ALGEBRA 2Sections 1, 2, and 3

Real Numbers

Rational Numbers

IrrationalNumbers

Integers

Whole NumbersNatural Numbers

See page 1

Real Number Line

𝜋2

≈ 1.5711112

2 ≈ 3.464−34

-2.45

Plot the numbers listed below on the real number line.

712,−√5 ,2𝜋 , 7

2

−√5≈−2.23672=3

12173,=5

23

2𝜋≈6.28

How can we use them in math?

Add

SubtractAdding the opposite or additive inverse

Multiply

DivideMultiplying by the reciprocal or

Multiplicative inverse

Order of OperationsPEMDASParenthesisExponentsMultiplication and division.As they appear from left to right.Addition and subtraction. As they appear from left to right.

PropertiesClosureCommutativeAssociativeIdentityInverseDistributive

Pages 3-4

Unit AnalysisYou work 4 hours and earn $36.

What is your earning rate?

You travel for 2.5 hours at 50 miles per hour. How far do you go?

You drive 45 miles per hour. What is your speed in feet per second?

Page 5

Numerical ExpressionConsists of numbers, operations,

and grouping symbols.A power is a numerical

expression.A power has two parts an

exponent and base.

Base

Exponent

Algebraic ExpressionHas at least one variable

−2 𝑥3+5 𝑥1+21

Coefficients

Variables

Constant

• Above is and expression written as a sum.

• The parts added together are called terms.

• Variable term has a variable.• A constant term has no variable.

Solve linear EquationsAn equation is a statement where two

expressions are equal.A linear equation in one variable can

be written in the form , where and are constants and .

A number is the solution to the equation if substituting the number for the variable makes it true.

Two equations are equivalent equations if they have the same solution(s).

PropertiesAddition Property of EqualitySubtraction Property of EqualityMultiplication Property of Equality

◦Nonzero numberDivision Property of Equality

◦Nonzero number

Solving EquationsSimplify both sides following

PEMDAS, and various properties.Bring variables to one sideUndo the operations in reverse

order, addition/subtraction, multiplication/division, powers, grouping symbols.

Solve

VocabularyReal numbersClosureCommutativeAssociativeIdentityInverseDistributive

VocabularyOpposite/additive inverseReciprocal/multiplicative inverseBase ExponentVariableAlgebraic expressionTerms (variable and constant)Coefficient

HomeworkPages 6 – 9

#7, 25-29 odd, 41-45 odd,49-53 oddPages 13-15

#9-15 odd, 37-49 odd, 53Pages21 – 23#21-49 e.o.o, 51, 53, 59-65 odd