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.
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 $23 \times 37$.
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