A few weeks ago, the Mathematical Ninja explained how to divide by 9 on the fly. This week, it’s multiplying that’s on his mind - a more common thing to have to do.

The multiplying method is easier, too. It’s just a case of adding and taking away - and writing a few numbers down. In this version, you work from left to right, which is quite the opposite of what you’re used to.

Here’s an example: $6134 \times 9 = 55,204$. How you do it:

  1. Write down the first digit, followed by the next with a vinculum: ($6 \bar 6$). The vinculum means ‘minus’.
  2. Add the second digit to the vinculummed number and add the same digit with a vinculum after what you’ve got: $6 \bar5 \bar 1$, because -6 + 1 = -5.
  3. Repeat this for the remaining digits. You should have: $6 \bar 5 2 \bar 3$ $6 \bar 5 2 1 \bar 4$
  4. Now go through - every time you see a vinculum, drop the preceding number by 1 and take the vinculummed number from 10 (so $6 \bar5$ becomes $5 5$ and $1 \bar 4$ becomes $0 6$). You end up with $55,206$, which is exactly what we wanted.

This is quite a tricky one to do in your head without practice, but doing it on paper can save you a lot of carrying - and once you’ve got the hang of it, you only need one line of working!