Easy Math: A Step-by-Step Guide to Solve Almost Any Math Problem

In my college experience, I have noticed that many students struggle through math problems, regardless of their complexity, and several of my classmates come to me for help. I have seen that they were not taught to solve math problems, but to find answers. In this tutorial, I will present a technique to problem solving that will bridge the gap between finding the answer and solving the problem.

The first step to solving a math problem is to put away your calculator. Too many people approach a math problem with a calculator in hand. Set the calculator aside, and grab your pen (or pencil) and paper. By writing your problem down (i.e. not doing the problem entirely in your head), you make it much easier to catch simple mistakes, such as dropping a negative sign, or forgetting an exponent.

Once you have your pen and paper, write down the original problem. If it is a word problem, write down all of the given information; this will let you construct an equation more easily. This tutorial will assume you already have an equation, as one could write an entire book on how to analyze a word problem.

A word of warning to you: this next part is where most people make the most mistakes. If you thought it was strange that I said to grab your pen, here’s why: if you make a mistake with a pencil, you will most likely erase it. If you write in pen, you cannot erase it. If you use a pen, your work is easier to see and it is easier to catch mistakes. If (when?) you make a mistake, it is not a big deal! Just cross it out and move on. By merely crossing it out, you can look back at it and keep yourself from doing the same thing again, or even catch your mistake later. Be bold! Make your mistakes easy to see, and make them only once.

Now, on to the hard part. The most basic part of solving a math problem is isolating like terms. Think of adding apples and oranges. If you have 3 apples and 1 orange, you can’t say “I have 4 orange-apples,” because you don’t! You have 3 apples and 1 orange. What you want to do in your math problem is move your like terms together and put them on opposite sides of the “equal” sign. For example:

12x + 7y = 2xy              //Move the y terms together by subtracting

12x = 2xy – 7y              //the same thing from both sides.

“Wait a minute,” I hear you saying, “That doesn’t look any better!” Ah, but wait. You have “something” times y, minus “something” times y. Now you can factor out the y, leaving you with y times “something.” In our example, that would be:

12x = 2xy – 7y              //Factor out the y term

12x = (2x - 7)(y)

Now we still want only like-terms together, so we undo the times function that is making the

(2x-7) stuck to the y. The inverse (or undo) function of “times” (multiplication) is “divided by” (division), so:

12x = (2x – 7)(y)

   12x    = (2x – 7)(y)     //Undo the function of y

(2x – 7)

 12x   = y                       //Flip so that y is on the left
 2x-7

y =  12x                         //(That's how your professors like it)
       2x-7

Ta-Da! You have solved an equation for y using this foolproof method. The only type of equation that I wouldn’t use this general method for is a quadratic (ax² + bx + c = 0), but you should already have a formula for that if you’ve had Algebra 1 and/or 2. Now, go forth, and conquer the world with your amazing mathematical skills!