1. 1-1 Properties of Real Numbers
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) 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 =
1/ 3/5 = 5/3

7. 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

8. Let’s Practice
To which set(s) of numbers does each number belong?
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.
Simplify each expression.
Natural, whole, integers, rational, real
Irrational, real
Rational, real
Whole numbers; rational numbers 25
1.6 -2

9. Contacts/Credits
Teacher
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