More about Checking Division Problems

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A few posts ago, I offered some tips about how to check large division problems without having to multiply huge divisors and quotients to get even huger dividends.

One of the drawbacks to using the “crunch” method, which I described, is that it is not 100% accurate.

Often, people who need to defend the status quo (you know who they are, they work in the principal’s office) insist that checking by crunching is not acceptable, because it is not foolproof.

Let me give an example:

You could divide 1206 by 18 and get 64

It looks like it works. But it doesn’t. The real answer is 67.

Sometimes you can transpose digits, or make a mistake, the crunch of which will work out to the crunch of the real answer. After all, there are only 10 digits which all integers can crunch to.

It is very seldom, though, that you will crunch mistaken digits and do the multiplication, and have the answer come out to a crunch number that still has the same crunch number as the real answer.

The reason that mistakes are so seldom, is that it is easy to add numbers like 1+8 and 6+4 and multiply the results.

Although mistakes still can be made, much less mistakes are made with this method than with the cumbersome method you probably learned in school. Consider this: What is easier to do,

(1+8)*(6+4)
=9*1
=0, (all of which you can do in your head, with no training, in seconds)
or
18*64? (Do you really want to multiply that mentally if you don’t have to?)

There are many small-minded people in education, who insist that methods other than theirs must be foolproof, when their own methods are even less foolproof.

The mission of MathMojo is not only to teach easier, more effective methods, but also to make math more meaningful to you. And one way to do that is to sharpen your critical thinking skills.

Here is a perfect opportunity to do just that. Can you see the flaw in the small-minded person’s argument? They set up conditions that new things must fulfill in order for them to consider using them. But they don’t put their own things under the same conditions.

That phenomenon is one of the most prevalent flaws of society. Catch it when you see it, and call them on it.

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