by David Kedrowski 14 years ago
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All rational and irrational numbers taken together.
Any number you can find on a number line.
Numbers that cannot be written as a ratio of two integers.
Includes all nonrepeating, nonterminating decimals
Any number of the form p/q, where p and q are integers and q is not zero
Includes all terminating decimals and all nonterminating repeating decimals
Integers
{ . . . , -3, -2, -1, 0, 1, 2, 3, . . . }
Whole Numbers
{ 0, 1, 2, 3, . . . }
Natural Numbers
{ 1, 2, 3, . . . }
When subtracting two real numbers:
Remember, to convert a subtraction problem to addition, you add the opposite of the value between subtracted
When adding two real numbers:
When dividing two real numbers:
Remember:
When multiplying two real numbers:
When multiplying more than two real numbers:
The absolute value of a number is the distance between that number and 0 on the number line
The absolute value of a number is always positive or zero (nonnegative).
Substituting values for the variables in an algebraic expression and simplifying using the order of operations.
Each term has a coefficient, or numeric part.
A term is a numbers or a variable or a product or quotient of numbers and variables.
An algebraic expression is a collection of numbers, variables, and grouping symbols connected by operations symbols.
Multiplication over addition: a(b+c) = ab + ac
Multiplication over subtraction: a(b-c) = ab - ac
Addition: a+(-a) = 0
Multiplication: a(1/a) = 1 [a not zero]
Addition: a+0 = a
Multiplication: 1a = a
Addition: a+(b+c) = (a+b)+c
Multiplication: a(bc) = (ab)c
Addition: a+b = b+a
Multiplication: ab = ba
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: 2 x pi x radius, or pi x diameter
Area: pi x radius squared
Quadrilateral with one pair of opposite sides parallel
Perimeter: The sum of the length of all four sides
Area: average length of the bases x height
Quadrilateral with opposite sides parallel
Perimeter: The sum of the length of all four sides
Area: base x height
Three sided enclosed figure
Perimeter: The sum of the length of all three sides
Area: 0.5 x base x height
Rectangle: Parallelogram with four right angles
Square: Rectangle with all sides equal
Perimeter: The sum of the length of all four sides
Area: Base x height
Two angles that add to 180 degrees
Two angles that add to 90 degrees
Perform addition and subtraction from left to right.
Perform multiplication and division from left to right.
Simplify expressions with exponents
If parentheses or other grouping symbols appear in an expression, simplify what is in these grouping symbols first.
Put the fractions over a common denominator
Subtract the second numerator from the first numerator and keep the common denominator
Write the answer in simplest terms
Put all fractions over a common denominator
Add the numerators and keep the common denominator
Write the answer in simplest terms
Make sure denominators are not zero at every step
Multiply the first fraction by the reciprocal of the second fraction
Write the answer in simplest terms
Denominators cannot be zero
Multiply straight across and express the answer in simplest terms
