Algebra Review

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Section 1.2: Arithetic & Properties of Real Numbers

Identities:

Addition – zero

Multiplication – one

Inverses:

Addition – opposites

Multiplication – reciprocals

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Section 1.3: Definition of Exponents

Exponents: repeated multiplication

In the expression: an a is the base and n is the exponent

Exponents are NOT factors

Means to multiply “a” n times

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Section 1.3: Definition of Exponents

Order of operations

If an algebraic expression has more than one operation, the following order applies:

Clear up any grouping.

Evaluate exponents.

Do multiplication and division from left to right.

Do addition and subtraction from left to right.

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Section 1.5: Solving Equations

Algebraic Expression vs. Equation

Expressions: a combination of numbers and operations

Equation: a statement that two expressions are equal

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Section 1.5: Solving Equations

Expressions

Terms

Like terms

When multiplying, the terms do not need to be alike

Can only add like terms!

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Section 1.5: Solving Equations

To solve an equation in one variable

If you see fractions, multiply both sides by the LCD. This will eliminate the fractions.

Simplify the algebraic expressions on each side of the equal sign (eliminate parentheses and combine like terms).

Use the addition property of equality to isolate the variable terms from the constant terms on opposite sides of the equal sign.

Use the multiplication property to make the coefficient of the variable equal to one.

Check your results by evaluating.

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Section 1.5: Solving Equations

Types of equations

CONDITIONAL: if x equals this, then y equals that.

IDENTITY: always true no matter what numbers you use.

CONTRADICTION: never true no matter what numbers you use.

FORMULAS: conditional equations that model a relationship between the variables.

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Section 1.6 & 1.7: Solving Problems, Applications

Types of problems

Geometry

Percent

Physics (forces)

Uniform motion

Mixtures

Good ‘ole common sense analysis

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