Variables
It’s not uncommon to hear people complain that they get confused about letters being used in math. What they don’t understand is that they have been using these letters the same way for most of their lives, and they just don’t know it.
Variables are letters that take the place of a number we don’t know in math.
So for example, if my girlfriend ate a number of pieces that I don’t know, I could represent that number as a variable. Let’s use the letter x as the variable for how many pieces of pizza she ate. If I know that I ate five pieces of pizza, then together I know we ate x + 5 pieces of pizza.
So what if the pizza only had 8 slices? We could use the following equation to represent the pizza-eating situation:
x + 5 = 8
Using some common sense, we can figure out that my girlfriend ate three pieces of pizza as long as we were the only two people to eat the pizza and the entire pizza is gone. It might seem like we don’t need to use algebra to figure this out, but the point is that we won’t be able to use common sense on more difficult situations, and instead we’ll need to rely on algebra and equations like the one above.
In general, we’ll use the letters x, y and z as variables, though we can also use a, b and c. Technically, we can use any letter we want (including some Greek letters), but some letters are really difficult to use because they look like numbers. For example, we’ll rarely use a lower-case L as a variable because it looks so much like the number 1. Additionally, we’ll rarely use the letter O as a variable because it looks so much like the number 0.
Variables, like many things in algebra, can be scary if you don’t know about them. However, they are much easier to use than their reputation, and you don’t have to be some kind of math genius to figure them out. Let’s look at a more complicated example.
Suppose there are 12 pieces of cake, and three people ate the cake with two pieces left over. We’ll use the letters a, b and c to represent how much each person ate. Then we’ll have the following equation:
a + b + c + 2 = 12
Since the about ‘a’ ate, plus the amount ‘b’ ate, plus the amount ‘c’ ate, plus the two pieces left over should equal a total of 12 pieces that the cake was cut into.
When doing multiplication with variables, you might see something like 4x. This is just a shorthand for 4 times x. That is, 4 * x simplifies to 4x, and they mean exactly the same thing. It’s similar to how we can write 2(3) instead of 2 * 3.
A major part of algebra is figuring out what a, b and c are using basic math ideas without having to get into anything extremely complicated and tricky.