative Identity

13. You can apply the properties of numbers to find the value of an algebraic expression. This is called evaluating an expression. Replace the variables with the known values and then use the order of operations.

14. Example 4 Evaluate each expression if a = 9 and b = 1. 7 + (a/b – 9) = 7 + (9/1 – 9) Replace a with 9 and b with 1 = 7 + (9 – 9) Substitution Property of Equality = 7 + 0 Substitution Property of Equality = 7 Additive Inverse

15. Example 5 Evaluate each expression if a = 9 and b = 1. (a + 4) – 3 ∙ b = (9 + 4) – 3 ∙ 1 Replace a with 9 and b with 1 = (13) – 3 ∙ 1 Substitution Property of Equality = 13 – 3 Multiplicative Identity = 10 Substitution Property of Equality

16. Your Turn Evaluate each expression if m = 8 and p = 2. 6 ∙ p – m ÷ p 8

17. Your Turn Evaluate each expression if m = 8 and p = 2. [m + 2(3 + p)] ÷ 2 9