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Introductory Algebra Glossary

Introductory Algebra Glossary

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Introductory Algebra Glossary

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  1. Introductory AlgebraGlossary 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.