Objectives: To evaluate and simplify algebraic expressions

Subsets of Real Numbers

Subsets of Real Numbers

• Natural Numbers: 1, 2, 3,… used for counting• Whole Numbers: 0, 1, 2, … include zero• Integers: …-2, -1, 0, 1, 2… include opposites• Rational Numbers: 7/5, -1/2, 0.25, 3

– Can be written as a fraction– Decimal will either repeat or terminate

• Irrational Numbers: , , 1.011011101111…– Cannot be written as a fraction– Decimal will not repeat or terminate

2

Definitions • Variable: symbol usually a letter that

represents one or more numbers• Algebraic Expression: expression that

contains one or more variables• Evaluate: substituting numbers for variables

in an expression and following order of operations

What are order of operations???

ReviewSimplify the following using order of

operations:1. 27 + 18 ÷ 9 – 32 + 1 2. (40 + 24) ÷ 8 – (23 + 1)

More Definitions• Term: number, variable, or product of one or

more variables• Coefficient: the numerical factor in a term

• Like Terms: have the same variables raised to the same powers

Example 1Evaluate 7x – 3xy for x = –2 and y = 5.

Example 2Evaluate –x2 – 2(x + 1) for x = 3

CAUTION!

-32 ≠ (-3)2

-x2 ≠ (-x)2

How many negatives?-x2 , (-x)3 ,-x5 , (-x)6 , (-x)4 , -x10

Example 3Simplify by combining like terms

2x2 + 5x – 4x2 + x – x2

y(1 + y) – 3y2 – (y + 1)

Example 4Find the perimeter of the figures and simplify

the answer.

Summary QuestionsSubtraction is the same as adding a ________.Division is the same as multiplying by ______.What’s the distributive property?What happens when you multiply by 0? -1?What does –(ab) equal?What happens when you take the opposite of

an opposite?