1-3 Study Guide and Intervention Properties of Numbers Identity and Equality Properties The identity and equality properties in the chart below can help you solve algebraic equations and evaluate mathematical expressions. Additive Identity For any number + 0 = a, a a. Additive Inverse For any number + (–a) = 0. a, a Multiplicative Identity For any number 1 = a, a a. • Multiplicative Property of 0 For any number 0 = 0. a, a • Multiplicative Inverse Property For number , where 0, there is exactly one number such that = 1. a, b ≠ • Reflexive Property For any number = a, a a. Symmetric Property For any numbers and if = then = a b, a b, b a. Transitive Property For any numbers and if = and = then = a, b, c, a b b c, a c. Substitution Property If = then may be replaced by in any expression. a b, a b Example: Evaluate 24 1 8 + 5(9 ÷ 3 3). Name the property used in each step. • – – 24 1 8 + 5(9 ÷ 3 3) = 24 1 8 + 5(3 3) • – – • – – Substitution; 9 ÷ 3 = 3 = 24 1 8 + 5(0) • – Substitution; 3 3 = 0 – = 24 8 + 5(0) – Multiplicative Identity; 24 1 = 24 • = 24 8 + 0 – Multiplicative Property of Zero; 5(0) = 0 = 16 + 0 Substitution; 24 8 = 16 – = 16 Additive Identity; 16 + 0 = 16 Exercises Evaluate each expression. Name the property used in each step. 1. 2. 15 1 9 + 2(15 ÷ 3 5) • – – 3. 2(3 5 1 14) 4 4. 18 1 3 2 + 2(6 ÷ 3 2) • • – – • • – • – 1-3 Study Guide and Intervention (continued)
1-3 Study Guide and Intervention Properties of Numbers Identity and Equality Properties The identity and equality properties in the chart below can help you solve algebraic equations and evaluate mathematical expressions. Additive Identity For any number a, a + 0 = a. Additive Inverse For any number a, a + (–a) = 0. Multiplicative Identity For any number a, a • 1 = a. Multiplicative Property of 0 For any number a, a • 0 = 0. Multiplicative Inverse Property For number , where a, b ≠ 0, there is exactly one number such that • = 1. Reflexive Property For any number a, a = a. Symmetric Property For any numbers a and b, if a = b, then b = a. Transitive Property For any numbers a, b, and c, if a = b and b = c, then a = c. Substitution Property If a = b, then a may be replaced by b in any expression. Example: Evaluate 24 • 1 – 8 + 5(9 ÷ 3 – 3). Name the property used in each step. 24 • 1 – 8 + 5(9 ÷ 3 – 3) = 24 • 1 – 8 + 5(3 – 3) Substitution; 9 ÷ 3 = 3 = 24 • 1 – 8 + 5(0) Substitution; 3 – 3 = 0 = 24 – 8 + 5(0) Multiplicative Identity; 24 • 1 = 24 = 24 – 8 + 0 Multiplicative Property of Zero; 5(0) = 0 = 16 + 0 Substitution; 24 – 8 = 16 = 16 Additive Identity; 16 + 0 = 16 Exercises Evaluate each expression. Name the property used in each step. 1. 2. 15 • 1 – 9 + 2(15 ÷ 3 – 5) 3. 2(3 • 5 • 1 – 14) – 4 • 4. 18 • 1 – 3 • 2 + 2(6 ÷ 3 – 2) 1-3 Study Guide and Intervention (continued)
1.3-Intervention-Properties-of-Numbers.docx