Dear Uncle Colin,

I have to work out 17.5% of 354 in my head. How would you go about it?

  • Various Arithmetical Tricks

Hi, VAT, and thanks for your message!

The traditional method is to take 10% of your base number (35.4), then add on half (17.7) and half again (8.85) to get 61.95. However, that’s quite a lot to keep in your head at once.

Alternatively, you can shuttle factors: 17.5% of 354 is 35% of 177, or 70% of 88.5. That’s still fairly tricky, but not too hard to reach 61.95.

My favourite method is to note that 17.5% is $\frac{7}{40}$, which can be written as $\frac{1}{6} + \frac{1}{120}$. A sixth of 354 is 59, and a twentieth of that is 2.95, and I think that’s a significantly less involved method than either of the others.

Hope that helps!

- Uncle Colin