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Introductory Algebra GlossaryPowerPoint Presentation

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.

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.

Return toIntroductory Algebra

- Created by
- James Q. Jacobs

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