Denominators cannot be zeroMultiply straight across and express the answer in simplest terms
Divide
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Make sure denominators are not zero at every stepMultiply the first fraction by the reciprocal of the second fractionWrite the answer in simplest terms
Add
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Put all fractions over a common denominatorAdd the numerators and keep the common denominatorWrite the answer in simplest terms
Subtract
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Put the fractions over a common denominatorSubtract the second numerator from the first numerator and keep the common denominatorWrite the answer in simplest terms
The Order of Operations
1. Grouping Symbols
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If parentheses or other grouping symbols appear in an expression, simplify what is in these grouping symbols first.
2. Exponents
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Simplify expressions with exponents
3. Multiplication and Division
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Perform multiplication and division from left to right.
4. Addition and Subtraction
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Perform addition and subtraction from left to right.
Review Concepts from Geometry
Angles
Complementary
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Two angles that add to 90 degrees
Supplementary
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Two angles that add to 180 degrees
Rectangle / Square
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Rectangle: Parallelogram with four right anglesSquare: Rectangle with all sides equal
Perimeter & Area
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Perimeter: The sum of the length of all four sidesArea: Base x height
Triangle
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Three sided enclosed figure
Perimeter & Area
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Perimeter: The sum of the length of all three sidesArea: 0.5 x base x height
Parallelogram
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Quadrilateral with opposite sides parallel
Perimeter & Area
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Perimeter: The sum of the length of all four sidesArea: base x height
Trapezoid
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Quadrilateral with one pair of opposite sides parallel
Perimeter & Area
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Perimeter: The sum of the length of all four sidesArea: average length of the bases x height
Circle
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The locus (or set) of all points in a plane a given distance (radius) from a given point in the plane (the center of the circle)
Circumference & Area
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Circumference: 2 x pi x radius, or pi x diameterArea: pi x radius squared
Addition: a+(-a) = 0Multiplication: a(1/a) = 1 [a not zero]
Distributive Properties
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Multiplication over addition: a(b+c) = ab + acMultiplication over subtraction: a(b-c) = ab - ac
Learn the Vocabulary for Algebraic Expressions
Algebraic Expression
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An algebraic expression is a collection of numbers, variables, and grouping symbols connected by operations symbols.
Term
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A term is a numbers or a variable or a product or quotient of numbers and variables.
Coefficient
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Each term has a coefficient, or numeric part.
Evaluate
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Substituting values for the variables in an algebraic expression and simplifying using the order of operations.
Define Absolute Value and Perform Operations on Real Numbers
Absolute Value
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The absolute value of a number is the distance between that number and 0 on the number lineThe absolute value of a number is always positive or zero (nonnegative).
Multiply
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When multiplying two real numbers:if both numbers are positive, the answer is positiveif both numbers are negative, the answer is positiveif one number is negative and one number is positive, the answer is negativeWhen multiplying more than two real numbers:if there are an even number of negative factors, the answer is positiveif there are an odd number of negative factors, the answer is negative
Divide
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When dividing two real numbers:if both numbers are positive, the answer is positiveif both numbers are negative, the answer is positiveif one number is negative and one number is positive, the answer is negativeRemember:if the numerator is zero, the answer is zeroif the denominator is zero, the answer is undefinedboth results have no sign
Add
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When adding two real numbers:if both numbers are positive, add them to get a positive answerif both numbers are negative, add their absolute values and then make the result negativeif one number is negative and one number is positive, take the difference between their absolute values and apply the sign of the number with the larger absolute value
Subtract
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When subtracting two real numbers:convert the problem to addition and then follow those rulesRemember, to convert a subtraction problem to addition, you add the opposite of the value between subtracted
Define and Identify Sets of Numbers
Real Numbers
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All rational and irrational numbers taken together.Any number you can find on a number line.
Rational Numbers
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Any number of the form p/q, where p and q are integers and q is not zeroIncludes all terminating decimals and all nonterminating repeating decimals
Integers
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{ . . . , -3, -2, -1, 0, 1, 2, 3, . . . }
Whole Numbers
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{ 0, 1, 2, 3, . . . }
Natural Numbers
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{ 1, 2, 3, . . . }
Irrational Numbers
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Numbers that cannot be written as a ratio of two integers.Includes all nonrepeating, nonterminating decimals
