# Basics: Fundamentals of Algebra

**pre-reqs:** *none*

I know who you are. I have seen you before and talked to you before. You are taking introductory physics and you are scared. Why does this have to be so difficult? It seems like there are a bazillion equations. Calm down, I will try to help. First, realize that algebra and trig are typically a pre requisite course for introductory physics. Your instructor probably expects that you have already mastered this material. Perhaps you did well in algebra (maybe you earned a B). But maybe you just worked hard and never really “got it”. That is ok. There are many others in the exact same position as you. The first thing to realize is that you NEED to figure this algebra stuff out in order to succeed in physics.

Algebra is not that difficult, but there are some key ideas you need to know. I will share the one that I think is the most important.

For most people, algebra is treated in the following manner:
– Here s an equation
– Here is a variable I am trying to solve for
– Here is a list of steps I can use to get that variable

Many times this method works, but it will also lead to disastrous effects sometimes.

**The One thing:**

**”Respect ye the meaning of the equal sign”**

Well, duh you may say – but no, its true. What does the equal sign mean? It says that some quantity or expression on one side of the equal sign is equivalent to the other side. They are the same, or equal if you may. I guess you could call it the “same sign”.
So, how does this help with algebra? Well, if you respect the equal sign, then whatever you do to the left side equation, you will do unto the right side. This is what algebra is all about. Doing the same thing to both sides of the equation so that it looks different in a way that you get what you want. Take the following example:

A common method to solve this would be (I have seen this done many times):
– Move the 2 to the other side and make it negative
– Put the 3 on the other side and put it on the bottom
– You are then just left with x = 5/3 (which is the correct answer)

The problem with this method is that it can lead to some pretty bad things. These bad things happen more often when you start with more complicated equations. Here is a better approach to the same problem:

– Subtract 2 from BOTH sides of the equation – this respects the equalness of the equation
– Divide BOTH sides of the equation by 3
– You are then left with the EQUATION x = 5/3

It seems like a small difference, but in the second method you do not anger the Equal-sgin gods. If you anger them, they throw down bolts of lighting that cause you to fail physics and or math. Respect the equal sign, and it will respect you.

**note:** This is a repost from my earlier stuff. Originally, this article referred to Curly’s Law of Algebra (you know, Curly from the movie “City Slickers”?) Well, maybe you don’t know what I am talking about. That is why I left him out of this post. Sorry Curly.

1. #1 Eddie Pasternak
September 16, 2008

The fundamentals of spelling on the internet.

FIAL.

2. #2 Rich
November 2, 2009

I realize that I’m a bit late to this posting, but I like what you’re saying because it’s something that as an Algebra teacher, I keep trying to hammer home throughout the year. It’s such a common mistake, and it’s a good indicator of whether a student “gets it” or not, when they suggest merely moving the constant (in your example, 2) to the other side of the equation. That pretty clearly shows that they don’t yet have a strong grasp of what that ever-more-important equal sign really means.

My best analogy so far is to think of an equation as a balanced see-saw. Most students can picture themselves sitting on one end while a friend (of equal weight) sits on the other end. If you add something to one side, say, a 5 lb. cat, then you’ve got to add the same weight to the other side of the see-saw if you expect it to remain balanced. If you triple the number of people on one side, then you’ll need to triple the number of people on the other side (this begins to push the idea of having all of these people with the exact same weight, but my students can usually handle it).

Usually, if they can get the idea with the simplest equations that only require a single step to solve, then they have a better chance of understanding multi-step solutions.

3. #3 Rhett
November 3, 2009

@Rich,

I think the biggest problem is that it is easy for students to move along to the next step just practicing the mechanics of algebra without the understanding.