Thirteenths (Part 1/3): Secrets of the Mathematical Ninja

I’ve always liked the number 13, perhaps because it’s got a bad reputation.

However, until Matt Parker’s recent ZOMG tweet, I couldn’t do thirteenths in my head. If you asked me ‘what’s 7/13?’, I’d have screwed my face up and said “a bit more than a half.” Now I know. It’s $0.\dot53846\dot1$. Easy peasy.

In this sequence of ninja secrets, I’ll show you how you too can learn thirteenths, why the trick works, and what it has to do with the ZOMG tweet.

First up: multiplying by 77.

Why would you multiply by 77? Good question. In a couple of weeks, you may understand. For now, do not question, simply do: if you have to work out a certain number of thirteenths, you start by multiplying the number by 77.

To multiply a number by 77, you can split it into two bits: multiply by 7 (and since you know your seven times table up to 12, that’s not tricky), and then multiply the result by 11.

Multiplying numbers by 11 isn’t as hard as it seems. For whole numbers up to 9, it’s super-easy (just repeat the digit — $3 \times 11 = 33$). For bigger numbers, follow these steps:

- Mentally add the digits together. (If you had 49, you’d get 13).
- Add ten times the tens digit (40, in this case) to the number — it’s 53.
- Stick the units on the end (making 539).

Great! We’re literally halfway there.

* Edited 2017-04-07 to add links


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


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