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Glossary
These may or may not be the "textbook" definitions of math terms. They are not meant to help you spit back memorized facts for teachers. They are meant to explain things in terms that you can use to make them meaningful to you. Click on the ones in blue to go to the pages which explain them.
Average - A way to describe a sample of data with a number. That way is to divide the sum of a group of numbers, divided by the amount of numbers in the group you are using. Example: There are three numbers in is group: 12, 43, and 20. The total of the group is 75. You have to divide that total by three, then. So the average of those three numbers would be 25.
Constant - A symbol which has only one value at any given time.
If you don't know the value of the constant, it usually is represented by a, b, c, etc. For example, a squared * b squared = c squared, because, in this case, you know that a, b, are the sides of the right angle of a triangle, and c is the hypotenuse. (Don't worry about that last part if you don't understand it yet - we'll get to it when we tackle geometry.)
Counting Numbers - (also called the natural numbers) all the simple numbers, like 1,2,3,4,5... These do not include fractions, like 1/2, 3/4, 2/3, etc., nor decimals, like 3.54, 78.4, etc. They also do not include zero.
Digit - Any of the following numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
Distributive Law - (click on the link)
Irrational Number - A number which cannot be expressed as a fraction. These are usually expressed as decimals which go on forever and don't repeat, for example, 45.829... Since you can't pinpoint these on a number line. They are on the number line, but you just figure out precisely where. You can't ever find out exactly where to make the break to make it a fraction. Since a fraction is a ratio, and one of these numbers can't be a fraction, it is called "irrational" (non-ratio).
Probably the most famous irrational number is pi (3.1415...) Another is the square root of 2.Integer - All the whole numbers, including zero, and their negatives. ...-3,-2,-1,0,1,2,3...
- The grammar of size (amount), shape, and/or order. (according to Lancelot Hogben in Mathematics for the Million)
- The study and description of patterns
- A way to describe measurements of reality in symbols
- There are many other ways to define, describe, and use math. No one can name them all, but it is fun and deeply satisfying to investigate them.
Monomial - a group of numbers or variable which are combined by multiplication. For example. 6y, or 2/3n, or 2x4^3. (That ^ thing means "to the power of...")
Monomials have certain rules. They cannot contain:
- square roots (or other roots)
- variable raised to a power which is negative (like n^-3, for example)
- variables in the denominator of fractions (like 4/y for example)
Expressions with more than one monomial, (3n -4y, for example) are called polynomials. If the polynomial has only two monomials in it, (like the previous example), it is also know as a binomial.
An example of a polynomial which is not a binomial would be 4x-9y +n^2.A general rule of thumb for monomials is that if you see a + or a - sign, you are not dealing with a monomial. This is not a perfect rule, though, (so I wouldn't go quoting this to any teachers if I were you).
Natural Numbers - (also called the counting numbers) 1,2,3,4...
Non-negative integers - All integers which are not negative. That leaves 0,1,2,3... (which are also know as the whole numbers)
Numbers - Symbols used to express measurement of amount
Numeral - Any symbol which represents a number. Examples:
- 1, 71, the Roman numeral MCCVI
- the tally-system numeral III
- googol (which means 10 to the 100th power),
- the scientific notation 5 x 10^3
- 1.32
- 6/11
Order of Operations - The mathematical rule which determines in which order you do the various operations(multiplication, subtraction, square roots, etc.) in a math problem. It is the rule which tells you what to do first when you see something like this, for example: 4 +3n x 5.
The rule is "You perform the operations in this order - Brackets, Parenthesis, Exponents (powers and roots), Multiplication or Division, then Addition or Subtraction." (Where there is an "or," it doesn't matter which comes first).
The rule is usually shortened to PEMDAS or "Please Excuse My Dear Aunt Sally." Lame, very lame. That doesn't even take Brackets into consideration. {} are brackets. () are parenthesis. Professor Homunculus's New World Order of Operations version is, "But Prison's Even More Dumb And Stupid." (Or something like that).Rational Numbers - Numbers which can be written as a fraction (example: 3/7), where both numerator (top number) and denominator (bottom number) are both integers, and the denominator is not zero.
Real Number - The rational numbers and the irrational numbers. That means about all the numbers you will ever deal with in everyday life.
So what numbers would not be real numbers? The imaginary numbers aren't real numbers. (Yes, there is such a thing as an imaginary number in math, and no, we are not going to deal with them here!)(Yet.)Variable - a symbol which may be replaced by a number which fulfills the equation. For example, in 3x = 12, the x is a variable. In this case it can be replaced by the number 4.
In a different equation, you could use x to represent an entirely different number, as in 4x + 2 =6. In this case x would equal the number 1.
Typical variables are a, b, c, x, y, z, or n. But a variable could be any symbol which is not normally used to stand for a definite number. For example, 3.17 could not be a variable. Nor could 4, 0, -2, 5/8, or pi.
Whole Numbers - zero and all the counting numbers from 1 on, forever. The whole numbers are 0,1,2,3,4,5... (The three dots mean "and so on).
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