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53: Properties of Operations What is Addition: Commutative a + b = b + a Property ? Multiplication: a(b) = b(a) What is the Addition: a + (b + c) = (a + b) + c Associative Property ? Multiplication: a(b∙c) = (a∙b)c Additive Identity : a + 0 = a a ∙ 1 = a Multiplication Identity : The commutative property states that the order in which numbers are added or multiplied does not change the sum or product. The associative property states that the way in which numbers are grouped when they are added or multiplied does not change the sum or product. When 0 is added to any number, the sum is the number. When the number is multiplied by 1, the product is the number. Multiplicative Property of Zero : Example 1a: Page 368 What is Counterexample ? Example 2c: Page 369 a ∙ 0 = 0 Name the property shown in the statement: a) 4 2 + x + y = 42 + y + x 15 ÷ 3 = 3 ÷ 15 State whether the following conjecture is true or false. If false, provide a counterexample. The difference of two different whole numbers When any number is multiplied by 0, the product is 0. 1. Name the property. If you find a counterexample , an example that shows that a conjecture is false, the property does not apply. 1. True or false? 2. Write an example to show it. is always less than both of the two numbers. Summary: Example 3d: Page 369 Example 45e: Page 370 Lance made four phone calls from his cell phone today. The calls lasted 4.7, 9.4, 2.3, and 10.6 minutes. Use mental math to find the total amount of time he spent on the phone. Simplify each expression. Justify each steps. 4 ∙ (3c ∙ 2) Summary: