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Warm up Determine if the set finite or infinite: 1. {Even numbers greater than 4, but less than 100} 2. {odd numbers} 3.{Fractions less than 1} 4. -3 is a member of what group(s)? 5. Is a member of what group(s)?

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Warm up Answers 1. Finite 2. Infinite 3. Infinite 4. integers, rational, real 5. irrational, real

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Lesson 1.2 Properties of Real Numbers Obj: SWBAT Justify manipulations of expressions using the properties of real numbers.

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Associative Property The grouping of the numbers does not change the sum or the product. Addition: a + (b + c) = (a + b) + c Multiplication: (a·b)·c = a·(b·c) Hint: The different GROUPS of numbers can all associate with each other….they are all friends!

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Commutative Property The order of the numbers does not change the sum or the product. Addition: a + b = b + a Multiplication: a·b = b·a No matter how you flip them…the answer is always the same!

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Distributive Property The term outside the parentheses can be multiplied by all the terms on the inside of the parentheses. a(b + c) = (a·b) + (a·c) a(b – c) = (a·b) – (a·c) You distribute so that everyone gets an equal turn…get it?!

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Identity Property of Addition The sum of a number and zero is the number. a + 0 = a Addition +

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Identity Property of Multiplication The product of a number and one is the number. a · 1 = a

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Inverse Property of Addition The sum of a number and its opposite is zero. -a + a =0

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Inverse Property of Multiplication The product of a number and its reciprocal is one. When might you use this property in solving equations?

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Zero Product Property The product of a number and zero is zero. a · 0 = 0

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Closure Property The sum or product of any two real numbers is a unique real number. (If you add or multiply any two real numbers, the sum or product is one and only one real number.) a + b = real number a * b = real number

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Summary Write down two properties and tell how you will remember them. Classwork: BD Book 1 pg 17 in class Homework: WS 1.3

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