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

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

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**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

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**The Real Number Line Ordering numbers**

Graphing numbers on a number line Interval Notation– ( ), [ ], ( ] Unbounded intervals

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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

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**Fractions Equivalent fractions Finding common denominators**

Adding, subtracting fractions- first find a common denominator Multiplying, dividing Adding mixed numbers Decimals and percents

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**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

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**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

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**Exponential Expressions**

An exponent tells you to multiply repeatedly a3=a x a x a Exponent also called “power”

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**Order of Operations Please Excuse My Dear Aunt Sally**

P- parentheses– grouping E- Exponents M- Multiply D- Divide A- Add S- Subtract

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**Algebraic Expressions and Equations**

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

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**Properties of Equalities**

Commutative Associative Distributive Additive Inverse Multiplicative Inverse

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**More Properties of Equality**

Addition/Subtraction Multiplication/Division Using these properties to solve linear equations; one step and multi step

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**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

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**More equations Equations involving fractions**

Equations involving decimals Identities—infinitely many solutions Conditional Equations- finite solutions Inconsistent Equations- no real solutions

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

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**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

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**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

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