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1-1 Properties of Real Numbers

1-1 Properties of Real Numbers

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1-1 Properties of Real Numbers

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  1. Chapter 1: Tools of Algebra 1-1 Properties of Real Numbers Algebra 2 Miss Santell

  2. Lesson Preview Check the skills you need! Simplify:

  3. Subsets of Real Numbers • Natural Numbers: #’s used for counting • Whole Numbers: natural #’s and 0 • Integers: whole #’s and their opposites • Rational Numbers: #’s that can be written as a fraction (“ratio”); terminating and repeating decimals • Irrational Numbers: #’s that cannot be written as fractions; decimals that neither terminate or repeat; radicals that are not perfect

  4. Real Numbers “anything on the number line” Examples: Rational Numbers Irrational Numbers Examples: 1/2, 0.3, 1, 2 2/3, -5/4, -1.07 Examples: Integers …,-2, -1, 0, 1, 2, … Whole Numbers 0, 1, 2, 3, … Natural Numbers 1, 2, 3, …

  5. Which set of numbers best describes the values for each variable? • The cost C in dollars of admission for n people • C is rational ($7.25) • n is a whole number (can’t have ½ person or negative) b.The height h in meters of a roller coaster • h is rational (80.5 feet) • The park’s profit (or loss) P in dollars for each week w of the year • w is one of the first 52 natural numbers • P is a rational number

  6. More properties of real numbers • The opposite or additive inverse of any number a is –a. a) -3.2b) 3/5 • The reciprocal or multiplicative inverse of any nonzero number a is 1/a. (The product of reciprocals is 1) a) -3.2 b) 3/5 3.2 -3/5 1/-3.2 = -0.3125 1/ 3/5 = 5/3

  7. Absolute Value • The absolute valueof a real number is its distance from zero on the number line. • All answers are positive because you can’t have a negative distance. -4 -3 -2 -1 0 1 2 3 4 units 2 units Simplify 1.5

  8. Let’s Practice To which set(s) of numbers does each number belong? • 4 2. 3. Which set of numbers best describes the value of each variable? • The number of times n a cricket chirps; the outdoor temperature T in tenths of a degree Find the opposite and the reciprocal of each number. 5. 6. Simplify each expression. 7. 8. 9. Natural, whole, integers, rational, real Irrational, real Rational, real Whole numbers; rational numbers 25 1.6 -2

  9. Contacts/Credits • Teacher email: rosa_santell@places.pcsb.org • Clip art, animation, and sound inserted from Microsoft organizers • Diagrams and Examples created by Miss Santell through the use of Prentice Hall’s Algebra 2 Textbook, 2004