Enter the maze

Brain Train: Imagining double digit dexterity

Numbers in a Crystal Ball

Everyone can do a speedy multiply by 10; you just add a zero to the end of the number. But you can prove your superior mental superpowers by speedy multiplication of a two-digit number by 11? Stretch your imagination and learn how to train your brain's double-digit dexterity and then challenge your friends.

Imagining the 11 Times Trick

To give us this super power, 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: 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 5_(5+2)_2 and that is it - you have the answer: 11 x 52 = 5 _(7)_ 2 = 572.

Double trouble?

Ahh, but what if the numbers add up to a double digit in the gap in the middle. For example, what if you want to multiply 98 by 11. Again you imagine, 9_(9+8)_8. That bit in the 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 (9+1)_7_9 = 10_7_9= 1079. Correct again.

Maths makes imagination

The maths behind this is fairly easy. It is the thing that allows us to have a visual picture in our imagination to do the calculation. Suppose you have the number AB (that's A tens and B ones, so Ax10 + B is another way to write it) and you want to multiply by 11. First you multiply by 10 then add AB on again. That's easy. AB x 10 = (Ax10 + B) x 10 = Ax100 + Bx10. Add AB on gives Ax100 + Bx10 + Ax10 + B. Combining the two bits that are multiplied by 10 we get Ax100 + (A+B)x10 + B. Put that back into decimal format and it gives the three digits A_(A+B)_B. That is exactly what all that sliding numbers around in your imagination has been doing without you knowing it. Of course if the middle A+B is more than 10, that is, it's a double digit, you just slide the digit up to the hundreds column (do a carry), and it's sorted.

Imagine that

Mathematicians and computer scientists make use of their imagination all the time. Both are very creative subjects. Our brains are really good at imagining things, of creating pictures in our heads, and often that's the way we solve tricky problems or come up with clever visual imagination tricks that can give new insights like this one.