How to Divide Numbers in Your Head

My quick method of mental division.

Fletcher Thompson
ILLUMINATION

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Source Pixabay

Having to do mental arithmetic isn’t a rarity. Whether it’s working out how much your shopping will cost before the checkout or adding up your daily protein intake, being lightning-fast at mental maths can’t hurt!

Suppose you’re considering a monthly subscription to some service. It’s £8 per month, but you can pay for a year’s subscription for £90. The service claims this is a discount.

To check, you can work out the effective price per month by dividing £90 by 12 months. This gives £7.50 per month, which is a discount. This would be quite a straightforward calculation, but you’ll need a method when the numbers get larger.

Here’s my method for dividing numbers in my head. This might seem to work only if the dividend (number being divided) is larger than the divisor, but I have a way around this which I’ll cover at the end.

The Method

Suppose we have two numbers m and n with n smaller than m. We want to divide m by n. Let’s follow an example with m = 1892 and n = 13.

We can rephrase the problem ‘Divide 1892 by 13’ as ‘13 multiplied by what gives 1892?’ The method revolves around constructing such a number, which will be the answer to 1892/13.

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Fletcher Thompson
ILLUMINATION

England | Mathematician. I want to help everyone learn the beauty of maths through my articles.