Transcript Elementary Algebra
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