1. Elementary Algebra A review of concepts and computational skills Chapters 1-2

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

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

4. 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

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

6. 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

7. 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

8. Exponential Expressions • An exponent tells you to multiply repeatedly • a3=a x a x a • Exponent also called “power”

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

10. Algebraic Expressions and Equations • Expressions– can evaluate or simplify only! • Equations– can solve for an unknown or variable • Language– Sum, Difference, Product, Quotient

11. Properties of Equalities • Commutative • Associative • Distributive • Additive Inverse • Multiplicative Inverse

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

13. 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

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

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

16. 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

17. Inequalities • a<b means a lies to the left of b on the number line • a>b 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