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Math
Algebra
Number Theory
Videotext Module A, Unit 1, Part B, Lesson 1-8
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VideoText Algebra Unit 1 Part A Lesson 2
Terms in this set (28)
Well-Deﬁned Operation
an operation which satisﬁes the conditions of Existence (must get an answer), Uniqueness (must get only one answer for each number combination), and Closure (answer must be in the set we are working in).
Natural Numbers
the numbers we use to count objects. The complete set of natural numbers is shown as { 1, 2, 3, ...}, usually called "the set N." These numbers are also called counting numbers.
Whole Numbers
the natural numbers combined with the number O. The complete set of whole numbers is shown as {0, 1, 2, 3, ...} and usually called "the set W."
Integers
the whole numbers combined with all of their opposites. The complete set is shown as {..., "-3, -2, -1, 0, 1, 2, 3, ...}.
Rational Numbers
the numbers that can be represented as a ratio a/b , where a and b are integers and b is not 0. This set still includes all of the integers and is shown in set-builder notation as {a/bI a,b are integers, b not 0}.
Irrational Numbers
the numbers that cannot be represented as a ratio of integers.
Real Numbers
the set of numbers consisting of both rational and irrational numbers.
Fraction
a rational number written in the form a/b , where a and b are integers with b not 0.
Numerator
the top number in a fraction. It tells "how many" of an object you have.
Denominator
the bottom number in a fraction. It tells "what kind" of object you have.
Equivalent Forms
forms that have "equal value."
Decimal
a special rational number in which the denominator is 10, 100, 1000, and so on (a power of 10).
Terminating Decimal
a decimal number in which, starting with some digit, all digits to the right are 0. This type of decimal number can be read accurately to a deﬁnite number of places.
Repeating Decimal
a decimal in which, starting with some digit, all digits to the right consist of a repeated group of digits, not all of which are zero. This type of decimal number cannot be read accurately to a deﬁnite number of places.
Repetend
the group of repeating digits in a repeating decimal, indicated by a bar over the repeating group. For example, 6.84 with a bar over the last two numbers means 6.84848484...
Percent
a term meaning "for each 100" or "for every 100" and referring to a ratio of some number to 100. It is written with the percent sign (%), as in 36%, which means "36 for each 100" or 36/100 or 36 parts of 100.
Prime Number
a number which can be written as a product of whole numbers in only one way, itself times 1. For example, 13 is a prime number because it can be written only as 13 x 1.
Composite Number
a number which is "composed" of other numbers in that it can be written as a product of whole numbers in more than one way. For example, 18 is a composite number because it can be written as 18 x 1, 9 x 2, or 3 x 6.
Factoring
the process of writing composite numbers as products of other numbers.
Prime Factored Form
the unique factored form of a number which consists only of prime numbers. For example, the prime factored form of 12 is 2 x 2 x 3.
Eratosthenes' Sieve
the chart of numbers we use to "sift" the prime numbers out from all numbers. It was named for the Greek mathematician who designed the process.
Multiples of a Number
numbers you get by multiplying a given number by any of the counting numbers.
Common Multiples of Several Numbers
numbers common to the lists of multiples of several numbers.
Least Common Multiple of Several Numbers
the smallest of the common multiples of several numbers. It is sometimes abbreviated as LCM
Factors of a Number
whole numbers which could be multiplied to get the given number. For example, for 24 we could multiply 1 x 24 , 2x12 , 3x8 , or 4x6. Therefore l, 2, 3, 4, 6, 8, 12, and 24 are factors of 24.
Common Factors of Several Numbers
numbers common to the lists of factors of several given numbers.
Greatest Common Factor of Several Numbers
the greatest of the common factors of several numbers. It is sometimes abbreviated as GCF.
Relatively Prime Numbers
numbers whose greatest common factor is 1. For example, 8 and 9 are not prime numbers, but the only factor they have in common is 1.Therefore, they are prime, relative to one another.
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