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# introductory algebra glossary - PowerPoint PPT Presentation

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 AlgebraGlossary

Unit One of Nine Units

• WELCOME

• Using the Introductory Algebra Glossary is simple.

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

• The numbers used for counting:

• {1, 2, 3, 4, ...}.

• The set of whole numbers is:

• {0, 1, 2, 3, 4, 5, ...}.

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

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

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

• 1, 2, 3 and 6 are factors of 6.

• The answer to a multiplication problem.

• 6 is the product of 2 times 3.

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

• 6 is factored as 2 times 3.

• A natural number (except one) that has only one and itself as factors.

• 2, 3, 5, 7, 11, 13, and 17 are prime numbers.

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

• The largest common factor of a list of integers or the largest term that is a factor of all terms in the polynomial.

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

• Pairs of numbers whose product is 1:

• 1/3 and 3 are reciprocals.

• The answer to a division problem.

• The answer to an addition problem.

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

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

• The answer to a subtraction problem.

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

• Given 23 the exponent is three.

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

• Given 23 the base is two.

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

• Examples: 23 or x6.

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

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

• In the term 3x the variable is x.

• 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.

• A statement that two algebraic expressions are equal:

• Example: 4x = 5y.

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

• A collection of objects.

• The objects that belong to a set.

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

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

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

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

• The set of integers is:

• {...-3, -2, -1, 0, 1, 2, 3,...}.

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

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

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

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

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

• 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.

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

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

• The order of numbers in an addition problem can be changed without changing the sum:

• 6 + 4 + 3 = 3 + 6 + 4

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

• 6 • 4 = 4 • 6

• The way in which numbers being added are grouped does not change the sum:

• 6 + (3 + 2) = (6 + 3) + 2

• The way in which numbers being multiplied are grouped does not change the product:

• 6 • (2 • 3) = (6 • 2) • 3

• 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

• A number added to its opposite is zero and a number multiplied by its reciprocal is one:

• 1 + (-1) = 0 1 • (1/2) = 1

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

• a (b + c) = ab + ac.

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

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

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

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

• 2x2 + 7x2 = 9x2.