# Ask Uncle Colin: Decimal arithmetic

Dear Uncle Colin,

How do people do decimal calculations like $80 \times 0.15$ in their heads? It seems impossible.

- Doesn’t Everyone Seem Clever, Answering Readily These Evil Sums

Hi, DESCARTES, and thank you for your message!

There are several possible strategies for a question like this - how I would do it, how I’d probably recommend you do it, and how I’d recommend you do it if I sensed the Mathematical Ninja was nearby are all different.

### How I’d do it

I would first think of it as $8 \times 10 \times 0.15$, or $8 \times 1.5$. With a bit of practice, this kind of ‘shuttling’ gets quite easy.

I’d then, noticing the second number ends in a 0.5 I can get rid of, think of it as $4 \times 2 \times 1.5$, or $4\times 3=12$.

### How I’d recommend you do it

The standard way to work with this is to think of 0.15 as 15%: you know that 10% of 80 is 8, and 5% of 80 is half of 8, or 4. Adding these together gives 12.

### Look out, a ninja!

“Fractions! 0.15 is $\frac{3}{20}$ so $80\times0.15 = \frac{240}{20}$, which is 12. Trivial.”

Hope that helps!

- Uncle Colin