Answer Man

Here’s how the Romans used fractions

Q: Your most recent answer on the Roman calendar reminded me of another question I’ve had for years. With their cumbersome system of using letters for numbers, how did Romans ever write fractions?

K.C., of Millstadt

A: This answer should have all students who struggle with their math homework wishing for a time machine: According to experts, there’s no evidence that young Romans ever sat around trying to find the lowest common denominator — at least, not as we know it today.

“The Romans didn’t have a standard way to write fractions using their numerals,” “Dr. Math” says at mathforum.com. “Instead, they just wrote out the word for the fraction. For example, two-sevenths was ‘duae septimae’ and three-eighths was ‘tres ocatavae.’”

To do actual calculations, they employed a unit known as the “uncia.” If that sounds familiar, it should. An “uncia” started out as one-twelfth of an “as,” which was a Roman unit of weight. As a result, ”uncia” evolved into our “ounce.” But eventually, the Roman uncia came to mean one-twelfth of anything, which made it a convenient standard for all problems involving fractions. For example, a half (six unciae) minus a third (four unciae) was two unciae, our one-sixth.

“You can add up twelfths to make halves, thirds, or quarters, so the uncia was fairly versatile,” Dr. Math explains. “When they wanted smaller fractions, the Romans usually cut the uncia into smaller parts. The system is very similar to measuring length in inches and fractions of the inch: You might not measure an object’s length exactly, but you can still come very close.”

Roger Schlueter: 618-239-2465, @RogerAnswer

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