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Another Multiplication Technique

I’ve written a few posts over the years on different multiplication techniques (see this and this), there are many and each has its own appeals and pitfalls.

Today I discovered another. I was looking over Q D1 exam paper and came across this flowchart:

image

The questions were all fairly reasonable and one of my students was completing the question to see if he had for it right. Afterwards I asked if he knew. What the algorithm was doing, he wasn’t sure at first but when another student explained it was finding the product of x and y he realised.

Then he asked, “but why does it work?

I looked at the algorithm and initially it didn’t jump out at me. I tried the algorithm with 64 and 8.

image

I could see it worked through mocking factors of 2 from the left to the right but this time there was no odd numbers, so I picked some other numbers:

image

And that’s when it all made sense. Basically, what’s happening is you are moving factors of 2 from x to y thus keeping the product equal. When x is odd, you remove “one” of y from your multiplication and put it in column t. Your product is actually xy + t all the way down, it’s just that until you take any out your value for t is 0. T is a running total of all you have taken from your product.

The above becomes:

40 × 20
= 20 × 40
= 10 × 80
= 5 × 160
= 4 × 160 + 160
= 2 × 320 + 160
= 1 × 640 + 160
= 0 × 640 + 160 + 640
= 0 × 640 + 800
= 800

I tried it out again to be sure:

image

This is an nice little multiplication method that works, I’m not sure it’s very practical, buy interesting nontheless.

Have you met this method before? Have you encountered any other strange multiplication techniques?

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  1. David Williams
    June 20, 2016 at 4:11 pm

    Russian peasant multiplication.

    • June 20, 2016 at 4:29 pm

      It’s similar, but different, to the version of “Russian peasant multiplication” that I’d encountered before.

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