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Objectives: To evaluate and simplify algebraic expressions

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Subsets of Real Numbers

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Natural Numbers: 1, 2, 3,… used for counting Whole Numbers: 0, 1, 2, … include zero Integers: …-2, -1, 0, 1, 2… include opposites Rational Numbers: 7/5, -1/2, 0.25, 3 – Can be written as a fraction – Decimal will either repeat or terminate Irrational Numbers:, , 1.011011101111… – Cannot be written as a fraction – Decimal will not repeat or terminate

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Definitions Variable: symbol usually a letter that represents one or more numbers Algebraic Expression: expression that contains one or more variables Evaluate: substituting numbers for variables in an expression and following order of operations What are order of operations???

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Review Simplify the following using order of operations: 1.27 + 18 ÷ 9 – 3 2 + 12.(40 + 24) ÷ 8 – (2 3 + 1)

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More Definitions Term: number, variable, or product of one or more variables Coefficient: the numerical factor in a term Like Terms: have the same variables raised to the same powers

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Example 1 Evaluate 7x – 3xy for x = –2 and y = 5.

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Example 2 Evaluate –x 2 – 2(x + 1) for x = 3 CAUTION! -3 2 ≠ (-3) 2 -x 2 ≠ (-x) 2 How many negatives? -x 2, (-x) 3,-x 5, (-x) 6, (-x) 4, -x 10

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Example 3 Simplify by combining like terms 2x 2 + 5x – 4x 2 + x – x 2 y(1 + y) – 3y 2 – (y + 1)

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Example 4 Find the perimeter of the figures and simplify the answer.

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Summary Questions Subtraction is the same as adding a ________. Division is the same as multiplying by ______. What’s the distributive property? What happens when you multiply by 0? -1? What does –(ab) equal? What happens when you take the opposite of an opposite?

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