Variables in Math

Defining Variables

Variables are nothing more than a placeholder. They stand for things that you want to find out but don't have the answer to yet. Think back to grade school when you were learning addition and multiplication. Did your teacher ask you, 'What plus two equals five?' Well, when the teacher uses the word 'what,' she actually used it as a variable. The 'what' is something you wanted to know but didn't have the answer to right away.

Now, of course, you wouldn't even blink at that question. You quickly would answer 'three' and not even think twice about the 'what.'

In math lingo, there is a formality when it comes to variables. When you write them, instead of using the word 'what,' you would use letters. You can use any letter you choose. Typically, we stick to the English alphabet but technically, you can use any easy-to-identify symbol as your choice.

The two most common variables you will encounter in your schooling career are the variables x and y. Don't ask the reason why these two are the most popular. They just are and have been in use for so many years past. They are easy to spot and to identify, which makes them ideal candidates for a wide variety of mathematical applications.

Just because x and y are the two most popular variables doesn't mean you have to use just those two. You can use anything you wish. You have numerous choices to pick from.

Examples of variables

Any letter you can think of can be used as a variable. They can be uppercase or lowercase. When you get into more complex math applications, you might have several variables in one equation, so your ability to use more than one variable at a time will become important.

Using Variables

Variables have always stood in the place of an unknown answer. Their use remains the same. They always stand for something you want to know but don't have the answer to. With the aid of variables and algebra, you can find out the answer.

Going back to grade school again, let's look more carefully at the question 'What plus two equals five?' We now know that the 'what' stands for a variable. We also know now that we can choose any letter for our variable. So, let us choose x. Why not? It's an easy letter to choose and there is a phrase that goes, 'X marks the spot.' That's easy to remember.

Using a variable part 1

We've changed our question into a written mathematical form using variables and math symbols. Now, to finish using our variable to find our answer, we use some algebra and reverse our operations to find our answer. We have a '+ 2,' so we need to subtract 2 to find our answer.

Look at what we found! We found our answer to be 3, what we've known all along. But now we have mathematical proof that 2 + 3 = 5. How cool is that?

When to Use Variables

Variables can be used anywhere an answer is required but not known. It can be used to find unknown numbers. It can be used to graph equations where you have two variables. To graph, you would choose various numbers to put into one of the variables and calculate the other. This would give you points you can plot on a graph. It is similar with graphs involving three variables. In this case, you would input numbers into two of the variables to calculate the third and then plot the points.

In higher math such as signal analysis, cell phone companies use variables to help them calculate the best signal system to use so that you get the crispest and clearest voice service. Really, variables are used wherever a best answer needs to be found.

Lesson Summary

Variables stand for things that you want to find but don't have the answer to yet. They are useful for finding out answers to something you don't currently know. Writing them mathematically is as easy as picking a letter from the alphabet. Variables have many useful applications, but all of them are when a best answer needs to be found.

Variables: Key Points

• Variable - a placeholder for an unknown number in an equation
  • Represented with lowercase or uppercase letters
  • Have many uses and applications, including graphs of equations and signal analysis

Learning Outcomes

After watching this video, check to see if you can:

• Define variable
• Identify examples of variables in equations
• Solve for variables in simple equations
• Recall some uses of variables in mathematics