Ch 5 algebra expressions

counter example

A specific case which proves a statement false. (an example given that proves any statement thought to be true, to actually be false.)

define a variable

Choose a variable and a quantity for the variable to represent in an expression or equation.

algebra

a branch of math that involves expressions with variables

algebraic exression

a combination of variables, numbers, expressions, and at least one math operation

monomial

a number, variable or product of a number and one or more variables

arithmetic sequence

a sequence in which the difference between any two consecutive terms is the same.

variable

a symbol, usually a letter, used to represent a number in a math expression or sentence. For example: n is the variable in the equation 3n=15

constant

a term that does not contain a variable

factored form

an expression expressed as the product of its factors

simplest form

an expression is in simplest form when it is replaced by an equivalent expression having no like terms or parenthesis

sequence

an ordered list of numbers (a pattern) such as 0,1,2,3 or 2,4,6,8,10

term

each number in a sequence (numbers or variables separated by + or - in a math expression or equation

equivalent expression

expressions that have the same value

property

statement that is true for any number or variable

like terms

terms that contain the same variables raised to the same power (have the same exponent)

additive identity property

the sum of any number and zero is the number. (adding zero to any number does not change the number)

linear expression

an algebraic expression in which the variable is raised to the first power (makes a straight line when graphed)

coefficient

The numerical factor of a term that contains a variable. For example in the term 5n, 5 is the coefficient. in the term 62, 62 is the coefficient.

commutative property

The order in which two numbers are added or multiplied does not change their sum or product. For example 3+5=5+3 and 4*6=6*4

multiplicative identity property

The product of any number and 1 is the number ------ 3*1=3, 640 *1 = 640

multiplicative property of zero

The product of any number and zero is 0.

associative property

The way in which numbers are grouped does not change the sum or product. (Examples, 5+ (3+4) = (5+3)+4 and 6*(7*8)=(6*7)*8

distributive property

To multiply a sum by a number, multiplying each added of the sum by the number outside the parenthesis. (Example: a(b+c) = ab + ac 2(5+3) = 2(5)+2(3)

factor

To write a number as a product of its factors