Study Guide

Algebraic Expressions

Algebraic Expressions Introduction


Algebra has its own language of symbols. Like any other language, first you've gotta learn the basic vocabulary and the correct ways to structure sentences, or, in this case, equations, before it'll all start making sense. Once you do understand it, you'll find that this is an incredibly useful language to know. Even in spite of the fact that it is impossible to swear in algebra.

Once we're familiar with expressions, equations, and formulas, we can rearrange them into different forms and evaluate (solve) them to calculate things. We don't just rearrange them to improve our equation's feng shui—there's actually a reason for it. The skills of rearranging and evaluating expressions will be called upon in almost every math class you ever take, and therefore, it would behoove you to become a pro at it. No worries if you don't know the word "behoove," however. This ain't English class.

The Language of Algebra

Ever feel like your math teacher is speaking a different language? Sometimes it isn't just the thick Chicago accent. Mathematics does have its own language: a language of symbols. Let's take a look at what some of those mysterious symbols are, and see if we can't decipher what they mean. If we can't, then this is a sad, sorry excuse for an algebra guide.

Algebraic Expressions Resources

Websites

Math.com: The Language of Algebra
If you're still not feeling too confident about the differences among variables, coefficients, constants, and whatnot, read through the explanations given here, check out the examples, and then take the algebra "workout." Drink plenty of fluids; we don't want you getting dehydrated.

Algebra-Class.com: Perimeter Formulas and Circumference of a Circle Formula
There will be plenty of times in the real world that you will need to be able to measure the distance around geometric shapes. Unless you have an infinitely long tape measure, you should take a look-see at this site for some help with perimeter and circumference formulas.

Algebra.help: Substitution Lessons
Just as a substitute teacher "fills in" for your regular teacher, you'll often be asked to take a number and substitute it for a variable. But please don't act up in front of these numbers and variables just because you think you can get away with it.

Analyzemath.com: Basic Rules and Properties of Algebra
All these properties with long, unfamiliar names (commutative, associative, distributive, and so on) can get confusing. Use this page to help you keep everything straight. That way, if you're still confused, you can't blame it all on us. See how that works?

Coolmath.com: The Distributive Property
Do you feel like you'd have an easier time getting a handle on the distributive property if all the numbers were in different colors? Then this is the link for you! Coolmath.com simplifies everything for you in this colorful, easy-to-follow guide. It won't hurt you any if you're color-blind—only if you're number-blind.

Video

Teachertube.com: Algebra 1 - Factoring
Wish you could take all factors and throw them into a factor compactor? Don't despair! Sit back, relax, and watch this short video about basic factoring to help drive things home. There's also a sick beat you can rock to while you learn. This'll totally be one of your new jams.

Algebra: Formulas from Geometry
Review some of the formulas we learned in this section, as well as glimpse a sneak peak at some of the more advanced geometric formulas that are coming around the bend. Caution: formulas in video are closer than they may appear.

Khanacademy.org: Unit Conversion - Metric Unit Conversion
Let the good people at Khan Academy hook you up with metric conversion. You'll have a hecto-good time.

Games and Tools

Algebra Tiles
Use this fun tool to solve, substitute, expand, and factor your way to algebra stardom. Can we get your autograph now?

Substitution
Nothing too fancy about this one—just a clean, simple substitution practice tool. Fill in the answers, click the green button, and see how you did. Refresh, and try again. Repeat that process about 300 times and then you'll be ready to pass your pop quiz. If you haven't gone completely crazy by then, that is.