# The Subtractive Principle

So, remember how I told you 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 numerals 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.

If this is your first time working with Roman Numerals, a good place to start your practicing is here.

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