Algebra 2

Chapter 1.2 Properties of Real Numbers

Target Goals:1. Use the properties of real numbers to

evaluate expressions

Real Number SystemSet Letter/

SymbolDefinition Examples

Natural (aka: counting)

N Basic counting numbers {1, 2, 3, …}

Wholes W Naturals + 0 {0, 1, 2, 3, …}

Integers Z Positive and negative whole numbers

{…, -3, -2, -1, 0, 1, 2, 3, …}

Rationals Q Fractions of two integersDecimal form is repeating or

terminating

½ , -¾ , 0.125, 1/3 = 0.333…

Irrationals I Decimal form doesn’t terminate and doesn’t repeat

π,

3

Name the set(s) of numbers to which each number belongs.

• Ex ) -185 Z, Q, R

• Ex ) Z, Q, R

• Ex ) I, R

• Ex ) Q, R

49

95

4

7

Properties of Real NumbersFor any real numbers a, b, and c, the following are true:

Property 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

Closure a + b is a real numbera * b is a real

number

Distributive a (b + c) = ab + ac and (b + c) a = ba + bc

1 11 where 0a a a

a a

Name the property illustrated by each of the following:

Ex 1) 2(x + 3) = 2x + 6Distributive Property

Ex 2) (-8 + 8) + 15 = 0 + 15Additive Inverse

Find the additive inverse and multiplicative inverse for each of the following:

Ex 3) -7A.I. = M.I. =

Ex 4) 1.25A.I. = M.I. =

Ex 5) -2 ½ A.I. = M.I. =

Ex 6) Application

Jimmy went to a post office and bought eight 42¢ stamps and eight 27¢ postcard stamps. What was the total amount of money Jimmy spent on stamps?

Ex 7) Application:

Kayla makes $8 per hour working at a grocery store. The number of hours Kayla worked each day in one week are 3, 2.5, 2, 1, and 4. How much money did Kayla earn this week?

Simplify each of the following:

Ex 8) 3(4x – 2y) – 2(3x + y)

Ex 9) 4(3a – b) + 2(b + 3a)

Target Goals

1. Use the properties of real numbers to evaluate expressions