# Mathsmagic: Multiplication Showing Double Digit Dexterity

Most people can do a speedy
multiply by 10. You just add a zero to the end of the number – 23 multiplied by
10 is 230, simple. Now you can prove your superior mental superpowers by speedy
multiplication of any two-digit number by 11. You explain to the audience that
this is clearly far more difficult. They have the calculators on their mobile
phones ready to check, but you do your calculations correctly before they even
start to click the keys.

**Imagining the 11 times trick**

To give us this superpower, we
make use of two things. One is maths and the other is the human brain’s power
of imagination.

To do a lightning calculation
multiplying any two-digit number by 11, you need to use some visual imagery and
use your imagination. Let’s take the number 52 for example. Now imagine a space
between the two digits, so in your minds eye you imagine 5 2. Add the two numbers together and imagine
putting the sum of them in the gap in the middle, so you see 5(5+2)2. And that
is it, you have the answer: 11x 2 = 5(7)2= 572.

**The double trouble trick**

But what if the numbers in the gap add up to a double digit?
For example, suppose you want to multiply 98 by 11. So, you imagine 9 (9+8) 8.
But that bit in gap in the middle gives you 9+8=17, so where do you put these
digits? 9 (17) 8?

Easy, just leave the second number (here the 7) in the gap
as before and imagine moving the 1 up a place, so you have (9+1) 7 9 = 10 7 9 =
1079. Correct again.

The maths behind this is fairly easy if you explore it.
Suppose you have the number AB (that’s A tens and B ones) and you want to
multiply by 11. First you multiply by 10. That’s easy, 10xAB = AB0 (A hundreds,
B tens and 0 ones). Then you add another AB so you’ve got 11 lots of AB
altogether, giving you A hundreds, (B+A) tens and (0+B) ones.

This is exactly what all that sliding numbers around in your
imagination has been doing without knowing it. Of course, if the middle A+B is
more than 10 (ie it’s a double digit number), you just slide the first digit up
to the hundreds column, and it’s sorted.

Lightning calculations by mind power and a maths trick. Mathematicians
make use of their imaginations all the time. Our brains are really good at
imagining things and creating pictures in our heads. Often that’s the way we
solve tricky problems or come up with clever visual imagination tricks like
this one.

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