“Arr!” said the Mathematical Pirate.
“Pieces of eight!” said the Mathematical Pirate’s parrot.
“How many pieces of eight?”
“That’ll be… seventy and ten minus twenty and four, making fifty and six!”
“Who’s a clever boy?” asked the parrot. “Awk!”
The Mathematical Pirate is, indeed, a clever boy. He’s using a combination of number bonds and the small times tables he knows by h-arrrr-t.
The way it works is this:
- He knows that $3 + 7 = 10$, so $7\times$ something is the same as $10\times$ the thing minus $3 \times$ the thing.
- He knows that $8 \times 10$ is 80 and $8 \times 3$ is 24.
- Now the clever bit: he thinks of 80 as seventy-and-ten before trying to take 24 away – saving himself from the terrors of borrowing and carrying ((Yeah, yeah, I know, that’s exactly what he’s doing.))
- Then he takes twenty from the seventy (leaving 50) and four from the ten (leaving 6), so his answer is 56
Alternatively, he could have worked the same thing the other way: since $2 + 8 = 10$, $8\times$ something is $10\times$ the thing minus $2\times$ the thing. Seven tens are 70, which he thinks of as sixty-ten; seven twos are 14; taking the ten from the 60 leaves 50, and taking the 4 from the 10 leave 6. 56 again!
This is a really powerful trick – the Mathematical Pirate claims he learnt it from a Ninja, but nobody saw it.
In a more general form, if you need to work out (big times table number) × (something else) – for instance, $7\times4$ you’ll need:
- What you add to (big times table number) to make 10 – here, it’s 3 – and call that (little number)
- $10\times$ (the something else) – which would be 40, which you think of as “next ten down and ten” – here, that’s 30 and 10.
- (little number) × (the something else) – $3 \times 4 = 12$
- Take the tens in this away from the tens above (giving 20); do the same with the units to get 8
- Add these up to get the answer, 28.
A selection of other posts
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