How to divide by 12 quickly?

Question

Let $n\in\mathbb N$ be divisible by 12 and $n/12<100$. Is there a way of computing $n/12$ rather quickly using mental arithmetic (e.g. for 972/12, 1044/12, etc.)?

For example, the number 11 seems to have a nice property. When we consider $836/11=d$ then
770<836, but 880>836, so the first digit of $d$ must be 7. And since the last digit of $836$ is $6$, so is the last digit of $d$. This gives us $d=76$.
Or consider $693/11=d$. Then $660<693$ (and 770>693), so the first digit of $d$ must be $6$ and the second is $3$ since this is the last digit of $693$. This gives us $d=63$.

Now, is there another (possibly similar) approach for dividing by 12 (or even 13, 14, etc.)? But I am mostly interested in a "trick" for the number 12 (just using mental arithmetic).

Answer 1

One can memorize multiples of $12$ that are less than $100$. Then if $n/12=10a+b$ you can guess $a$ quite fast. And there are two options for $b$. Now if $n=100a+(2a+b)10+2b$ then you can decide about $b$ by comparing $2a+b$ and the second least significant digit of $n$.

Answer 2

You can divide by $10$ by shifting the decimal point, then subtract $1/6$ and round. So for example $1044/10=104.4, 1/6$ of $104.4$ is about $17, 104.4-17=87.4$

Answer 3

When I were a lad, there were twelve pennies to a shilling, and we all had to learn our tables up to $12 \times 12$. So I can do these in my head just by the usual process of short division.