If you are a relative newcomer to the wide and wonderful field of mathematics, you may have seen such symbols as “x”, “n”, “y”, “a” or “b” in otherwise normal math problems, such as 5=16-x. If you are a novice mathematician in training, you most likely know all about variables, and if you are a battle-weary veteran you’ve most likely dealt with more variables than you’d ever care to. However, despite your familiarity with them, you will be introduced to them eventually, and they are insanely important.
How Variables are Used
Variables are used in mathematical expressions to take the place of any unknown value of any type (not just an integer- it could be a decimal. It could even be an imaginary or irrational number!). A variable is normally represented by a lower-case letter, such as “a”, “x”, or “n”, but can be represented by symbols, such as the greek letters &alpha (alpha) and &beta (or beta). In a single problem, each variable will only have one value (notice “problem”, not “equation”- eventually you’ll get to things like systems of linear equations which have 3 or more equations, but are only one math problem).
Solving with variables
For a normal math problem, you are trying to find a numerical number- for example 3*3=9 or 5-2=3. When variables are involved, solving the equation is figuring out what the variable’s value is in that problem. To do this, you must (basically) get all of the number values to one side of the equals sign, and all of the variables on the other side. Then you simplify each side so that there is only one variable equal to one numerical value. Depending on the type of equation, though, this process may be completely different or much more complicated.
By far, the most common letter used for variables in school texts is “x”. However, you will often commonly see y,z,n,a and b. “n” is often used in elementary schools, and less often in algebra. “x” and “y” are most often used in algebra (though “x” is used alone often) since they refer to the x and y coordinates on a graph of a point. “z” is used in three-dimensional equations.
However, the thing to remember is that a variable can have any letter as its symbol, even though some are used more often than others. Even so, it is normal that people “reserve” some letters for certain tasks- for example, “p” and “q” are used almost always in logic problems. As a general rule, start with “x”, then go to “y”, “n”, and then “a” and “b”.
Variables between problems
Just because a variable can only have on value on a single problem doesn’t mean that it can’t have other, completely different values outside of that problem. You can use the same variable in every single separate problem, if you wish.