Math Variables & Expressions

In mathematics, variables are used within mathematical expressions, and are most commonly denoted by the letter "X," which originates from the ancient Arabic works of Al-Jabr in Andalusian Spain. The "X" symbol comes from a shortened version of the term "xei," which is an Old Spanish spelling of the Arabic term for "thing," pronounced as "shay'un."
The use of "X" as a symbol for a variable is also accompanied by "Y" and "Z" when more than one variable appears in a mathematical expression. With proper explanations and examples, the relationship between variables and their expressions is not too difficult to comprehend.

What Is a Variable?

A variable is nothing more than a letter or symbol that represents a hidden number. The value of a variable may change, or vary, based on the information provided. When dealing with mathematical lines graphed on an "X-Y" grid, the value of "X" or "Y" varies based upon what point along the line is the focus of the problem.
Modern-day mathematicians try to eliminate some of the ambiguity of the "X" by teaching students to use a letter that reminds them of the item they're problem-solving. So if it's a number of cars, they may use either "N" for number or "C" for cars.

What Is an Expression?

A mathematical expression is akin to a meaningful word phrase. It is a combination of mathematical symbols--variables, numbers and arithmetic symbols--that work together to solve mathematical problems.
A mathematical expression may be made up of one mathematical term or the algebraic addition (which includes the addition and subtraction of integers) of more than one mathematical term. A mathematical expression can be formed of only numbers, only variables, or both numbers and variables.
These are some examples of mathematical expressions:
7
x
y
5 + 2
3 + 9 í-- y
(6 í-- 5) + y - 2
10 -- x (z + 6)

Considerations

Evaluating expressions is the process of replacing its variables with the actual number value it represents. Once it is replaced, the expression can be solved or simplified.
For example: Evaluate 10 í-- y -- 6, when y = 9.
The first step is to write the number 9 in place of the y. The new expression is: 10 í-- 9 -- 6.
The next step is to perform the multiplication: 10 í-- 9 = 90, and then subtract the 6: 90 -- 6 = 84.

Function

Expressions are not always solved. The task may only be to write an expression, using a variable or variables, for the given information. For example:
Julie purchased 19 handbags. Kate purchased y bags. Write an expression for sum of their purchases. We would write the following expression: 19 + y
Another example:
John picked apples at a rate of 50 apples an hour. Write an expression for the amount of apples he will pick after n hours. Therefore, we would write: 50 í-- n, for the total number of apples picked.

What Is a Variable Expression?

Another concept related to variables and expression is the variable expression. A variable expression is numbers, variables or terms combined into an expression. This is an example of a variable expression:
Laura picked a total of 100 berries. The black berries sell for x cents and the red berries sell for y cents. What is the variable expression if she picked 40 black berries?
Well, she has a total of 100 berries, so since 40 are black, there must be 60 red berries.
Now we will combine these quantities with their values: 40x + 60y.
When the values are provided for x and y we will be able to solve the expression, calculating her total profit.

Resources

• Operations, Expressions and Variables
• Beginning Algebra Tutorial 4: Introduction to Variable Expressions and Equations

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