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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