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; nonrepeating, 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
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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
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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
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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
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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
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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