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A review of concepts and computational skills Chapters 1-2

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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

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