Multiply like a Roman

The Romans used weird, weird math. To multiply two terms, they repeatedly doubled one of them in one column while halving the other term in another column, throwing away any remainders that came up, crossed off half the numbers in the first column, added up what remained, and — voila! — got the right answer.

How on earth did they come up with it? And why on earth does it work?

Here’s what it looks like. If you’re not a mathy person, don’t worry, I’m not asking you to do any calculations–just to enjoy the strangeness.

1. Start with two numbers

536 * 42

= (500 + 30 + 5 + 1) * (40 + 2)

= DXXXVI * XXXXII

2. Multiply the first column and halve the second

Multiply these Divide these
DXXXVI XXXXII
MLXXII XXI
MMCXXXXIIII X
MMMMCCLXXXVIII V
(8M)DLXXVI II
(17M)CLII 1

3. If a number in the second column is even, cross it off in the first column.

XXXXII
MLXXII XXI
X
MMMMCCLXXXVIII V
II
(17M)CLII I

4. Add up all the remaining numbers in the first column.

(22M)CCCLLLXXXXXVIIIIIII

= (22M)DXII
= 22,000 + 500 + 10 + 2

5. And here’s the answer!

= 22,512

That’s all I have. If you want to know why it works, one of these links should satisfy.

A Different Kind of Multiplication

Roman Arithmetic

Or, if this is too much math for you, just be glad I didn’t tell you about multiplying infinity.

2000px-nc3bameros_romanos-svg

wikimedia commons

 

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3 responses to “Multiply like a Roman

  1. The ancient Egyptians also used this method and perhaps, they are the originator of this. There are people in some parts of the world who still use this (e.g. in Ethiopia).

    This is based on the binary number system. If you’re familiar with binary numbers, then you can figure it out from there.

    • Wow, that’s interesting! I wonder what happens when kids from Ethiopia come to the U.S. in the middle grades and are expected to know the multiplication system. Also, now I want to look up more about the ancient Egyptians. Thanks.

    • The mathematics of the ancient Egyptians was impressive. They were able to build the pyramids after all.

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