Introductory Algebra Glossary

1
Introductory Algebra Glossary

• Unit One of Nine Units

2
Introduction

• WELCOME
• Using the Introductory Algebra Glossary is
  simple.
• Click thru the slide show and check your
  knowledge of definitions before you display them.

3
natural numbers

• The numbers used for counting
• 1, 2, 3, 4, ....

4
whole numbers

• The set of whole numbers is
• 0, 1, 2, 3, 4, 5, ....

5
numerator

• The number above the fraction bar that shows how
  many equivalent parts are being considered.

6
denominator

• The number below the fraction bar in a fraction.
  It shows the number of equal parts in a whole.

7
factor

• Any number that divides evenly (without
  remainder) into the given number
• 1, 2, 3 and 6 are factors of 6.

8
product

• The answer to a multiplication problem.
• 6 is the product of 2 times 3.

9
factored

• A number is factored by writing it as the product
  of two or more numbers.
• 6 is factored as 2 times 3.

10
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.

11
composite number

• A composite number has at least one factor other
  than itself and one.

12
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.

13
lowest terms

• A fraction is in lowest terms when there are no
  common factors in the numerator and denominator
  (except 1).

14
reciprocals

• Pairs of numbers whose product is 1
• 1/3 and 3 are reciprocals.

15
quotient

• The answer to a division problem.

16
sum

• The answer to an addition problem.

17
least common denominator (LCD)

• Given several denominators, the smallest
  expression that is divisible by all the
  denominators is called the least common
  denominator.

18
mixed number

• A whole number and a fraction written together
  and understood to be their sum.

19
difference

• The answer to a subtraction problem.

20
exponent (power)

• A number that indicates how many times a factor
  is repeated
• Given 23 the exponent is three.

21
base

• The number that is a repeated factor when written
  with an exponent
• Given 23 the base is two.

22
exponential expression

• A number or letter (variable) written with an
  exponent
• Examples 23 or x6.

23
grouping symbols

• Parentheses, ( ), square brackets, , or
  fraction bars.

24
variable

• A variable is a symbol used to represent an
  unknown number
• In the term 3x the variable is x.

25
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.

26
equation

• A statement that two algebraic expressions are
  equal
• Example 4x 5y.

27
solution of an equation

• Any replacement for the variable that makes the
  equation true.

28
set

• A collection of objects.

29
elements (members)

• The objects that belong to a set.

30
number line

• A line with a scale that is used to show how
  numbers relate to each other.

31
negative number

• A number located to the left of zero on a number
  line.

32
positive number

• A number located to the right of zero on the
  number line.

33
signed numbers

• Numbers that can be written with a positive or
  negative sign.

34
integers

• The set of integers is
• ...-3, -2, -1, 0, 1, 2, 3,....

35
graph of a number

• The point on a number line that corresponds to a
  number is its graph.

36
rational numbers

• Rational numbers can be written as the quotient
  of two integers, with denominator not zero.

37
set-builder notation

• Set-builder notation is used to describe a set of
  numbers without actually having to list all of
  the elements.

38
irrational numbers

• Irrational numbers cannot be written as the
  quotient of two integers but can be represented
  by points on the number line.

39
real numbers

• All numbers that can be represented by points on
  the number line, that is, all rational and
  irrational numbers.

40
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.

41
absolute value

• The distance between zero and a number on a
  number line.

42
multiplicative inverse (reciprocal)

• The multiplicative inverse of a nonzero real
  number a is 1/a. The product of multiplicative
  inverses is one.

43
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

44
commutative property of multiplication

• The product in a multiplication problem remains
  the same regardless of the order of the factors
• 6 4 4 6

45
associative property of addition

• The way in which numbers being added are grouped
  does not change the sum
• 6 (3 2) (6 3) 2

46
associative property of multiplication

• The way in which numbers being multiplied are
  grouped does not change the product
• 6 (2 3) (6 2) 3

47
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

48
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

49
distributive property

• For any real numbers a, b, and c, the
  distributive property states that
• a (b c) ab ac.

50
term

• A number, a variable, or the product or quotient
  of a number and one or more variables raised to
  powers.

51
numerical coefficient

• The numerical factor in a term. In the term 6x2
  the numerical coefficient is 6.

52
like terms

• The same variables raised to exactly the same
  powers. The terms 2x2 and 7x2 are like terms.

53
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.

54
combining like terms

• A method of adding or subtracting like terms by
  using the properties of real numbers
• 2x2 7x2 9x2.

55
Return to Introductory Algebra

• Created by
• James Q. Jacobs