52 terms

threlkeldmathTEACHER

solution of an equation

Any value or values that make an equation true.

substitution

Replacing a variable with a number to solve an equation.

equivalent equations

Equations that have the same solution.

addition property of equality (EOA)

Adding the same amount to both sides of an equation to keep it equal.

subtraction property of equality (EOS)

Subtracting the same amount from both sides of an equation to keep it equal.

multiplication property of equality (EOM)

Multiplying the same amount to both sides of an equation to keep it equal.

division property of equality (EOD)

Dividing the same amount to both sides of an equation to keep it equal.

solving for the variable

Using equality properties to simplify an equation to the point of finding the value or values of the variable that make the equation true.

isolating the variable

Using equality properties to isolate the variable to one side of the equation.

like terms

Terms that are only constants or are terms with variables that are identical. For example x^2y is a like term to -5x^2y, but is not a like term to 2xy. The x is not squared in 2xy, so the variables in the terms are not considered alike.

combining like terms

Simplifying like terms by combining their coefficients.

multiplicative inverse (reciprocal)

The flip side of a fraction or of a number written in fraction form. Example, the M.I. to 3 is 1/3 and the M.I. to -4/3 is -3/4. When multiplied, their solution is 1.

integer addition

Adding a negative number is the same as subtracting the positive of that number.

integer subtraction

Subtracting a negative number is the same as adding the positive of that number (2 - (-4) = 2 + 4)

integer multiplication

Multiplying a negative number by a positive number results in the product having a negative value. If both numbers being multiplied are negative, then their product is positive.

integer division

Dividing a negative number by a positive number results in the quotient having a negative value. If both numbers being divided are negative, then their quotient is positive.

matrix

A rectangular arrangement of numbers. The number of rows and columns determine its size. Each item in a matrix is called an element.

Inequality

When one expression is less than, greater than, less than or equal to, or greater than or equal to another expression.

solving an inequality with a negative coefficient

When dividing or multiplying an entire inequality by a negative number, the inequality will flip. > will become <, and vice versa.

compound inequalites

Two inequalities that are joined by the word "and" or the word "or".

coefficient

The number that is multiplied by the variable with exponents that are whole numbers (like the 3 in 3x)

algebraic expression

An expression that contains at least one variable.

order of operations

A rule for evaluating expressions (PEMDAS/GEMDAS).

constant

A value that does not change.

numerical expression

An expression that contains only numbers and operations.

terms

The parts of an expression that are added or subtracted.

binomial

A polynomial with two terms.

monomial

A number or a product of numbers and variables with exponents that are whole numbers.

trinomial

A polynomial with three terms.

polynomial

An algebraic expression that is the sum or difference of two or more monomials.

additive inverse

The opposite of a number.

natural numbers

Counting numbers starting at one.

integers

Positive and negative whole numbers.

whole numbers

Counting numbers starting at zero.

absolute value

The distance a number is from zero on the number line.

inequality

A mathematical sentence that shows the relationship between quantities that are not equivalent.

equality

A mathematical sentence that shows the relationship between quantities that are equivalent.

algebraic equality

A mathematical sentence with at least one variable that shows two expressions are equivalent.

numerical equality

A mathematical sentence with only numbers that shows two expressions are equivalent.

real number

A number that exists and behaves rationally or irrationally.

imaginary number

A number that can't exist, such as zero to the zero power or the square root of a negative number.

factor

A number that is multiplied by another number to get a product.

power

A number produced by raising a base to an exponent.

variable

A symbol (usually a letter of the alphabet) used to represent a quantity that can change.

base

The number that is used as a factor when it is raised to a power.

exponent

The number that indicates how many times the base is used as a factor.

zero property

a(0) = 0 and a + -a = 0

associative property

(a+b)+c = a+(b+c) and (ab)c = a(bc)

commutative property

a+b+c = b+c+a and abc = cab

identity property

a+0 = a and a(1) = a

distributive property

3(a+b) = 3a + 3b (multiply what is on the outside of the parenthesis by each term inside, then lose the parenthesis)

U.P.S.C.

Understand, Plan, Solve, Check