Subtractive notation of Roman numerals:

• A numeral of a lesser value placed in front (next to the left) of a larger value numeral is subtracted from the larger one. This group of two numerals is called a group in subtractive notation.
• Except for symbol I (1), any other symbol may be used in a subtractive notation group as the larger value numeral.
• But only these symbols are allowed to be used in subtractive notation as numerals of lesser value: I (1), X (10), C (100), M (1,000), (X) (10,000), (C) (100,000), (M) (1,000,000).
• Numerals V (5), L (50), D (500), (V) (5,000), (L) (50,000), (D) (500,000) are NOT allowed to be used as numerals of lesser value in subtractive notation groups of Roman numerals.

Subtraction. Learn by an example how to subtract the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

The only possible groups of numerals in subtractive notation are:

• IV, IX, XL, XC, CD, CM, M(V), M(X), (X)(L), (X)(C), (C)(D), (C)(M).
• IV: calculated as V - I = 5 - 1 = 4;
• IX: calculated as X - I = 10 - 1 = 9;
• XL: calculated as L - X = 50 - 10 = 40;
• XC: calculated as C - X = 100 - 10 = 90;
• CD: calculated as D - C = 500 - 100 = 400;
• CM: calculated as M - C = 1,000 - 100 = 900;
• M(V): (V) - M = 5,000 - 1,000 = 4,000;
• M(X): (X) - M = 10,000 - 1,000 = 9,000;
• (X)(L): (L) - (X) = 50,000 - 10,000 = 40,000;
• (X)(C): (C) - (X) = 100,000 - 10,000 = 90,000;
• (C)(D): (D) - (C) = 500,000 - 100,000 = 400,000;
• (C)(M): (M) - (C) = 1,000,000 - 100,000 = 900,000;

Subtraction. Learn by an example how to subtract the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

How to use the lesser value numerals in subtractive notation groups

• The symbol I (1) may precede only a V (5) and a X (10) - the next two larger symbols up in the basic set of Roman numerals; the groups IL, IC, ID, IM, ... are not correct;
• The symbol X (10) may precede only an L (50) and a C (100) - also the next two larger symbols up in the basic set of Roman numerals; the groups XD, XM, X(V), X(X)... are not correct;
• The symbol C (100) may precede only a D (500) and an M (1,000) - again, also the next two larger symbols up in the basic set of Roman numerals; the groups C(V), C(X), C(L), C(C)... are not correct;
• As a rule, when used in subtractive notation as the lesser value numerals, the symbols I, X, C, M, ... may only precede their correspondent two larger symbols up in the basic set of Roman numerals.

Subtraction. Learn by an example how to subtract the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

Examples:

• 99 is written as: 99 = 90 + 9 = (100 - 10) + (10 - 1) = (C - X) + (X - I) = XC + IX = XCIX and not IC (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 (we are not allowed to subtract V from C to get 95).

I. The set of the basic symbols of the Roman numerals

II. The rule of the repetition of the Roman numerals

III. The groups of the Roman numerals written in subtractive notation

IV. The additive notation of the Roman numerals

How to convert the Hindu-Arabic numbers to Roman numerals: breaking down the numbers into place value subgroups

Examples of converting Hindu-Arabic numbers to Roman numerals

The list of the first 100 Roman numerals: the Roman numerals from 1 to 100

The list of the first 1,000 Roman numerals: the Roman numerals from 1 to 1,000

I. Addition. Learn by an example how to add the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

II. Subtraction. Learn by an example how to subtract the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

III. Addition and subtraction. Learn by an example how to add and subtract the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations