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Mathsmagic : Division The Fast Five Trick

Look all around, fives are everywhere. Five fingers, five toes. Now think about division. Divide by 10? Easy you say – just move the decimal point one place to the left. But by 5? Far more of a challenge! Now you can impress your friends with your ability to divide any number by 5 at super speed - and do the calculation correct to three decimal places!

Not a lot of people know this, but dividing a large number by 5 can actually be done by a very simple two-step method.

Step 1 : multiply the number by 2.
Step 2 : move the decimal point.

That’s all there is to it.

Now you can impress you friends with your ability to divide any number by 5 at super speed.

Of course, your claim to do the calculation correct to ‘three decimal places’ is just presentation to make it sound more impressive. It’s really easy. All you do is get the answer, say 23.7, and add two zeros after the 7 to give 23.700. So that’s the answer right to three decimal places as you promised. Our maths proof below will actually show us that we will only ever get an answer with one decimal place. The rest is just magical flim-flam!

It is always a good idea to start easy with a simple example to test our method works so let’s look at 10 divided by 5. First, our method says we double the number, so doubling 10 we get 20. Then we shift the decimal point, so 20 now becomes 2.0 or 2. The answer’s correct. Good start.

Now for a harder example, say 190 divided by 5 . This looks tough without a calculator, but following our method, step [1], double 190 to get 380, and step [2], move the decimal point, so 380 becomes 38.0 or just plain old 38.

Harder still: how about 4567 divided by 5. Again, step [1], double the number, so we have 4567 x 2 = 9134. Then step [2], shift the decimal point to get 913.4. It’s correct - check with a calculator if you don’t believe it.

And lets get silly: 123456789 divided by 5. Step [1], double it, so 2 x 123456789 = 246913578. Step [2], shift the decimal point and the answer is 24691357.8. (You may really want to check this on a calculator!)