Videotext Module A, Unit 1 Flashcards

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Questions and Answers

What does a Well-Defined Operation satisfy?

Existence

Uniqueness

Closure

All of the above (correct)

What are Natural Numbers?

the numbers used to count objects, represented as {1, 2, 3,...}

What are Whole Numbers?

the natural numbers combined with the number 0, represented as {0, 1, 2, 3,...}

Define Integers.

the whole numbers combined with all of their opposites, represented as {..., -3, -2, -1, 0, 1, 2, 3,...} Signup and view all the answers

What are Rational Numbers?

numbers that can be represented as a ratio a/b, where a and b are integers and b is not 0. Signup and view all the answers

What are Irrational Numbers?

numbers that cannot be represented as a ratio of integers. Signup and view all the answers

Define Real Numbers.

the set of numbers consisting of both rational and irrational numbers. Signup and view all the answers

What is a Fraction?

a rational number written in the form a/b, where a and b are integers with b not 0. Signup and view all the answers

What is a Numerator?

the top number in a fraction, telling how many of an object you have. Signup and view all the answers

What is a Denominator?

the bottom number in a fraction, indicating what kind of object you have. Signup and view all the answers

Define Equivalent Forms.

forms that have equal value. Signup and view all the answers

What is a Decimal?

a special rational number in which the denominator is 10, 100, 1000, and so on. Signup and view all the answers

What is a Terminating Decimal?

a decimal number in which, starting with some digit, all digits to the right are 0. Signup and view all the answers

What is a Repeating Decimal?

a decimal in which all digits to the right consist of a repeated group of digits. Signup and view all the answers

What is a Repetend?

the group of repeating digits in a repeating decimal. Signup and view all the answers

What does Percent mean?

for each 100 or for every 100, referring to a ratio of some number to 100. Signup and view all the answers

Define Prime Number.

a number that can be written as a product of whole numbers in only one way, itself times 1. Signup and view all the answers

What is a Composite Number?

a number that can be written as a product of whole numbers in more than one way. Signup and view all the answers

What is Factoring?

the process of writing composite numbers as products of other numbers. Signup and view all the answers

What is Prime Factored Form?

the unique factored form of a number which consists only of prime numbers. Signup and view all the answers

What is Eratosthenes' Sieve?

the chart of numbers used to sift the prime numbers out from all numbers. Signup and view all the answers

What are Multiples of a Number?

numbers you get by multiplying a given number by any of the counting numbers. Signup and view all the answers

What are Common Multiples of Several Numbers?

numbers that are common to the lists of multiples of several numbers. Signup and view all the answers

Define Least Common Multiple of Several Numbers.

the smallest of the common multiples of several numbers, often abbreviated as LCM. Signup and view all the answers

What are Factors of a Number?

whole numbers which could be multiplied to get the given number. Signup and view all the answers

What are Common Factors of Several Numbers?

numbers common to the lists of factors of several given numbers. Signup and view all the answers

What is the Greatest Common Factor of Several Numbers?

the greatest of the common factors of several numbers, often abbreviated as GCF. Signup and view all the answers

What are Relatively Prime Numbers?

numbers whose greatest common factor is 1. Signup and view all the answers

Study Notes

Well-Defined Operations

Satisfies conditions of Existence (must yield an answer), Uniqueness (only one answer for each combination), and Closure (results remain within the defined set).

Natural Numbers

Used for counting objects, represented as {1, 2, 3,...}, referred to as "set N" or counting numbers.

Whole Numbers

Combine natural numbers with the number 0, represented as {0, 1, 2, 3,...}, known as "set W."

Integers

Comprise whole numbers and their opposites, represented as {..., -3, -2, -1, 0, 1, 2, 3,...}.

Rational Numbers

Can be expressed as a ratio a/b, where both a and b are integers and b ≠ 0; includes all integers and denoted in set-builder notation as {a/b | a, b are integers, b ≠ 0}.

Irrational Numbers

Cannot be expressed as a ratio of integers, representing non-repeating and non-terminating decimals.

Real Numbers

Include both rational and irrational numbers.

Fractions

A rational number formatted as a/b, where a and b are integers and b ≠ 0.

Numerator

The top number in a fraction indicating the quantity of the object.

Denominator

The bottom number in a fraction specifying the type of object.

Equivalent Forms

Different representations that have equivalent values.

Decimals

Special rational numbers with denominators as powers of 10 (10, 100, 1000, etc.).

Terminating Decimal

A decimal with digits ending after a certain point, allowing specific decimal places to be read accurately.

Repeating Decimal

A decimal that continues indefinitely with a repeating sequence of digits, making it impossible to read precisely to the last digit.

Repetend

The group of digits that repeat in a repeating decimal, denoted by a bar above the repeating part.

Percent

Means "for every 100" and is a ratio expressed as a fraction of 100, e.g., 36% equals 36/100.

Prime Numbers

Numbers with exactly two distinct positive divisors: 1 and themselves; e.g., 13 can only be factored as 13 x 1.

Composite Numbers

Numbers that can be expressed as a product of whole numbers in multiple ways; e.g., 18 can be factored as 18 x 1, 9 x 2, or 3 x 6.

Factoring

The process of expressing composite numbers as products of their factors.

Prime Factored Form

The unique representation of a number using only prime factors; for instance, the prime factored form of 12 is 2 x 2 x 3.

Eratosthenes' Sieve

A systematic method for identifying prime numbers, named after the Greek mathematician.

Multiples of a Number

Products obtained by multiplying a specified number by any natural number.

Common Multiples

Shared multiples found in the lists of multiples for multiple numbers.

Least Common Multiple (LCM)

The smallest shared multiple among several numbers.

Factors of a Number

Whole numbers that can multiply together to produce the original number; for 24, factors include 1, 2, 3, 4, 6, 8, 12, and 24.

Common Factors

Shared factors among multiple numbers.

Greatest Common Factor (GCF)

The largest shared factor among several numbers.

Relatively Prime Numbers

Numbers that share no common factor other than 1; e.g., 8 and 9 have no common divisors besides 1.

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Test your knowledge with these flashcards from Videotext Module A, Unit 1. This set covers important mathematical concepts including well-defined operations and natural numbers. Perfect for reviewing definitions and improving your understanding of basic operations.