Ask Uncle Colin: A mental quotient

Dear Uncle Colin,

I have to work out $851 \div 37$ without pen, paper or calculator. How would you do it?

- Simple Mental Arithmetic Looks Easy

Hi, SMALE, and thanks for your message!

I have three ways to tackle it.

Brute force and estimation

It's fairly obvious that the answer is between 20 and 30.

Knowing that $20 \times 37 = 740$ means you're 111 short, which is $3 \times 37$ - making a total of $23 \times 37$.

Number fact alert!

One of my favourite things about 37 is that $3 \times 37 = 111$, a very pleasing number.

In particular, multiplying everything by 3 gives $851 \div 37 = 2553 \div 111 = 23$.


You might also spot that $851 = 900 - 49$, which is $30^2 - 7^2$ or $37 \times 23$.

The first of these is probably the most useful, as the others involve special properties of 37 or spotting something that's not obvious -- however, having several ways to do something is always a good thing!

Hope that helps!

- Uncle Colin


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


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I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

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