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variable expression

numeric expression

simplifying expression

grouping symbols

an expression that contains a variable (a symbol used to repr…

an expression, such as 4.50 x 4, that names a particular number

replacing a numerical expression by the simplest name for its…

a device, such as a pair of parentheses, used to enclose an e…

variable expression

an expression that contains a variable (a symbol used to repr…

numeric expression

an expression, such as 4.50 x 4, that names a particular number

properties of equality

equivalent equations

solutions of equations

identity

When you perform a math operation to one side of an equation,…

Equations that have the same solution set over a given domain

values of the variable that make equations true.

an equation that is true for every value of the variables

properties of equality

When you perform a math operation to one side of an equation,…

equivalent equations

Equations that have the same solution set over a given domain

whole numbers

integers

rational numbers

irrational numbers

0,1,2,3,4,5,...

...,-3,-2,-1,0,1,2,3,...

numbers such as (3/4), (1/3), and (-4/1) (or -4) that can be…

real numbers that are not rational, such as √2 and π. when wr…

whole numbers

0,1,2,3,4,5,...

integers

...,-3,-2,-1,0,1,2,3,...

variable expression

numeric expression

simplifying expression

grouping symbols

an expression that contains a variable (a symbol used to repr…

an expression, such as 4.50 x 4, that names a particular number

replacing a numerical expression by the simplest name for its…

a device, such as a pair of parentheses, used to enclose an e…

variable expression

an expression that contains a variable (a symbol used to repr…

numeric expression

an expression, such as 4.50 x 4, that names a particular number

Graph of an Inequality

< or >

_< or _>

Equivalent Inequalities

One variable is the set of points that represent all solution…

open circle

closed circle

inequalities that have the same solutions

Graph of an Inequality

One variable is the set of points that represent all solution…

< or >

open circle

variable

variable expression

numerical expression

power

a symbol (like x or y) that is used in mathematical or logica…

consists of constants (numbers), variables, and operations

an expression that includes numbers and operations

a mathematical expression with a base and an exponent

variable

a symbol (like x or y) that is used in mathematical or logica…

variable expression

consists of constants (numbers), variables, and operations

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

changing the order of addends does not change the sum, i.e. i…

changing the order of factors does not change the product, i.…

when we add more than two numbers the grouping of the addends…

when we multiply more than two numbers the grouping of the fa…

commutative property of addition

changing the order of addends does not change the sum, i.e. i…

commutative property of multiplication

changing the order of factors does not change the product, i.…

real number

integer

opposite

absolute value

any positive or negative number that can be shown on the numb…

the whole numbers and their opposites plus zero

two numbers that are the same distance from zero on the numbe…

The distance a number is from zero on a number line

real number

any positive or negative number that can be shown on the numb…

integer

the whole numbers and their opposites plus zero

Quantity

Variable

Algebraic expression

Numerical expression

Anything than can be measured or counted.

A symbol, usually a letter, that represents one or more numbe…

A mathematical phrase that includes one or more variables.

A mathematical phrase involving numbers and operation symbols…

Quantity

Anything than can be measured or counted.

Variable

A symbol, usually a letter, that represents one or more numbe…

Real Number

Real Number Line

Origin

Positive Numbers

The set of numbers consisting of the positive numbers, the ne…

A line that pictures real numbers as points.

The point labeled zero on a number line.

Any of the numbers greater than zero.

Real Number

The set of numbers consisting of the positive numbers, the ne…

Real Number Line

A line that pictures real numbers as points.

variable

algebraic expression

power

exponent

a letter used to represent one or more numbers

consists of numbers, variables, and operations

expression that represents repeated multiplication of the sam…

the number of times a base is used as a factor

variable

a letter used to represent one or more numbers

algebraic expression

consists of numbers, variables, and operations

variable

variable expression

numerical expression

power

a symbol (like x or y) that is used in mathematical or logica…

consists of constants (numbers), variables, and operations

an expression that includes numbers and operations

a mathematical expression with a base and an exponent

variable

a symbol (like x or y) that is used in mathematical or logica…

variable expression

consists of constants (numbers), variables, and operations

variable

variable expression

numerical expression

power

a symbol (like x or y) that is used in mathematical or logica…

consists of constants (numbers), variables, and operations

an expression that includes numbers and operations

a mathematical expression with a base and an exponent

variable

a symbol (like x or y) that is used in mathematical or logica…

variable expression

consists of constants (numbers), variables, and operations

Quantity

Variable

Algebraic expression

Numerical expression

Anything than can be measured or counted.

A symbol, usually a letter, that represents one or more numbe…

A mathematical phrase that includes one or more variables.

A mathematical phrase involving numbers and operation symbols…

Quantity

Anything than can be measured or counted.

Variable

A symbol, usually a letter, that represents one or more numbe…

relation

domain x

range y

function

mapping, or pairing, of input values with output values

the set of input values

the set of output values

relation with only one output value for each input value

relation

mapping, or pairing, of input values with output values

domain x

the set of input values

variable

algebraic expression

power

exponent

a letter used to represent one or more numbers

consists of numbers, variables, and operations

expression that represents repeated multiplication of the sam…

the number of times a base is used as a factor

variable

a letter used to represent one or more numbers

algebraic expression

consists of numbers, variables, and operations

Variable

Value

Variable expression

Power

A variable is a letter used to represent an unknown number.

Numbers are the values of a variable.

A collection of numbers, variables, and operations.

An expression like 4 to the 6th

Variable

A variable is a letter used to represent an unknown number.

Value

Numbers are the values of a variable.

variable

variable expression

numerical expression

power

a symbol (like x or y) that is used in mathematical or logica…

consists of constants (numbers), variables, and operations

an expression that includes numbers and operations

a mathematical expression with a base and an exponent

variable

a symbol (like x or y) that is used in mathematical or logica…

variable expression

consists of constants (numbers), variables, and operations

Power

Exponent

Base

Simplify

A number produced by raising a base to an exponent

A mathematical notation indicating the number of times a quan…

a number that is multiplied repeatedly

to write an expression in a simpler form

Power

A number produced by raising a base to an exponent

Exponent

A mathematical notation indicating the number of times a quan…

real number

integer

opposite

absolute value

any positive or negative number that can be shown on the numb…

the whole numbers and their opposites plus zero

two numbers that are the same distance from zero on the numbe…

The distance a number is from zero on a number line

real number

any positive or negative number that can be shown on the numb…

integer

the whole numbers and their opposites plus zero

variable

algebraic expression

numerical expression

sum

A letter that stands in place of a value

a phrase (or expression) that includes one or more variables

a phrase (or expression) that only includes numbers and opera…

variable

A letter that stands in place of a value

algebraic expression

a phrase (or expression) that includes one or more variables

variable

algebraic expression

numerical expression

sum

A letter that stands in place of a value

a phrase (or expression) that includes one or more variables

a phrase (or expression) that only includes numbers and opera…

variable

A letter that stands in place of a value

algebraic expression

a phrase (or expression) that includes one or more variables

y-intercept

slope

slope-intercept form

point-slope form of a line through a g…

the y-coordinate of a point where the graph crosses the y-axis

the ratio of the vertical change (the rise) to the horizontal…

y=mx+b

y=m(x-h)+k

y-intercept

the y-coordinate of a point where the graph crosses the y-axis

slope

the ratio of the vertical change (the rise) to the horizontal…

Exponent

Inequality

Integer

Distributive Property

The little number above a bigger number

Greater than, less than signs, or greater than/less than equa…

Any number that is positive or negative that is a whole numbe…

Multiplying a number on the outside of a set of parenthesis t…

Exponent

The little number above a bigger number

Inequality

Greater than, less than signs, or greater than/less than equa…

relation

domain x

range y

function

mapping, or pairing, of input values with output values

the set of input values

the set of output values

relation with only one output value for each input value

relation

mapping, or pairing, of input values with output values

domain x

the set of input values

real number

integer

opposite

absolute value

any positive or negative number that can be shown on the numb…

the whole numbers and their opposites plus zero

two numbers that are the same distance from zero on the numbe…

The distance a number is from zero on a number line

real number

any positive or negative number that can be shown on the numb…

integer

the whole numbers and their opposites plus zero

Quantity

Variable

Algebraic expression

Numerical expression

Anything than can be measured or counted.

A symbol, usually a letter, that represents one or more numbe…

A mathematical phrase that includes one or more variables.

A mathematical phrase involving numbers and operation symbols…

Quantity

Anything than can be measured or counted.

Variable

A symbol, usually a letter, that represents one or more numbe…

constant

variable

numerical expression

variable expression

a number (without a variable)

a symbol representing one or more numbers

a phrase that only includes numbers and operations

a mathematical phrase that includes a variable

constant

a number (without a variable)

variable

a symbol representing one or more numbers

Equivalent equations

Inverse operations

Solution step

similar triangles

equations with the same solutions as the original equation

operations that undo each other, such as addition and subtrac…

The result of applying a transformation to an equation when s…

Two triangles are similar if they have equal corresponding an…

Equivalent equations

equations with the same solutions as the original equation

Inverse operations

operations that undo each other, such as addition and subtrac…

Origin

Graph of a number

Opposites

Absolute value

The point on a number line or graph labeled zero.

The point on a number line that corresponds to the number

Two numbers that are the same distance from the origin, but o…

The distance between the origin and the point representing th…

Origin

The point on a number line or graph labeled zero.

Graph of a number

The point on a number line that corresponds to the number

variable

variable expression

numerical expression

power

a symbol (like x or y) that is used in mathematical or logica…

consists of constants (numbers), variables, and operations

an expression that includes numbers and operations

a mathematical expression with a base and an exponent

variable

a symbol (like x or y) that is used in mathematical or logica…

variable expression

consists of constants (numbers), variables, and operations

Def. of a (binary) operation on A

Def. of a Group

Def. of an abelian group

Division algorithm

a rule that assigns each ordered pair (a,b) in A exactly one…

a group, (G,**) consists of a set, G, with an operation, **, s.…

a**b=b**a for all a,b in G (commutativity)

m=nq+r ... q=quotient, r=remainder, m,n are any integers... 0≤r<n

Def. of a (binary) operation on A

a rule that assigns each ordered pair (a,b) in A exactly one…

Def. of a Group

a group, (G,**) consists of a set, G, with an operation, **, s.…

The Division Algorithm

Divisibility Remark 1

Divisibility Remark 2

Definition of Divisibility

Let a, b be integers with b > 0. Then there exist unique inte…

If b divides a then -a = b(-c). In other words a and -a have…

a is a divisor of b where -a <=b <=a which is the same as |b|…

Let a and b be integers with b != 0. We say that b divides a…

The Division Algorithm

Let a, b be integers with b > 0. Then there exist unique inte…

Divisibility Remark 1

If b divides a then -a = b(-c). In other words a and -a have…

variable

algebraic expression

equation

open sentence

a symbol, usually a letter, that represents one or more numbers

a mathematical phrase that can include numbers, variables, an…

a mathematical sentence that uses an equal sign

an equation that contains one or more variables

variable

a symbol, usually a letter, that represents one or more numbers

algebraic expression

a mathematical phrase that can include numbers, variables, an…

additive identity

multiplication identity

commutative property of addition

commutative property of multiplication

the sum of a number, and the additive identity, 0, is the num…

the product of a number and the multiplication identity, 1, i…

changing the order of the addends will not change the sum: *a…

changing the order of the factors will not change the product…

additive identity

the sum of a number, and the additive identity, 0, is the num…

multiplication identity

the product of a number and the multiplication identity, 1, i…

Quantity

Variable

Algebraic expression

Numerical expression

Anything than can be measured or counted.

A symbol, usually a letter, that represents one or more numbe…

A mathematical phrase that includes one or more variables.

A mathematical phrase involving numbers and operation symbols…

Quantity

Anything than can be measured or counted.

Variable

A symbol, usually a letter, that represents one or more numbe…

Quantity

Variable

Algebraic expression

Numerical expression

Anything than can be measured or counted.

A symbol, usually a letter, that represents one or more numbe…

A mathematical phrase that includes one or more variables.

A mathematical phrase involving numbers and operation symbols…

Quantity

Anything than can be measured or counted.

Variable

A symbol, usually a letter, that represents one or more numbe…

Quantity

Variable

Algebraic expression

Numerical expression

Anything than can be measured or counted.

A symbol, usually a letter, that represents one or more numbe…

A mathematical phrase that includes one or more variables.

A mathematical phrase involving numbers and operation symbols…

Quantity

Anything than can be measured or counted.

Variable

A symbol, usually a letter, that represents one or more numbe…

RATIONAL NUMBER

IRRATIONAL NUMBER

INCREASED BY

DIMINISHED BY

Real number that can be a fraction, terminating decimal or re…

A number that goes on forever. It is a non-repeating or non-t…

RATIONAL NUMBER

Real number that can be a fraction, terminating decimal or re…

IRRATIONAL NUMBER

A number that goes on forever. It is a non-repeating or non-t…

relation

domain x

range y

function

mapping, or pairing, of input values with output values

the set of input values

the set of output values

relation with only one output value for each input value

relation

mapping, or pairing, of input values with output values

domain x

the set of input values

variable

algebraic expression

numerical expression

sum

A letter that stands in place of a value

a phrase (or expression) that includes one or more variables

a phrase (or expression) that only includes numbers and opera…

variable

A letter that stands in place of a value

algebraic expression

a phrase (or expression) that includes one or more variables

Quantity

Variable

Algebraic expression

Numerical expression

Anything than can be measured or counted.

A symbol, usually a letter, that represents one or more numbe…

A mathematical phrase that includes one or more variables.

A mathematical phrase involving numbers and operation symbols…

Quantity

Anything than can be measured or counted.

Variable

A symbol, usually a letter, that represents one or more numbe…

term

variable

coefficient

constant term

A number, a variable, or the product of a number and a variable

A letter that represents a value that can change or vary

A number multiplied by a variable in an algebraic expression.

A value that does not change; an integer without a variable i…

term

A number, a variable, or the product of a number and a variable

variable

A letter that represents a value that can change or vary