Elementary Algebra

A review of concepts and computational skills Chapters 1-2

Real Numbers  Natural – 1, 2, 3,4….

 Whole – 0, 1, 2, 3, 4…..

 Integers- …-2, -1, 0 1, 2….

 Rational – can be written as p/q; ½, -3, 4.3

 Irrational – cannot be written as p/q; non repeating, non-terminating decimals

The Real Number Line  Ordering numbers  Graphing numbers on a number line  Interval Notation – ( ), [ ], ( ]  Unbounded intervals

Absolute Values  Think of absolute value as distance from zero on the number line  |a| = a if a > 0 and |a| = -a if a < 0

Fractions  Equivalent fractions  Finding common denominators  Adding, subtracting fractions- first find a common denominator  Multiplying, dividing  Adding mixed numbers  Decimals and percents

Adding and Subtracting Reals   In general, adding means moving right on the number line, subtracting means moving left Adding a negative number —same as subtracting  Adding 2 positive numbers  Adding 2 negative numbers  Adding a positive and a negative

Multiplying and Dividing Reals  Multiply or divide 2 positive numbers  Multiply or divide 2 negative numbers  Multiply or divide 1 positive, 1 negative number  Divide by zero

Exponential Expressions  An exponent tells you to multiply repeatedly  a 3 =a x a x a  Exponent also called “power”

Order of Operations   Please Excuse My Dear Aunt Sally P- parentheses – grouping  E- Exponents  M- Multiply  D- Divide  A- Add  S- Subtract

Algebraic Expressions and Equations  Expressions – can evaluate or simplify only!

 Equations – can solve for an unknown or variable  Language – Sum, Difference, Product, Quotient

Properties of Equalities  Commutative  Associative  Distributive  Additive Inverse  Multiplicative Inverse

More Properties of Equality  Addition/Subtraction  Multiplication/Division  Using these properties to solve linear equations; one step and multi step

Strategies for Solving Equations  Use distributive property to get rid of parentheses  Simplify both sides of equation  Use addition/subtraction to get like terms on opposite sides  Use multiplication/division to isolate variable  Check your solution in original equation

More equations  Equations involving fractions  Equations involving decimals  Identities —infinitely many solutions  Conditional Equations- finite solutions  Inconsistent Equations- no real solutions

Formulas  Just like solving linear equations for a particular variable given values for others  Distance  Temperature conversions  Interest  Geometric formulas

Translating Verbal Expressions into Algebraic Expressions  Addition: Sum, add to, more than, increased by  Subtraction: less than, difference, decreased by  Multiplication: Product, twice, triple, half, percent  Division: ratio, quotient, half

Inequalities  ab means a lies to the right of b on the number line  Solution will be a set rather than 1 value  Graphing solution sets on the number line  Solve inequalities like equations; express answer as a set of numbers