## Introduction

- This rule is an addition to the third rule, the rule of subtraction; we treat it separately since it's important that you understand it correctly.
- Remember the main Roman numerals, the ones that were used to build all the other ones? We'll be using them in a second, so let's write them down: I (one, 1), V (five, 5), X (ten, 10), L (fifty, 50), C (one hundred, 100), D (five hundred, 500), M (one thousand, 1,000), (V) (five thousand, 5,000), (X) (ten thousand, 10,000), (L) (fifty thousand, 50,000), (C) (one hundred thousand, 100,000), (D) (five hundred thousand, 500,000), (M) (one million, 1,000,000).
- Romans, as a rule, were placing a numeral of smaller value in front of another larger one (next to the left of it) in order to decrease the value of the larger one, but there is a set of simple rules that must be remembered, see it below.

## What numerals were allowed to be subtracted from the larger value ones and how?

- Numerals V (five, 5), L (fifty, 50), D (five hundred, 500), (V) (five thousand, 5,000), (L) (fifty thousand, 50,000), (D) (five hundred thousand, 500,000) were not allowed to be used to decrease numbers' value.
- I (one, 1) could be placed only in front of V (five, 5) or X (ten, 10).
- The only new numerals we get by subtracting I from V or X are:
- V - I = IV = 5 - 1 = 4 (four);
- X - I = IX = 10 - 1 = 9 (nine).

- X (ten, 10) could be placed only in front of L (fifty, 50) or C (one hundred, 100).
- The only new numerals we get by subtracting X from L and C are:
- L - X = XL = 50 - 10 = 40 (forty);
- C - X = XC = 100 - 10 = 90 (ninety).

- C (one hundred, 100) could be placed only in front of D (five hundred, 500) or M (one thousand, 1,000).
- The only new numerals we get by subtracting C from D and M are:
- D - C = CD = 500 - 100 = 400 (four hundred);
- M - C = CM = 1,000 - 100 = 900 (nine hundred);

- M (one thousand, 1,000) could be placed only in front of (V) (five thousand, 5,000) or (X) (ten thousand, 10,000).
- The only new numerals we get by subtracting M from (V) and (X) are:
- (V) - M = M(V) = 5,000 - 1,000 = 4,000 (four thousand);
- (X) - M = M(X) = 10,000 - 1,000 = 9,000 (nine thousand).

- ... And so on, I hope you've got the idea...

## Examples:

- 99 is written as: 99 = 90 + 9 = (100 - 10) + (10 - 1) = (C - X) + (X - I) = XC + IX = XCIX and not IC (thus we are not allowed to subtract I from C to get 99).
- 95 is written as: 95 = 90 + 5 = (100 - 10) + 5 = (C - X) + V = XC + V = XCV, and not VC (thus we are not allowed to subtract V from C to get 95).
- And by the examples above we just had a sneak peek on the next rule, the one of numerals addition :-).