# 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.

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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)?

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

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

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!

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!

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?!

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

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

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

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

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

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

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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