Chpt. 1, Expressions, Equations, and Inequalities Flashcards
constant
A quantity whose value does not change.
variable
A quantity that is capable of variation. It is indicated with a symbol, usually a letter, that represents a number or expression. Example = “x”
numerical expression (or just expression)
A mathematical phrase that contains numbers and operation symbols. Example = 3 + 5
algebraic expression (or just expression)
A mathematical phrase that contains one or more variables. Example = 3x +_5
opposite
The opposite, or additive inverse, of any number a, is -a. the sum of opposites is zero, the additive identity.
reciprocal
The reciprocal, or multiplicative inverse, of any number a is 1/a. The product of inverses is 1, the additive identity.
commutative property of addition
commutative property of multiplication
associative property of addition
a + b = b + a
ab = ba
a + (b+c) = (a+b) + c
associative property of multiplication
distributive property
additive identity property
a * (bc) = (ab) * c
a * (b-c) = ab - ac
a + 0 = 0 +a = a
multiplicative identity property
additive inverse property
multiplicative inverse
a1 = 1a = a
a +(-a) = 0
a*(1/a) = 1
reflexive property
symmetrical property
transitive property
a = a
if a = b, then b = a
if a = b, and b = c, then a = c
substitution property
definition of subtraction
definition of division
if a = b, then b can replace a in any equation
a - b = a +(-b)
0/a = 0, a/a =1, a/0 = undefined
zero product property
closure property
if ab = 0, then a = 0, or b = 0
if a and b are real numbers, then a +b and ab are also real numbers
evaluate (an expression)
To do this, numbers must be plugged into each of the variables in the expression, and the expression must be simplified using the order of operations.
term (of an expression)
This is a number, a variable, or the product of one or more numbers or variables.
coefficient
The numerical factor in a term. Example is the number “3” in y = 3x.
