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