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, Im talking about elementary algebra not abstract algebra which is a completely awesome, but different thing).
Think back to arithmetic. Yes, adding and subtracting – all that stuff. When you do arithmetic, you are typically dealing with specific numbers. In algebra, we shift that perspective into something a little more general and a little more abstract. Instead of talking about specific numbers, we will start including variables, which are letters or any other type of symbol that represents either a specific unknown number or a general number that we would allow to be anything.
You may be wondering why this is useful. Let’s take a look at a simple example: What if I told you, that in a certain game, the second player always gets 5 more points than the first player. This is a general statement and you can figure out how many points the second player will get if you know how many points the first player got. Instead of a general statement like this, we could have made a huge list like this: “if the first player gets 5 points then the second player gets 10″, “if the first player gets 10 points then the second player gets 15 points”, etc. The problem with this list is that I would have to list every possible number of points the first player gets. Our first statement was a lot more compact but had the same information.
That first statement could also be stated with a variable. Let x represent the number of points that the first player got, then the second player will get x+5 points. A general statement like this is much easier to work with than simply listing all of the possibilities – and this is just a little example! In areas like computer science, it is near impossible to write a decent program without some variables.
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.
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Often, I will explain to students that Algebra has to do with the relationship between quantities. We may not know what X is or X+1 is, but we do know that the second quantity is one more than the first. And that can be very useful.
If we know two items purchased totaled $13 and the second item was one dollar more than the first, we automatically can determine that one item was $6 and the other was $7.
Much of Algebra has to do with relationships between quantities.