Drill #2Evaluate each expression if a = 6, b = ½, and

c = 2.

1.

2.

3.

4.

ca

cab

bbac )(

2ab

cb

aacab

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.

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)

Examples:

8.5,34.1,9,3

1

7,,2

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, …}

Venn Diagram for Real Numbers *

Reals, R

I = irrationals

Q = rationals

Z = integers

W = wholes

N = naturals

IQ

ZW

N

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

11.0.

9.

025.0.

126573.3.

17.

e

d

c

b

a

I, R

Q, R

W, Z, Q, R

Z, Q, R

Q, R

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

Example 1: Name the property**

a. (3 + 4a) 2 = 2 (3 + 4a)

b. 62 + (38 + 75) = (62 + 38) + 75

c. 5 – 2(x + 2) = 5 – 2 ( 2 + x)

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

Example 2: Find the additive inverse and multiplicative inverse:

a. ¾

b. – 2.5

c. 0

d. 3

21