**Roman Numerals**

The Subtractive Principle

The Subtractive Principle

**Reflection**

What the Letters Mean

What the Letters Mean

Here is a chart that has all the Roman Numerals, and what they stand for. The system is based on seven different symbols in total. These symbols can be used to write any Roman Numeral!

Roman Numeral Value

I 1

V 5

X 10

L 50

C 100

D 500

M 1,000

Once you have familiarized yourself with these, let's move on to the Additive Principle, where we'll begin to learn how to construct other numbers using these.

Practice

Check out http://www.abcya.com/roman_numerals.htm for a Roman Numeral game that has increasing levels of difficulty.

Practice

Create at least two problems for the following operations: addition, subtraction, multiplication, and division. Write your problems in Roman Numerals and make an answer key.

Finding Roman Numerals

Roman numerals were used by the Ancient Romans as their numbering system. We still use them sometimes today. You see them in the Super Bowl's numbering system, after king's names (King Henry IV), in outlines, and other places. Roman numerals are base 10 or decimal, like the numbers we use today. They are not entirely positional, however, and there is no number zero.

The Additive Principle

The system for writing Roman Numerals is an additive system. This means to calculate the value of a Roman Numeral, you simply have to add up all the digits in the Roman Numeral!

Examples:

VIII = 5 + 1 + 1 + 1 = 8

XXXIII = 10 + 10 + 10 + 1 + 1 +1 = 33

CLXXVIII = 100 + 50 + 10 + 10 + 5 + 1 + 1 + 1 = 178

MMX = 1,000 + 1,000 + 10 = 2,010

There are a couple of other rules to follow:

Roman Numerals are always written with the largest numbers on the left, down to the smallest on the right. For example, you wouldn't write 8 above as IIIV, it's written as VIII.

Roman Numerals are always written with the shortest number of numerals as possible. For example, you wouldn't write 5 as IIIII, you'd always write it as V.

Video Lesson

To watch Roman Numeral Instruction go to:

http://www.roman-numerals.org/videos.html

So, remember how you are not to put smaller Roman Numerals to the left of larger ones? There's one exception where you're allowed to do this. For numbers where you'd have to write four numerals in a row, there is a shortcut to save precious writing space. You can write a smaller numeral to the left of a larger one to subtract from it! The table below has all the allowed subtractive combinations:

Roman

Numeral Value

IV 4

IX 9

XL 40

XC 90

CD 400

CM 900

As you can see above, there are only certain cases where subtraction is allowed. You can remember this because the numeral being subtracted is always 1 or 2 numerals away from the numeral being subtracted from. So you can subtract I from V or X, but not L, and X from L or C, but not D.

You might think it would be easy to write 99 as IC, but only the combinations above are allowed. You can have multiple subtractions in the same Roman Numeral, which we need to write 99 correctly, as XCIX = XC + IX = 90 + 9 = 99.

1. What was the most interesting thing you learned about Roman Numerals?

2. What was the most challenging thing to remember about Roman Numerals?

3. Which do you think is a more effective number system: ours or Roman numerals? Why?