A review of concepts and computational skills Chapters 1-2 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 a3=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 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