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1-2 Algebraic Expressions

1-2 Algebraic Expressions. Objectives: To evaluate and simplify algebraic expressions. Subsets of Real Numbers. Subsets of Real Numbers. Natural Numbers: 1, 2, 3,… used for counting Whole Numbers: 0, 1, 2, … include zero Integers : …-2, -1, 0, 1, 2… include opposites

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1-2 Algebraic Expressions

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  1. 1-2 Algebraic Expressions Objectives: To evaluate and simplify algebraic expressions

  2. Subsets of Real Numbers

  3. Subsets of Real Numbers • 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

  4. 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???

  5. 1. 27 + 18 ÷ 9 – 32 + 1 2. (40 + 24) ÷ 8 – (23 + 1) Review • Simplify the following using order of operations:

  6. 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

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

  8. Example 2 CAUTION! -32 ≠ (-3)2 -x2 ≠ (-x)2 Evaluate –x2 – 2(x + 1) for x = 3 How many negatives? -x2 , (-x)3 ,-x5 , (-x)6 , (-x)4 , -x10

  9. Example 3 • Simplify by combining like terms 2x2 + 5x – 4x2 + x – x2 y(1 + y) – 3y2 – (y + 1)

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

  11. 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?

  12. Homework:Pgs. 16-17 # 38-53, 67 a,b

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