The DIMENSIONAL TRICK for solving algebraic equations. Theory

We have tried to solve many problems that we had no idea how to deal with. We have some data, but we don´t know what to do with them. I present you the dimensional trick useful in this type of problems.

First we have to state as follow. When we use an equation, we have a first member equal to a second member, so both sides of the equation must be referred to the same kind of "things".

You must notice that in the first member we can see an addition or a subtraction. This is obviuos. If I calculate "oranges + oranges", the only posible answer must be "oranges" (not apples).

No matter how many oranges we are dealing with. This is not the point. We are focus now only in the type of things that are involved in equations.

Other examples of the same idea:

I remark: always referred to an addition or a subtraction. Obviously, if we interchange first and second member, the concept is the same.

So, in contrary sense, we must say that:

Of course, my dear friend, if I calculate "oranges + stones" the result can´t be "oranges" nor "stones". (Again, no matter how many oranges or stones).

Another step forward. Now we are thinking about flow formula. Flow is the amount of something that flows through any kind of place in certain time.

As we can state easily, if flow is amount over time, then time must be amount over flow. Now we are going to use this "new" view of time as a fraction, so:

If we add "amount over flow" (I mean, time) and "amount over flow" (I mean, time too), then the result must be time.

If we use another kind of matters, the result is the same:

So:

"Velocity · time" (space) plus "velocity · time" must be an space. No other result is posible.

Thinking about this idea, we have to apply it to solve a realistic algebraic problem in a second part of this article very soon.