variable
a letter or symbol used to represent a value that can change
constant
a value that does not change
numerical expression
a mathematical expression that may contain only constants and operations
algebraic expression
a mathematical expression that may contain variables, constants, and operations
evaluate
to find the value of an expression
absolute value
the distance a number is from zero on the number line
opposites
two numbers are ___________ if their sum is zero
additive inverses
a number and its opposite
reciprocals
two numbers are ____________ if their product is 1
multiplicative inverses
a number and its reciprocal
power
an expression written with an exponent and a base
square root
a number that is multiplied by itself to form a product
perfect square
a number whose positive square root is a whole number
natural numbers
the counting numbers: 1, 2, 3, ...
whole numbers
the natural numbers and zero: 0, 1, 2, 3, ...
integers
whole numbers and their opposites: -3, -2, -1, 0, 1, 2, 3, ...
rational numbers
a number that can be expressed in the form a/b, where a and b are both integers and b does not equal zero.
terminating decimals
rational numbers in decimal form that have a finite number of digits: 1.5, 2.75, 4.0
repeating decimals
rational numbers in decimal form that have a block of one or more digits that repeats continuously
irrational numbers
a number that cannot be expressed in the form a/b. They include square roots of whole numbers that are not perfect squares and nonterminating decimals that do not repeat.
order of operations
PEMDAS.....parenthesis, exponents, multiplication/division from left to right, addition/subtraction from left to right
terms
the parts of an expression that are to be added or subtracted
like terms
terms that contain the same variables raised to the same powers
Commutative Property
you can add numbers in any order and multiply numbers in any order
Associative Property
when you are only adding or multiplying, you can group any of the numbers together
Distributive Property
you can multiply a number by a sum or multiply by each number in the sum and then add...the result is the same
coefficient
a number multiplied by a variable
coordinate plane
formed by the intersection of two perpendicular number lines called axes
axes
two perpendicular number lines that form the coordinate plane
origin
the point of intersection on the coordinate plane, which is 0
x-axis
the horizontal number line
y-axis
the vertical number line
ordered pair
used to describe a point on the coordinate plane and consists of an x-coordinate and a y-coordinate and is written (x, y)
x-coordinate
tells how many units to move left or right from the origin
y-coordinate
tells how many units to move up or down from the origin
quadrants
the axes divide the coordinate plane into four ________
input
the value substituted for x in a function
output
the value generated for y in a function