We’ve all heard the classic comment from algebra students, whether teenagers or adults: “I’ll never use this in real life!”

Some people of course, like engineers, computer scientists, physicists, or chemists use algebra in their daily work, but how would someone uninterested in these studies ever use algebra?

The purpose of studying algebra is to exercise your mind in the development of algebraic thinking. Algebraic thinking is a daily activity, and for those who are more practiced improve their lives with sharpened skills in estimating time, understanding quantities, and insight into relationships between multiple moving parts of a system, which can be made up of people or something non-human, like a machine or process that takes several steps to complete.

Practitioners of algebraic thinking enrich their lives no matter what profession.

Evidence in Everyday Life

If you want to double a cake recipe you are exercising algebraic thinking. What would you do to make twice as much as well as sweeter?

If you are rearranging objects to efficiently fit them in a box you are thinking algebraically.

If you have ever weighed the pros and cons when making a tough decision, you’ve internalized a multivariable algebraic equation where several factors had differing importance.

Mental Push Ups

Without further ado, let’s try an activity to help exercise that part of our mind which can look at something and see hidden parts within it. The goal is simplification and the name of this algebraic concept is factoring.

  • square root of 18 times square root of 8

Anywhere one writes 18, you many substitute 9 * 2 as they’re equal.

  • square root of 9 times 2 times square root of 8

Similarly, anywhere you see a value of 8, you can rewrite that as 4 * 2. These values are exactly the same

  • square root of 9 times 2 times square root of 4 times 2

We factored these expressions into smaller parts in search of perfect squares -- 9 and 4 -- which are taken outside of the square root symbol.

  • 3 times square root of 2 times 2 times square root of 2

Multiply the 3 * 2 to get 6.

  • 6 times square root of 2 times square root of 2

The square root of anything times the square root of anything is that number itself.

  • 6 times 2

Of course that leaves us with 12.

  • 12

Check your work in Wolfram Alpha!

If you want to draw mathmatical formulas on your computer, try Open Office’s math.