Think Like a Maths Genius part 2

I explained here about how to multiply any two digit number by 11 instantly.

Just to recap, you take the two numbers, add them together and then put that number between the original pair of numbers.

For example, 72 x 11

7+2 = 9

Put the 9 between 7 and 2 and the answer is: 792

72 x 11 = 792

But what do you do, when the numbers add up to a digit more than 10?

For example, 85 x 11?

8 + 5 = 13, but the answer to 85 x 11 is NOT 8135

The answer is you take your 13, and put the five in the middle as normal, but add the one to the eight.

85 x 11 = 935

Think of like this, with the 13 (i.e. the result of adding together your two numbers) in red.

1

835

935

Another example: 75 x 11

7 + 5 = 12. … Put the 2 in the middle and add the 1 to the first digit. …

75 x 11 = 825

Voila!

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Think Like a Maths Genius

I’m still enjoying going through Arthur Benjamin and Michael Shermer’s Think Like a Maths Genius. It’s full of great tricks.

For example, how to multiply anything by 11.

We all know how to do this with one digit – you just repeat the number.

7 x 11 is 77

3 x 11 is 33 etc

But Benjamin and Shermer show a trick for two digit numbers.

e.g. 34 x 11

The answer – I can tell you instantly – is 374

All you do is add the two digits together (3+4 = 7) and put that number between the two original digits:

3 & (3+4) & 4

= 374

Another example:

81 x 11 = 891

How?

8 & (8+1) & 1 = 891

As long as the two digits that go in the middle add up to less than 10 it works every time.

But what do you do when the two digits add up to more than 10? Can you work it out?