ALGEBRA READINESS Chapter 5 Section 5

5.5 Use the Properties of Multiplication Commutative Property The order in which you multiply two numbers does not change the product. ab = ba2∙3 = 3∙2 Associative Property The way you group three numbers when multiplying does not change the product. (ab)c = a(bc)(2∙3)4 = 2(3∙4) Identity Property The product of a number and 1 is the number. The number 1 is called the multiplicative identity. a∙1 = a2 ∙ 1 = 2

Inverse Property The reciprocal of a nonzero number a, written 1/a, is also called the multiplicative inverse of a. The product of a nonzero number and its multiplicative inverse is 1. a ∙ 1/a = 12 ∙ ½ = 1 Property of Zero The product of a number and 0 is 0. a ∙ 0 = 03 ∙ 0 = 0 Property of -1 The product of a number and -1 is the opposite of the number. a ∙ (-1) = -a8 ∙ (-1) = -8 or -8 ∙ (-1) = 8

Example 1 Identifying the Properties of Multiplication Identify the property illustrated. Commutative property of multiplication a. 3 1 x 3 1 x = StatementProperty Illustrated b. 6 5 – () 1 – 6 5 = Multiplicative property of – 1 c – () x =3 – x () 2.7 Associative property of multiplication Multiplicative property of zero d. 7 3 – 0 = 0

Example 1 Identifying the Properties of Multiplication Identify the property illustrated. StatementProperty Illustrated Inverse property of multiplication e = 1 Identity property of multiplication f =9.8

Identify the property illustrated. 1. x – 1 = x – ANSWER Identity property – 8 3 = 7 5 – ANSWER Associative property 3. = 0 () 21.5 – 0 ANSWER Property of zero Practice for Example 1

Example 2 Simplifying Algebraic Expressions Simplify. Justify your steps. 3 1 – 3x3x – () Commutative property of multiplication 3 1 – 3x3x – () = 3 1 – 3x3x – () Associative property of multiplication = 3 1 – 3 – () x = 1x Inverse property of multiplication = x Identity property of multiplication

Example 3 Using the Identity Property The African elephant is the largest living land animal. Its average weight is 4.54 metric tons. What is the African elephant’s average weight in pounds? 1 t 1000 kg = 1 and 1 kg 2.2 lb 1 ≈ Use the fact that 1 metric ton 1000 kilograms and 1 kilogram 2.2 pounds to write conversion factors. = ≈ STEP 1

Example 3 Using the Identity Property Multiply 4.54 metric tons by the conversion factors and use unit analysis. Because each conversion factor is equal to (or almost equal to) 1, the identity property tells you that you are not changing the weight, just the units. ≈ 10,000 lb Simplify and round. ANSWER The average weight of the African elephant is about 10,000 pounds. 1 kg 2.2 lb ≈ 4.54 t 1 t 1000 kg Multiply by conversion factors. STEP 2

Example 3 Using the Identity Property CHECK To check reasonableness, round 4.54 and 2.2 and use mental math. Round 4.54 and 2.2. ≈ () () 4.54 () () 4.5 Commutative property of multiplication () () 4.5 = Multiply 4.5 and 2. () = Multiply 9 and =

Find the product. Justify your steps. ANSWER 0 4. () +0.9 – x – x ANSWER –x x 5 2 () 1 – ANSWER –x 5 9 Practice for Examples 2 and 3

7.Use a conversion factor to convert years to months ANSWER 39 months Practice for Examples 2 and 3