This is Day 17 of 31 Days of Math Learning Success. Follow all the days here and check out others that are writing for 31 days here.

There are two kinds of people in the world — those who divide everything in the world into two kinds of things and those who don’t.
~Kenneth Boulding

When I go to calculate my gas mileage, I do it twice. One way is always wrong, and one way is always right.

I know that I have to do something with the number of miles and the number of gallons. In particular, I know I have to divide them. But I can never remember which number divides by which. Or which is the dividend and which is the divisor.

But it doesn’t really matter. There’s only two numbers. And there’s only two ways to do it.

I drive 245 miles on a tank of gas that’s about 20 gallons. I know it’s either 20÷245 or 245÷20. The first one gives 0.0816, And the second one gives 12.25.

Neither of these is that desirable, I’ll admit. I drive a 1995 Chevy pickup. And I love it.

But there’s no way my gas guzzler gets 0.0816 miles per gallon. If it did, driving to the neighbor’s house would use a whole tank of gas.

So I know that the second answer, 12-ish, is the correct answer.

Experiment with numbers.

The “translate statements to expressions” is another common “two-way” problem.

“7 less than x” screams subtraction. And as soon as you have a little experience with this, you know that it could be or . But which one?

Well, suppose is 539 (pick your favorite crazy number here). Then 7 less than 539 is 532.

So that was or .

Try it both ways.

It’s like trying on a wedding dress. You don’t have to know what dress you want. You can try them on and see which works better.

And unlike wedding dresses – there are only a few (or two) ways to do many problems.

Picking a wedding dress, well, you have bazillions.

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