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

Lesson Preview Check the skills you need! Simplify:

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

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, …

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

More properties of real numbers The opposite or additive inverse of any number a is –a. a) -3.2 b) 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

Absolute Value Simplify 1.5 The absolute value of 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 1 2 3 4 units 2 units Simplify 1.5

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

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