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Types of Numbers

Types of Numbers

Algebra Terms

Get down with the lingo

Absolute Value

The number's distance from 0 on a number line. The absolute value of a number x is denoted by |x| and 

|x| = x

x > 0 - x

x < 0

So with absolute value, we're not concerned with whether x is positive or negative, we just want to know how far it is away from 0. Because 0 has had some problems with x in the past, and has applied for a restraining order.

Additive Identity

The number 0 is the additive identity, because if 0 is added to any number, the number doesn't change. Prime example: your mother has been adding 0 to her age for 12 years now, and she's still 29.

Additive Inverse

The number that, when added to a given number, results in the additive identity (0). It's basically going to be the same number but with a negative sign removed or attached to the front of it. The additive inverse of x is –x, as x + (–x) = 0. So if you start with "hero" and add "-hero," you can go from hero to zero.

Associative Property

The sum and product of three or more numbers is same no matter how you group them. For example:

(a + b ) + c = a + (b + c ) and (a ) × b ) )× c ) = a ×(b × c )

Unfortunately, this doesn't work with subtraction or division. They're a little more rebellious. They dare to be different.

Commutative Property

The sum and product of three or more operands (the numbers on which an operation is performed) is the same no matter how you order them. For example: 

(a + b ) + c = (b + c ) + a and (a × b c = (c × b

For commutative property, think "commute," like your commute to and from school. Doesn't matter how many times you go back and forth or what different routes you take, you keep ending up back at the same place.

Decimal

Representation of a number using base 10. If you have an extra finger, try using base 11.

Denominator


Distributive Property

Multiplication of numbers distributes over addition and subtraction:

a (b ± c) = ab ± ac

And so you see, distributive property has nothing to do with Socialism. You were so worried.

Dividend

A number that is to be divided by another number. Apparently, this other number got hold of a butcher's knife.

Divisor

The number which a dividend is divided by. Or, the number doing the dividing. Whichever way makes the most sense to you. Either way, there's going to be some good old-fashioned dividing going on.

Equivalent Fraction

Two fractions that have the same value but are represented differently. For example, 1/2 and 11/22 are equivalent. If you and your sister decide to go splitsies on a burger, don't think you're getting any more than half just because she offers you 11/22 of it.

Even Number

A natural number that, when divided by 2, has a remainder of 0. Your friend Steve who's turning 18 next month? He'll soon be an even Steven. (Right now, he's a little odd.)

Exponentiation

Part of the word "Supercalifragilisticexponentiation." Okay, okay, you called our bluff. It's the mathematical operation of raising a number a to a power (exponent) n.
an = a× a× … × a (n times)

Josh Groban sings an inspiring tribute to the power of exponents. You may be familiar with it.

Factor


Factorization

Expressing a number as the product of its factors. This is just a way of breaking a number down into smaller numbers so that you can easily tell what factors it has in common with another number. If two numbers have a lot of factors in common, you can try setting them up on a date. Matchmaker, matchmaker, make me a match.

Keep in mind that factorization is not unique. For example, 24 can be factorized as 8 × 3 or 6 × 4. So in a single day, you could either watch Gandhi 8 times or Gone With the Wind 6 times. Either way, you'll never want to see either of those movies ever again.

Finite Decimal

A decimal number that has a finite number of decimal places. Get outta here, pi. This has nothing to do with you.

Fraction

The ratio of two numbers or variables. 1/2 is the most famous of all the fractions. It lives in the Hollywood Hills and has its own driver.

Googol

The number 10100, or the number 1 followed by 100 zeros. Don't even think about trying to Google "googol." Your computer will explode.

Greatest Common Factor (GCF)

The largest positive integer that divides evenly into two or more non-zero numbers. For example, the GCF of 18 and 24 is 6.

It is also known as the greatest common divisor or highest common factor. It goes by many names, and has a different passport for each. How Jason Bourne is that?

Imaginary Number

A number that, when squared, gives a negative real number. The imaginary unit is i, defined as i2 = -1. Since any number multiplied by itself won't necessarily give you a positive result, this number had to be made up.

What's that? You say you can see the number i typed out in the preceding sentence? Shh—you're imagining things. Just go back to sleep.

Improper Fraction

A fraction that tells bawdy jokes in mixed company.

Oh, all right. You're no fun. An improper fraction is one in which the numerator is larger than the denominator, like 13/5 or 25/4. These can be expressed as mixed numbers. Keeping with the examples, these fractions could be written as 2 3/5 and 6 1/4, respectively. There, now our fractions aren't so top-heavy.

Infinite Decimal

A nonterminating decimal representation of real numbers. Wha-huh? Basically, in an infinite decimal, the numbers after the decimal point continue on forever. Perpetually. Without end. Ceaselessly. Ad infinitum. Evermore. Like this catalog of synonyms.

You've got two kinds of infinite decimals—recurring or repeating (if the denominator in the rational number has any prime factors other than 2 or 5, for example: 1/3=0.333…) and nonrecurring (decimal representation of irrational numbers). You may notice that these are also your DVR recording options. No connection.

Infinity

If you've seen any of the Toy Story movies, you should know what infinity is. That's where Buzz Lightyear is headed. (And beyond, obviously.) In short, infinity is the concept of a quantity that is endless and unbounded. Its symbol looks like an "8" drank too much Nyquil and tried to find its way to the bathroom in the dark (∞).

Integer

The natural numbers (1, 2, 3, 4...), their negatives (...-4, -3, -2, -1), and zero. These are the numbers that are the easiest to work with. Some of those fractions and decimals have severe social disorders.

Irrational Number

A number that feels safer in a car than on an airplane, even though statistics clearly indicate that you're much more likely to be in an automobile accident than a plane crash.

Also, it's a real number that cannot be expressed as a fraction p/q, q ≠ 0. Irrational numbers do not have finite or repeating decimal representation. For example the square roots of 2, π, and e are irrational numbers. If you think about it, it's pretty irrational to expect anyone to be able to write out something that has an infinite number of decimal places.

Least Common Multiple (LCM)

The smallest integer that is a multiple of two or more integers. For example, the LCM of 4 and 6 is 12. If you take 36, on the other hand, it's a multiple of both numbers, but it is not the least common multiple. Don't get down on yourself, 36. You'll have your day in the sun.

Lowest Common Denominator (LCD)

The least common multiple (LCM) of the denominators of two or more fractions. For example, the LCD of 3/4 and 5/18 is 36. What did we tell you, 36?!

Lowest Term

The only common factor of the numerator and denominator of a fraction is 1. This should make sense, because if they shared a common factor, they could be simplified further. You may see the glass as 13/26 empty, but we see it as 1/2 full.

Mixed Number

A number expressed as a whole number and a fraction, like 2½ or 4¾. You'd never be able to bake a cake without these bad boys.

Multiple

The product of any number and an integer. For example, 0, -6, 12, and -72 are multiples of 6, whereas 15 and -32 are not. Be careful of where you put your multiple, because you don't want to be accused of dodgy product placement.

Multiplicative Identity

The number 1. That's a pretty fancy way of just saying "1," isn't it? Yes, we suppose so. What the term means is that if 1 is multiplied to any number, that number doesn't change. However, let's not make a big deal about how ineffectual he is. He's a little sensitive about it.

Multiplicative Inverse

The non-zero number that, when multiplied to a given non-zero number, results in the multiplicative identity 1. The multiplicative inverse of x (x ≠ 0) is 1/x, as:

x × 1/x = 1

This is not to be confused with the Multiplicative Converse, which says that when you multiply one Chuck by 2, you get a pair of Chucks.

Natural Numbers

These are numbers that walk about unclothed in an effort to rebel against the constraints of society.

Okay, so they're not that natural. Natural numbers are those in the set of positive integers {1, 2, 3...}. Any time you are counting a number of real life objects, you are using exclusively natural numbers to do so. Unless you have zero of something. In which case, why are you bothering to count? Zero. There—you're done.

Number Line

A straight line on which every point corresponds to a real number. Sometimes it's hard keeping all of those numbers in a single straight line, especially when one of them suddenly has to use the bathroom.

Numerator

The top part of a fraction.

"I'll be back... on top of the denominator." - Numerator II: Judgment Day

Odd Number

A natural number that, when divided by 2, has a 0 remainder. Also, it acts strangely and is a little funny-lookin'.

Operation

A procedure by which a new value is obtained from one or more input values. Addition, subtraction, multiplication, division, exponentiation are examples of operations on real numbers. Depending on the severity of the condition of the real number, it may first have to be anesthetized. (Before the operation, you see. It's a homonym. Oh, never mind.)

Order Of Operations

The rule that states which operation takes precedence over others. The correct order is given by the acronym "PEMDAS," which can be remembered by using the mnemonic "Please Excuse My Dear Aunt Sally." It stands for "Parentheses, Exponents, Multiplication and Division, Addition and Subtraction." It's something like a ranking system or a chain of command. So an exponent had better never go over a parenthesis' head, or it might be cited for insubordination.

Percent

The portion of a number out of 100. We're sure you can grasp this concept if you just give it 110%.

Prime Factorization

Expressing a number as a product of its prime factors. For example, 24 = 2 × 2 × 2 × 3, or 23 × 3. It's like breaking Humpty-Dumpty apart to see all the little pieces that make him tick. Good luck putting him back together again, buddy.

Proper Fraction

A fraction in which the numerator is less than the denominator. If you know anything about making a snowman, for example, you know that it is only proper to put the smaller balls of snow on top. Otherwise, you really run the risk of that carrot being misinterpreted.

Quotient

The number obtained by dividing one number by another. (Did you know that I.Q. stands for Intelligence Quotient? That's because we can tell how smart you are by dividing your brain up into pieces. Sounds rough, but it's a relatively painless procedure.)

Rational Number

A real number that can be expressed in the form of a fraction, p/q, where q ≠ 0. Remember, rational numbers put the "ratio" in "rational." And a ratio is nothing more than a fraction. It's just a cooler sounding word.

Real Number

A number contained within the set of rational and irrational numbers. Real numbers can be represented by all points on a number line. So pretty much any number whatsoever (except for those sneaky imaginary numbers) is a real number. Some of them used to be wooden numbers, but then they had their wishes granted by the Blue Fairy.

Remainder

The number that is left over after division of two integers with an integer quotient. For example, when 6 is divided by 4 the quotient is 1 and the remainder is 2. Don't feel bad for remainders just because they're leftovers. Tomorrow, they'll make some really great remainder sandwiches.

Sequence

A list of numbers that are in some type of order. For example, 2, 4, 6, 8… is a sequence of even numbers. 2, 3, 5, 7... is a sequence of prime numbers. 4, 9, 2, 6 is the combination for our gym locker. Whoops.

Unit Fraction

A fraction with a numerator of 1. For example, 1/2, 1/15. Easy way to remember this: if you have a unit of something, you have 1 of it. Hard way to remember this: "U," the first letter of "Unit," is the 21st letter of the alphabet, and "T," the last letter of "Unit," is the 20th letter of the alphabet; 21 - 20 = 1. Don't say we never gave you any options.

Whole Number

A number belonging to the set of natural numbers {1, 2, 3...} including zero. Zero is the only whole number that is not also a natural number. What's wrong with zero, you ask? Oh, it's nothing.
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