Common Math Mistake 9

Pay attention to restrictions on formulas

This is an error that is often committed by teachers too (I must admit this fact!). Teachers don’t give or make a big deal about restrictions on formulas. In some cases the teacher forget the restrictions, in others they seem to have the idea that the restrictions are so obvious that they don’t need to give them, and in other cases the teachers just don’t want to be bothered with explaining the restrictions so they don’t give them.

For instance, in an algebra class you should have run across the following formula.

The problem is there is a restriction on this formula and many instructors don’t bother with it and so students aren’t always aware of it. Even if instructors do give the restriction on this formula many students forget it as they are rarely faced with a case where the formula doesn’t work.
Take a look at the following example to see what happens when the restriction is violated.

So clearly we’ve got a problem here as we are well aware that step 6 is not true! The problem arose in step 3. The property that I used has the restriction that a and b can’t both be negative. It is okay if one or the other is negative, but they can’t BOTH be negative!

Ignoring this kind of restriction can cause some real problems as the above example shows.