At a Glance - Basic Elements
You wanted to learn the basic elements of the basics? Very well. Shmoop is a river to our people.
Algebra has a lot to do with the fundamental arithmetic operations, otherwise known as +, -, ×, and ÷. By now, you may have already "put two and two together," as you should have been able to "take away" from this paragraph that algebra focuses on only the very essentials of the mathematical universe. You don’t need a knowledge of quantum mechanics, you’re not going to be asked to write any complex equations that take up half a chalkboard, and you'll be presented with very few unfamiliar numbers or symbols, although we can't promise that you won't see any.
In algebra, we introduce the idea of a variable, which is just a secret letter that stands for something else that hasn't been identified. For example, if you're introducing your friend to someone you've only met once and whose name you can't remember, you may find yourself saying, "Brian, this is...x." You may get some funny looks, but at least it’s better than trailing off completely. It does show some modicum of effort.
In most cases, we attempt to fill in all of those x’s and y’s with real values, and we’ll provide you with the tools to do just that in any given situation. Sometimes, when more than one variable is present, the best you can do is to simplify an equation: you might still be left with a variable or two, but at least it won’t be such a mess.
We’ll take a closer look at the number line and help you look at numbers in a whole new way. It'll almost be as if you're seeing them for the first time. Although to be fair, it probably also has a little bit to do with your new contact prescription.
We’ll delineate between natural, whole, real, rational, and irrational numbers, so you can pick any one of them out of a lineup. (If you haven’t seen π’s mug shot, you need to; it’s hilarious.) You’ll also become best buds with decimals, fractions, and percents, in addition to learning how to convert one to another and perform arithmetic operations on any of them. You can perform other types of operations on them as well...but only if they’ve signed a consent form.
See? Nothing too scary here. No derivatives or logarithms or inflection points. Just the nuts and bolts of numbers—and we’re about to hand you the wrench.