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## Introductory Algebra Glossary

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**Introductory AlgebraGlossary**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: • {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.