# Variables

Variables are just an efficient way of asking a mathematics question, when you don't know all the facts.  In grade school you were asked to fill in the blanks, now we are asking you to find the value of x or some other letter.  The fact that we're using letters has nothing to do with anything.  We could just as easily used any kind of symbols.  The advantage of using letters is that you've hopefully already memorized the alphabet.  If you want to know more about this check out todayifoundout.

## The Purpose of Variables

When we don't know the value of some data, we call that a variable.  Because, the value might vary.  What's the temperature at 2:00am tomorrow?  Who, knows?  We say that the temperature at 2:00am is x.  Then we'll check at 2:00am and we will have our answer.

We're getting a group together to go to a special movie showing.  Our cost will be \$5 each, but we don't know how many are going to show up.  And, until we know how many are going to show up, we won't know how much money we owe for the performance.  So, we say 5x = y.  Or 5 times whatever value x is going to be equals our total cost which is y.

Wait a minute!  Where's the times sign?  We've played a bit with some of the operators.  Operators are things like plus, minus, multiply, and divide (there are others, but we'll stick with these four for now).  Because we like to use x for a variable, we have to stop using it for the times symbol.  Why did we start using for the times symbol in the first place?  Mainly because we're a bunch of random idiots who don't really know what we're doing.  (Sorry, that was probably a bit out of line).

Anyway, the following symbols are used to denote multiplication.  The first isn't really a symbol at all.  If a number is right next to a variable, we assume we're multiplying.  So 5x is 5 times x.  We also use the * or asterisk as multiply.  So, we could have written 5*x and that would mean multiply.  We could write it as (5)(x) because two parenthesis next to each other denote multiplication. ## Dependent and Independent

Hopefully, we now know what variables are.  They actually come in a couple different flavors.  There are Dependent and Independent variables.  Remember our \$5 movie tickets?  We used x for the number of people showing up and y for the total amount we owed for the performance.  So, the number of people who showed up, told us how much we had to pay.  The amount we had to pay depended on how many people showed up.  x is the independent variable.  We will just let x be the number of people, it doesn't depend on any other variable.  But y depends on the value of x.  So, y is a dependent variable.

The difference between Dependent and Independent variables will come up later.  It's really not hard, but a lot of people struggle with it.

III. Algebra

VI  Equations

VII. Exponents

IX Fractions

XIII.  Linear Equations

XVII.  Real Numbers

XIV.  Math Terms

XVIII.  Percentages

XV.  Matrices

XIX.  PEMDAS Order of Operations

XXII. Slope