If I missed a definition, let me know and I'll put it on.

###
arithmetic operations

addition, subtraction, multiplication, division

###
expression

collections of numbers, operation signs, and indusion symbols

###
evaluating

finding the number for which the expressions stands

###
variable

a letter representing a number

###
terms

numbers that are added or subtracted from each other.

###
additive inverses

two numbers that their sum is zero

###
multiplicative inverses

two numbers that product equals 1

###
division

multiplying by its reciprocal

###
commute

an expression meaning to interchange their positions

###
associate

to associate two of the numbers in an expression means to group them with parenthesis so that the operation between them is done first

###
property

the property of a mathematical symbol is a fact that is true concerning the system

###
axiom

a property that forms the basis of a mathematical system. assumed without proof

###
distributive axiom

x(y+z)=xy+xz

###
like terms

two terms in an expressions are like terms if they have the same variables raised to the same power

###
numerical coefficient

the numerical coefficient of a term is the constant that is multiplied by the variables

###
common factor

in an expression c is a common factor if c is a factor of each term