What Are Variables? Part 2

How do variables work? How do you work with variables? And what do they have to do with algebraic expressions? Math Dude has the scoop!

Jason Marshall, PhD,
April 19, 2013
Episode #150

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What Are Variables? Part 2

Over the past few weeks we’ve learned about the nature of algebra and the nature of the variables that we use in algebra. Now that we have a firm grasp on these key ideas, it’s time for us to spend some time figuring out why all of this stuff matters in the first place. With that in mind, let’s start today by talking about how variables work and how you can work with variables..

How Do Variables Work?

In our first episode on variables, we decided to use a symbol that looks like a little box as our variable…at least for a while. As we talked about, this decision is completely arbitrary—it really doesn’t matter what the symbol looks like. What matters is what we can do with it. So, what can we do with our little box? The short answer is: anything that we can do with numbers. For example, we can add our variable to the number 3:

3 + ?

Afterwards, we can subtract our variable from this sum

3 + ? – ?

Of course, when we first add and then subtract our variable from the number 3, the net result is doing nothing…just as it would be if we instead added and then subtracted a number like 2. In other words, 3 + 2 – 2 = 3, and similarly

3 + ? – ? = 3

The important thing to realize is that the answer is always 3…no matter what value the variable represents.

What else can we do? Among other things, we can add our variable to itself:

? + ?

We can multiply it by a number:

9 • ?

We can even multiply our variable by itself:

? • ?



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