Isn’t it funny that so many people talk about algebra, do algebra, or even fear algebra but have never thought about what it actually is? Well, let’s take care of that right now. (and for the record, I’m talking about elementary algebra not abstract algebra which is a completely awesome, but a different thing).
Back to arithmetic
Think back to when you were learning adding and subtracting, multiplying and dividing – all that stuff. When you do arithmetic, you deal with specific numbers. In algebra, we shift that perspective into something more general and more abstract. Instead of talking about specific numbers, we will start including variables, which represent either a specific unknown number or a general number that we could allow to be anything.
Why would variables be useful?
Let’s take a look at a simple example to think about this a bit.
Kaitlyn’s mom always gives $5 more to Kaitlyn than to her brother Alex.
This means that if Alex gets $10, then Kaitlyn gets $15 right? In fact, we could keep doing this forever! If the mom wins the lotto and gives Alex $50,000, then Kaitlyn should be getting $50,005. (Kind of weird but go with it.)
Variables can describe what is happening in general. If we let be the amount that Alex gets, then we know that is how much Kaitlyn will get.
Not only does this show the relationship between the two in a compact way, but it also allows a deeper analysis. Imagine if the situation was more complicated. You can’t just explain it in words to a computer so it can figure it out. Variables would have to be used!
It’s just a different way of looking at things
In the end, think of algebra as a shift in perspective. You now have the freedom to let a symbol stand in when you don’t know the value of a number or want to know what happens when it is any number. This is a powerful ability! Algebra really is the study of expressions (and equations) with unknown values. What general rules apply? Are there certain situations where some rule is not true? These are the questions you can answer with algebra.