Roman arithmetic

In mathematics, Roman arithmetic is the use of arithmetical operations on Roman numerals.

In modern education, Roman arithmetic is seldom taught. The preferred method is to convert the Roman numeral into Arabic numerals and solve the equation using positional notation.

The ancient Romans used a counting board or an abacus for calculations; Roman numerals were used only to record results.

Calculations with Roman numerals

The use of subtractive notation with Roman numerals increased the complexity of performing basic arithmetic operations without conveying the benefits of a full positional notation system. The first step in Roman arithmetic is to remove the subtractive notation from the numerals before any arithmetic operations. The subtractive notation is then reapplied to the solution at the end of the operation.

When subtractive notation is not used (such as IIII representing 4 instead of IV), addition can be performed by combining the symbols in all terms and grouping similar symbols together. Then the answer can be represented in standard form by reducing the symbols to their highest form, so that 5 Is will reduce to a single V, 2 Vs reduce to an X, and so on.

External links

• Roman Numerals (Mathworld)
• How can I use Roman numerals to do arithmetic problems? (Ask Dr Math)