## Introduction

- This rule is an addition to the third rule, the rule of subtraction in subtractive notation; 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're going to use 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 a smaller value in front of another larger one (next to the left of it) in order to decrease the value of the larger one (this is called subtractive notation), but there is a set of simple rules that must be remembered, see it below.

## What numerals are NOT allowed and what numerals are allowed to be used in subtractive notation 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) are NOT allowed to be used in this kind of operation.
- Only these symbols were allowed to be used in subtractive notation:
**I**(1),**X**(10),**C**(100),**M**(1,000),**(X)**(10,000),**(C)**(100,000),**(M)**(1,000,000): - 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 :-).