How to Add and Subtract Roman Numerals

What’s 51 + 12? Easy, right? How about LI + XII? Not so easy…or is it? Keep on reading to learn all about adding and subtracting Roman style.

Jason Marshall, PhD,
February 1, 2013
Episode #140

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Do you think math is fun? I absolutely think that it should be. After all, math problems are really just puzzles. And puzzles are fun, right? I realize that not all math problems are created equally—sometimes you have to use math to get real world work done. And that certainly isn’t always tons of fun. But math should be fun most of the time. The key to this is approaching problems with the right attitude. For example, do you think today’s topic—adding and subtracting Roman numerals—sounds like fun? For many of you, the answer is “No!” And you may be wondering how this could possibly be useful?

While those are fair questions, the truth is that math doesn’t always have to be serious and practical. Even though you may never need to use the math we talk about today, it’s still fun to puzzle out how ancient Romans could have added and subtracted their rather cryptic numerals. No, this isn’t a skill you need to survive in the modern world. But learning to see the many challenges you’ll face in life as puzzles that can be solved is a skill that will help you survive, thrive, and have fun. So, with that in mind, let’s spend today having a bit of fun puzzling out how the Romans managed to do arithmetic.

Recap: What Are Roman Numerals?

Before we begin figuring out how to add and subtract Roman style, let’s recap how the Roman numeral system that we learned about last time works. In this system, the letter “I” represents 1, “V” represents 5, “X” represents 10, “L” represents 50, “C” represents 100, “D” represents 500, and “M” represents 1,000. To write numbers other than these we combine various symbols together. If a symbol that represents a smaller number is written to the right of a symbol representing an equal or larger number, we add the values together. In common usage, symbols are repeated no more than 3 times in a row.

For example, the number 1,272 is written MCCLXXII. Since each symbol represents a number that’s equal to or smaller in size than the number represented by the symbol to its immediate left, all of the values represented by the various symbols here are added together. So the “M” represents 1,000, the two symbols “CC” represent 100 + 100 = 200, the “L” represents 50, the two “X”s represent 10 + 10 = 20, and the two “I”s represent 1 + 1 = 2—for a grand total of 1,000 + 200 + 50 + 20 + 2 = 1,272.

If, on the other hand, a symbol representing a smaller value is written just before a symbol representing a larger value, we have to subtract the smaller value from the larger. For example, “IX” represents the number 10 – 1 = 9, and “CM” represents 1,000 – 100 = 900. “I” is allowed to be subtracted from “V” and “X,” “X” is allowed to be subtracted from “L” and “C,” and “C” is allowed to be subtracted from “D” and “M,” but nothing else can be subtracted from anything else. And that’s it! Once you know these rules, you know everything necessary to read and write Roman numerals.


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