Bell Quiz

Objectives Multiply and Divide signed numbers. Discuss the properties of real numbers that apply specifically to multiplication. Explain the rules for multiplying and dividing real numbers.

Multiplying and Dividing Real Numbers The sum of three 2’s and the sum or two 3’s is = = 6 Multiplication is a way to show repeated addition of the same number. The repeated addition above can be shown as multiplication of the same number. 3 x 2 = 6or2 x 3 = 6

Multiplying and Dividing Real Numbers There are properties of real numbers that apply to all real numbers –rational and irrational. We use these properties when evaluating and simplifying numeric and algebraic expressions.

Properties of Real Numbers Multiplication Property of – 1 For every real number a a ∙ – 1 = – 1 ∙ a = – a Example 9 ∙ – 1 = – 1 ∙ 9 = – 9 Multiplication Property of Zero For every real number a a ∙ 0 = 0 Example 9 ∙ 0 = 0 Inverse Property of Multiplication For every real number a, where a ≠ 0 a ∙ (1/a) = (1/a) ∙ a = 1 Example 3 ∙ (1/3) = (1/3) ∙ 3 = 1

Multiplying Signed Numbers The product of two numbers with the same sign is a positive number (+)(+) = (+) (–)(–) = (+) Example (3)(4) = 12 (– 5)(– 3) = 15 The product of two numbers with opposite signs is a negative number (–)(+) = (–) (+)(–) = (–) Example (– 2)(4) = – 8 6(– 2) = – 12

Example 1 Multiplying Rational Numbers Simplify each expression. a.4(– 8) b.(– 6)(– 0.7)

Lesson Practice Simplify each expression. a.9(– 0.8) b.– 12(– 2.5)

Example 2 Raising a Number to a Power Simplify each expression. a.(– 3) 4 b.(– 3) 3 c.– 3 4

Lesson Practice Simplify each expression. a.(– 4) 3 b.(– 8) 4 c.– 5 4

Dividing Signed Numbers The quotient of two numbers with the same sign is a positive number. (+) ÷ (+) = (+) (–) ÷ (–) = (+) Example (6) ÷ (3) = 2 (– 8) ÷ (– 2) = 4 The quotient of two numbers with opposite signs is a negative number. (–) ÷ (+) = (–) (+) ÷ (–) = (–) Example 10 ÷ (– 5) = – 2 (– 12) ÷ 3 = – 4

Example 3 Dividing Real Numbers Simplify each expression. a.– 16 ÷ (– 2) b.2.8 ÷ (– 7)

Lesson Practice Simplify each expression. a.– 105 ÷ (– 7) b.63.9 ÷ (– 3)

Example 4 Dividing Positive and Negative Fractions Evaluate each expression a.– (2 / 3) ÷ – (3 / 4) b.(2 / 9) ÷ – (3 / 5)

Lesson Practice Evaluate each expression a.– (4 / 5) ÷ – (9 / 10) b.(3 / 8) ÷ – (3 / 4)