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Section 1.1

Section 1.1. Real Numbers and Number Operations. Real numbers can be pictured on a number line. Different types of real numbers. Whole numbers: 0, 1, 2, 3, 4 … Integers:...-3, -2, -1, 0, 1, 2, 3 … Rational numbers: ¾, ½, (Terminating or repeating decimals)

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Section 1.1

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  1. Section 1.1 Real Numbers and Number Operations

  2. Real numbers can be pictured on a number line

  3. Different types of real numbers • Whole numbers: 0, 1, 2, 3, 4 … • Integers:...-3, -2, -1, 0, 1, 2, 3 … • Rational numbers: ¾, ½, (Terminating or repeating decimals) • Irrational numbers: (Non-terminating or non-repeating decimals)

  4. Inequality signs > Is greater than < Is less than = is equal to ≤ is less than or equal to ≥ is greater than or equal to

  5. Use inequality signs to order the numbers: 1) – 2 and 5 -2 < 5 2) -1 and -2 -1 > -2

  6. Addition Properties (Let a, b, and c be real #s) 1) Closure: a + b is a real number 2) Commutative: a + b = b + a 3) Associative:(a + b) + c = a + (b + c) 4) Identity: a + 0 = a 5) Inverse: a + (-a) = 0

  7. Multiplication Properties (Let a, b, and c be real #s) 1) Closure: a x b is a real number 2) Commutative: a x b = b x a 3) Associative: (axb)xc = ax(bxc) 4) Identity: a x 1 = a 5) Inverse: a x (1/a) = 1

  8. Distributive Property a(b + c) = a x b + a x c

  9. Identify the property shown. Be specific. 1) (2 + 7) + 4 = 2 + (7 + 4) Associative of Addition 2) 14 x 1 = 14 Identity of Multiplication

  10. Unit Analysis: Perform the given operation. Give the answer with the appropriate unit of measure. 1) 100 miles – 14 miles = 86 miles 2) 4.5 miles 3) 18 dollars / 6 hours = 3 dollars per hour

  11. Unit Analysis: Perform the given operation. Give the answer with the appropriate unit of measure. 4) 60 miles per hour

  12. Section 1.2 Algebraic Expressions and Models

  13. Exponents • Used to represent repeated factors being multiplied • Evaluate: 1) 33 2) (-4)2 27 16

  14. Order of Operations • 1) Grouping symbols • 2) Exponents • 3) Multiplication and Division from left to right • 4) Addition and Subtraction from left to right

  15. Example -4 + 2(-2+5)2 -4 + 2(3)2 -4 + 2(9) -4 + 18 14

  16. Variable: letter used to represent a number • Algebraic expression: expression involving variables • Evaluate: -3x2 – 5x + 7 when x = -2 -3(-2)2 – 5(-2) + 7 -3(4) – 5(-2) + 7 -12 + 10 + 7 = 5

  17. Example • You have $50 and are buying some movies that cost $15 each. Write an expression that shows how much money you have left after buying n movies. • Original amount: $50 • Per video $15 • Number of videos: n 50 – 15n

  18. Example continued • How much money would you have left if you buy 2 movies? 50 – 15n 50 – 15(2) 50 – 30 = $20

  19. Like terms • Terms of an expression with exactly the same variable • Simplify: 1) 7x + 4x 2) 3n2 + n – 2n2 = 11x = n2 + n 3) 2(x + 2) – 3(x + 1) 2x + 4 – 3x – 3 -x + 1

  20. Assignment • Section 1.1: page 7 – 8 # 15 – 54 (÷3) , 55 – 56 • Section 1.2: page 14 – 15 # 15 – 54 (÷3), 58

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