Strategic Division

mental math series, part 9

Versatile. Adaptable. Modular. Empowering.

The technique I’m showing you today is all of these things and more. It will make long-hand division a thing of the past and encourage you to divide mentally more often. It will improve your number sense and impress your boss. It’s an incredibly valuable tool.

The method is called strategic division.

Strategic Division

In strategic division we utilize numbers that are exceptionally easy to divide by (such as 10 and 2) to break the division down into stages.

example 1

For example, suppose I want to divide 1840 by 20.

Equivalently, this can be written with a fraction bar.

Begin by breaking 20 into some convenient factors. I like 10 and 2.

We may choose to divide out the 10 and 2 in any order we like. I’ll begin with dividing out 10 in the first step followed by 2 in the second. Once all the factors of 20 are divided out, you have your final answer.

That’s so much easier than dividing by 20 directly!

example 2

Let’s try another. How about 2960 ÷ 80 ? That seems sufficiently difficult. Again, start by selecting factors of 80. I chose 10, 4 and 2.

I started with dividing out 10.

I chose to divide by 4 instead of dividing by 2’s repeatedly because in this scenario I think this is the easiest route, although either way would work.

Since 296 is 4 away from 300, let’s find out how many 4’s are in 300 first. 300 can be quartered easily in stages by dividing by 2 twice.

This means that there are 75 fours in 300. We can deduce that 296 must be composed of 74 fours since it is 1 four less than 300.

Lastly, we need to divide by 2. To do so, I’ll split 74 into 70 + 4 and divide them both individually by 2.

Hence 2960 ÷ 80 = 37.

example 3

Alright, one more example for the road!

Sixty has many factors. I’ll choose 10, 2 and 3.

Begin by dividing by 10.

Next I’ll divide the expanded version of 738 by 2.

Which results in:

Lastly, we must divide by 3. Conveniently each digit is a multiple of 3, so this step turns out easy.

We’ve found that 7380 ÷ 60 = 123.

See, division doesn’t have to be difficult. Sometimes it can even be a cinch! And with practice this method will become second nature and you’ll find yourself thinking like this routinely!

Next Lesson: The Most Valuable Everyday Math Skill

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