Algebra is a subject which helps us to find unknown quantities with minimal information. But how do we carry all mathematical operations when something is not known? We assign letters from alphabet (mostly small case letters) for the unknown.
Such letters are only called as variables or changeable. Why the name is selected as such? Because the value assigned to these could be varied according to our wish but gives the correct information at a required condition. For example I earn $100 per day.
How do I calculate the total earnings after a certain number of days? Here the word certain is really uncertain! In other words it is an unknown. So we assign ‘x’ as the number of days and I can formulate that my total earnings in dollars will be 100x. Now my job is simple. I just to need to replace ‘x’ by the actual number of days I decide and I get the required information correctly.
Thus basically the changeable are employed as algebra variables or simply math variables. But why we had done away with the prefixes ‘algebra’ or ‘math’ and we simply refer as such?
Because, such uses of letters even in other subjects are subjected to mathematical or algebraic operations.
The types of variables are many. In most cases more than one forms are used. For example one may represent an input and another may be the corresponding output. Obviously the former can be assigned any value and hence it is described either as independent forms and the latter, because of the dependence on the input is referred as dependent forms.
In most of the cases they are represented by the letters ‘x’ and ‘y’ respectively. In such cases they are related by equations or functions.
Further, different types of variables are used depending on the context. For example when you study about distance versus time for a moving object, lettert is used for the unknown time and ‘s’ is used for the corresponding distance.
The same letter tis also used for denoting temperatures in normal scale. (whereas, T is used for temperature in absolute scale!). Letters p and v are used for denoting pressure and volume respectively.
We mostly see that the letters at the second half of English alphabet are mostly used for the unknown quantities. It is just a convention and the first of half is generally reserves for constants. However use of letters like ‘a’, ‘b’ ‘c’ is common in geometry.
In addition to English alphabetical letters Greek letters are also extensively used especially in the topics of trigonometry.