1. Drill #3 Evaluate each expression if a = 6, b = ½, and c = 2. 1. 2. 3.4.

2. Drill #4 Evaluate each expression if a = -3, b = ½, c = 1.
Name ALL sets of numbers to which each number belongs:

3. Drill #5 Name the property illustrated by each statement
1. (3 + 4a) 2 = 6 + 8a
2. ¼ - ¼ = 0
3. 1(10x) = 10x
5(6*7) = (5*6)7
State the Additive and Mult. Inverse of each ½

4. 1-2 Properties of Real Numbers
Objective: To determine sets of numbers to which a given number belongs and to use the properties of real numbers to simplify expressions.

5. Rational and Irrational numbers*
Rational numbers: a number that can be expressed as m/n, where m and n are integers and n is not zero. All terminating or repeating decimals and all fractions are rational numbers.
Examples:
Irrational Numbers: Any number that is not rational. (all non-terminating, non-repeating decimals)

6. Rational Numbers (Q)*
The following are all subsets of the set of rational numbers:
Integers (Z): {…-4, -3, -2, -1, 0, 1, 2, 3, 4, …}
Whole (W): {0, 1, 2, 3, 4, 5, …}
Natural (N): { 1, 2, 3, 4, 5, …}

7. Venn Diagram for Real Numbers *
Reals, R
I = irrationals
Q = rationals
Z = integers
W = wholes
N = naturals Q I Z W N

8. Find the value of each expression and name the sets of numbers to which each value belongs:
I, R
Q, R
W, Z, Q, R
Z, Q, R

9. Find the value of each expression and name the sets of numbers to which each value belongs:

10. Properties of Real Numbers**
For any real numbers a, b, and c
Addition
Multiplication
Commutative
a + b = b + a
a(b) = b(a)
Associative
(a + b)+c =a+(b + c)
(ab)c = a(bc)
Identity
a + 0 = a = 0 + a
a(1) = a = 1(a)
Inverse
a + (-a) = 0 = -a + a
a(1/a) =1= (1/a)a
Distributive
a(b + c)= ab + ac & a(b - c)= ac – ac

11. Name the property: Examples*
(3 + 4a) 2 = 2 (3 + 4a)
62 + ( ) = ( ) + 75
5 – 2(x + 2) = 5 – 2 ( 2 + x)

12. Simplify An Expression: Examples
Simplify each expression:
#1: 3( 2q + r) + 5(4q – 7r)
#2: 3(4x – 2y) – 2(3x + y)
#3: 9x +3y + 12y -0.9x

13. Multiplicative and Additive Inverses: Examples
#1. ¾
#2. – 2.5
#3. 0
#4.

14. Inverses And the Identity*
The inverse of a number for a given operation is the number that evaluates to the identity when the operation is applied.
Additive Identity = 0
Multiplicative Identity = 1