# 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 $851 \div 37 = 2553 \div 111 = 23$.

### Sneaky

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