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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; nonrepeating, 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