Transcript Introductory Algebra Glossary

Introductory Algebra
Glossary
Unit One of Nine Units
Introduction
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natural numbers
The numbers used for counting:
{1, 2, 3, 4, ...}.
whole numbers
The set of whole numbers is:
{0, 1, 2, 3, 4, 5, ...}.
numerator
The number above the fraction
bar that shows how many
equivalent parts are being
considered.
denominator
The number below the fraction
bar in a fraction. It shows the
number of equal parts in a
whole.
factor
Any number that divides evenly
(without remainder) into the
given number:
1, 2, 3 and 6 are factors of 6.
product
The answer to a multiplication
problem.
6 is the product of 2 times 3.
factored
A number is factored by writing it
as the product of two or more
numbers.
6 is factored as 2 times 3.
prime number
A natural number (except one)
that has only one and itself as
factors.
2, 3, 5, 7, 11, 13, and 17 are
prime numbers.
composite number
A composite number has at least
one factor other than itself and
one.
greatest common factor
(GCF)
The largest common factor of a
list of integers or the largest
term that is a factor of all terms
in the polynomial.
lowest terms
A fraction is in lowest terms when
there are no common factors in
the numerator and denominator
(except 1).
reciprocals
Pairs of numbers whose product
is 1:
1/3 and 3 are reciprocals.
quotient
The answer to a division
problem.
sum
The answer to an addition
problem.
least common
denominator (LCD)
Given several denominators, the
smallest expression that is
divisible by all the denominators
is called the least common
denominator.
mixed number
A whole number and a fraction
written together and understood
to be their sum.
difference
The answer to a subtraction
problem.
exponent (power)
A number that indicates how
many times a factor is repeated:
Given 23 the exponent is three.
base
The number that is a repeated
factor when written with an
exponent:
Given 23 the base is two.
exponential expression
A number or letter (variable)
written with an exponent:
Examples: 23 or x6.
grouping symbols
Parentheses, ( ), square
brackets, [ ], or fraction bars.
variable
A variable is a symbol used to
represent an unknown number:
In the term 3x the variable is x.
algebraic expression
Any collection of numbers or
variables joined by the basic
operations of addition,
subtraction, multiplication, or
division (except by zero), or the
operation of taking roots.
equation
A statement that two algebraic
expressions are equal:
Example: 4x = 5y.
solution of an equation
Any replacement for the variable
that makes the equation true.
set
A collection of objects.
elements (members)
The objects that belong to a set.
number line
A line with a scale that is used to
show how numbers relate to
each other.
negative number
A number located to the left of
zero on a number line.
positive number
A number located to the right of
zero on the number line.
signed numbers
Numbers that can be written with
a positive or negative sign.
integers
The set of integers is:
{...-3, -2, -1, 0, 1, 2, 3,...}.
graph of a number
The point on a number line that
corresponds to a number is its
graph.
rational numbers
Rational numbers can be written
as the quotient of two integers,
with denominator not zero.
set-builder notation
Set-builder notation is used to
describe a set of numbers
without actually having to list all
of the elements.
irrational numbers
Irrational numbers cannot be
written as the quotient of two
integers but can be represented
by points on the number line.
real numbers
All numbers that can be
represented by points on the
number line, that is, all rational
and irrational numbers.
additive inverse
Two numbers that are the same
distance from zero on a number
line but on opposite sides of
zero. The sum of two additive
inverses equals zero.
absolute value
The distance between zero and a
number on a number line.
multiplicative inverse
(reciprocal)
The multiplicative inverse of a
nonzero real number a is 1/a.
The product of multiplicative
inverses is one.
commutative property of
addition
The order of numbers in an
addition problem can be
changed without changing the
sum:
6+4+3=3+6+4
commutative property of
multiplication
The product in a multiplication
problem remains the same
regardless of the order of the
factors:
6•4=4•6
associative property of
addition
The way in which numbers being
added are grouped does not
change the sum:
6 + (3 + 2) = (6 + 3) + 2
associative property of
multiplication
The way in which numbers being
multiplied are grouped does not
change the product:
6 • (2 • 3) = (6 • 2) • 3
identity property
The sum of zero and any number
equals the number, and the
product of one and any number
equals the number:
X+0=x
x•1=x
inverse property
A number added to its opposite is
zero and a number multiplied by
its reciprocal is one:
1 + (-1) = 0
1 • (1/2) = 1
distributive property
For any real numbers a, b, and c,
the distributive property states
that:
a (b + c) = ab + ac.
term
A number, a variable, or the
product or quotient of a number
and one or more variables
raised to powers.
numerical coefficient
The numerical factor in a term. In
the term 6x2 the numerical
coefficient is 6.
like terms
The same variables raised to
exactly the same powers. The
terms 2x2 and 7x2 are like
terms.
unlike terms
Terms that do not have the same
variable or the variables are not
raised to the same powers. The
terms 2x2 and 7x3 are unlike
terms.
combining like terms
A method of adding or
subtracting like terms by using
the properties of real numbers:
2x2 + 7x2 = 9x2.
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Introductory Algebra
Created by
James Q. Jacobs