Introductory algebra glossary
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Introductory Algebra Glossary. Unit One of Nine Units. Introduction. WELCOME Using the Introductory Algebra Glossary is simple. Click thru the slide show and check your knowledge of definitions before you display them. natural numbers . The numbers used for counting:

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Introductory algebra glossary l.jpg

Introductory AlgebraGlossary

Unit One of Nine Units


Introduction l.jpg
Introduction

  • WELCOME

  • Using the Introductory Algebra Glossary is simple.

  • Click thru the slide show and check your knowledge of definitions before you display them.


Natural numbers l.jpg
natural numbers

  • The numbers used for counting:

  • {1, 2, 3, 4, ...}.


Whole numbers l.jpg
whole numbers

  • The set of whole numbers is:

  • {0, 1, 2, 3, 4, 5, ...}.


Numerator l.jpg
numerator

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


Denominator l.jpg
denominator

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


Factor l.jpg
factor

  • Any number that divides evenly (without remainder) into the given number:

  • 1, 2, 3 and 6 are factors of 6.


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product

  • The answer to a multiplication problem.

  • 6 is the product of 2 times 3.


Factored l.jpg
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 l.jpg
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 l.jpg
composite number

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


Greatest common factor gcf l.jpg
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 l.jpg
lowest terms

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


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reciprocals

  • Pairs of numbers whose product is 1:

  • 1/3 and 3 are reciprocals.


Quotient l.jpg
quotient

  • The answer to a division problem.


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sum

  • The answer to an addition problem.


Least common denominator lcd l.jpg
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 l.jpg
mixed number

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


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difference

  • The answer to a subtraction problem.


Exponent power l.jpg
exponent (power)

  • A number that indicates how many times a factor is repeated:

  • Given 23 the exponent is three.


Slide21 l.jpg
base

  • The number that is a repeated factor when written with an exponent:

  • Given 23 the base is two.


Exponential expression l.jpg
exponential expression

  • A number or letter (variable) written with an exponent:

  • Examples: 23 or x6.


Grouping symbols l.jpg
grouping symbols

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


Variable l.jpg
variable

  • A variable is a symbol used to represent an unknown number:

  • In the term 3x the variable is x.


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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 l.jpg
equation

  • A statement that two algebraic expressions are equal:

  • Example: 4x = 5y.


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solution of an equation

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


Slide28 l.jpg
set

  • A collection of objects.


Elements members l.jpg
elements (members)

  • The objects that belong to a set.


Number line l.jpg
number line

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


Negative number l.jpg
negative number

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


Positive number l.jpg
positive number

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


Signed numbers l.jpg
signed numbers

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


Integers l.jpg
integers

  • The set of integers is:

  • {...-3, -2, -1, 0, 1, 2, 3,...}.


Graph of a number l.jpg
graph of a number

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


Rational numbers l.jpg
rational numbers

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


Set builder notation l.jpg
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 l.jpg
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 l.jpg
real numbers

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


Additive inverse l.jpg
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 l.jpg
absolute value

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


Multiplicative inverse reciprocal l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
distributive property

  • For any real numbers a, b, and c, the distributive property states that:

  • a (b + c) = ab + ac.


Slide50 l.jpg
term

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


Numerical coefficient l.jpg
numerical coefficient

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


Like terms l.jpg
like terms

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


Unlike terms l.jpg
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 l.jpg
combining like terms

  • A method of adding or subtracting like terms by using the properties of real numbers:

  • 2x2 + 7x2 = 9x2.


Return to introductory algebra l.jpg
Return toIntroductory Algebra

  • Created by

  • James Q. Jacobs


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