a number that is either rational or irrational. ex: 5, -3, √11, 0.6666.., 5 4/11, 0, and π.

real numbers

a number that shows repeated multiplication.

exponent

a rate with a denominator of 1. ex: the ___ ___ of 120 miles driven in 2 hours is 60mi/hr.

unit rate

whole numbers and their opposites.

integers

terms with exactly the same variable factors in a variable expression.

like terms

numbers whose square roots are integers. ex: the numbers 1, 4, 9, 16, 25, 36… are the squares of integers.

perfect square

- performing any operations inside grouping symbols
- simplify powers
- multiply and divide in order from right to left
- add and subtract in order from right to left.

order of operations

the distance that a number is from zero on a number line. ex: -7 is 7 units from 0, so |-7| = 7.

absolute value

a number that is multiplied repeatedly. ex: 4^5= 4•4•4•4•4. the ____ 4 is used as a factor 5 times.

base

a process of reasoning logically from given facts to a conclusion. ex: based on the fact that the sum of any two even numbers is even, you can deduce that the product of any whole number and any even number is even.

deductive reasoning

a mathematical phrase that includes one or more variables. ex: 7+x is an ______ _____.

algebraic expression

an expression made up of a _____ symbol and a radicand. ex: √a.

radical

anything that can be measured or counted. ex: a dozen is another way to describe a ____ of 12 eggs.

quantity

to replace an expression with it’s ____ name or form. ex: 3+5=8.

simplify

given a nonzero rational number a/b, the ________ ______, or reciprocal, is b/a. the product of a ________ ______ is 1.

multiplicative inverse (reciprocal)

to substitute a given number for each variable and then simplify.

evaluate

a real number that can be written as a ratio of two integers. _____ numbers in decimal form are terminating or repeating. ex: 2/3, 1.548,and 2.292929…

rational number

a number *b* such that a^{2}=b. -√b is the negative _____ ____. ex: -3 and 3 are square roots of 9.

square root

the expression under the radical sign. ex: the ____ of the radical expression √x+2 is x+2.

radicand

a symbol, usually a letter, that represents one or more numbers. ex: x is the ____ in the equation 9-x=3.

variable

for every real number a, b, and c: a(b+c)=ab+ac, (b+c)a=ba+ca, a(b-c)=ab-ac,(b-c)a=ba-ca.

distributive property

the base and the exponent of an expression of the form a^n, ex: 5^4.

power

a mathematical phrase involving numbers and operation symbols, but no variables.

numerical expression

the counting numbers. ex: 1, 2, 3, 4 …

natural numbers

a number that cannot be written as a ration of two integers. ________ ________ in decimal form are non terminating and non repeating.

irrational number

the non-negative numbers. ex: 0, 1, 2, 3, 4…

whole numbers

an example showing that a statement is false. ex: all apples are red. the _____ ______ would be granny smith apples are green.

counter example

a term that has no variable factor. ex: in the expression 4x+13y+17, 17 is a ______ term.

constant

the opposite or ______ ______ of any number a is -a. the sum of the opposites is 0. ex: -5 and 5 are ______ ______ because -5+5=0.

additive inverse

the process in of making something look like another thing

modeling

the numerical factor when a term has a variable. ex: in the expression 2x+3y+16, 2 and 3 are _______.

coefficient