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In Rome, merchants used Roman numerals to perform basic arithmetic operations. In modern education, the Roman arithmetic used by the Romans is seldom taught. The preferred method is to convert the Roman numeral into an Hindu-Arabic numeral and solve the equation using a modern positional notation system. While this is more practical, it is not really learning how to add, subtract, multiply and divide Roman numerals, it is only making the student practice converting from Roman to Arabic and back again. Except for historical purposes, none of this is particularly useful to the grade student unless it is used to demonstrate the existence of different numeral systems and their impact on arithmetic and to do that, the student needs to learn how to perform arithmetic operations in the native numeral system. Image File history File links Information_icon. ... Wikibooks logo Wikibooks, previously called Wikimedia Free Textbook Project and Wikimedia-Textbooks, is a wiki for the creation of books. ... Nickname: The Eternal City Motto: SPQR: Senatus PopulusQue Romanus Location of the city of Rome (yellow) within the Province of Rome (red) and region of Lazio (grey) Coordinates: Region Lazio Province Province of Rome Founded 21 April 753 BC Mayor Walter Veltroni Area    - City 1,285 km²  (580 sq mi... Roman numerals are a numeral system originating in ancient Rome, adapted from Etruscan numerals. ... Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple daily counting to advanced science and business calculations. ... The Hindu-Arabic numeral system (also called Algorism) is a positional decimal numeral system documented from the 9th century. ... Positional notation is a system in which each position has a value represented by a unique symbol or character. ... A numeral is a symbol or group of symbols, or a word in a natural language that represents a number. ...

The two most basic operations of arithmetic are addition and subtraction. Multiplication is specialized form of addition where you quickly add identical numbers and division is a specialized form of subtraction where you quickly remove identical numbers. 3 + 2 with apples, a popular choice in textbooks Addition is the basic operation of arithmetic. ... 5 - 2 = 3 Subtraction is one of the four basic arithmetic operations; it is essentially the opposite of addition. ... In mathematics, multiplication is an elementary arithmetic operation. ... In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ...

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. In the algorithms that follow, the first step is to remove the subtractive notation from the numerals before any arithmetic operations. The subtractive notation is then reapplied to the solution as the end of the operation. Subtractive notation is an early form of positional notation used with Roman numerals as a shorthand to replace four or five characters in a numeral representing a number with usually just two characters. ... Flowcharts are often used to represent algorithms. ...

The Roman abacus was a hand-held tool for assisting in the computations using Roman numerals. The Romans developed the so-called fucken Roman abacus, or rather a portable counting board, based on previous Greek counting boards. ...

Basic operations

All arithmetic operations can be broken down to combinations of addition and subtraction.

Addition

Example

CXVI + XXIV =  ?

Solution: CXVI + XXIV = CXL

Discussion

Step 1 decodes the positional data in the terms and replaces it with primitive counts. Now represented as a pure counting system, the concatenation of the terms in Step 2 gives the correct solution to the problem: CXVIXXIIII represents the same number as CXL — both terms convert to 140 in Arabic numerals. Steps 3 & 4 now reduce the result to the simplest expression possible and Step 5 reintroduces subtractive notation transforming the result back into a positional number.

Subtraction

Example

CXVI − XXIV =  ?

Solution: CXVI − XXIV = XCII

Discussion

Step 1 decodes the positional data in the terms and replaces it with primitive counts. In Step 2, like numerals are eliminated from both terms: a count of X and a count of I are each removed from each term, leaving a simplified problem of CV − XIII. Step 3 then expands the first term until it contains a common numeral (X) to the highest numeral in the second term. Step 2 is then repeated, followed by Step 3 until all of the numerals in the second term have been eliminated. Once all of the numerals of have been eliminated, the remaining numerals in the first term represent the solution as a primitive count. Step 5 reintroduces subtractive notation transforming the result back into a positional number.

Compound operations

Having defined the process where by addition and subtraction operations can be performed using only Roman numerals, the other two traditional operations of arithmetic, multiplication and division, can now be accomplished.

Multiplication

multiplicand × multiplier = product

Example

XIV × VII = ?

Solution: XIV × VII = XCVIII

Discussion

Step 1 decodes the positional data in the terms and replaces it with primitive counts. Step 2 adds the multiplicand to product. Since subtractive notation has been removed in Step 1 and is later encoded in Step 5, there is no longer a requirement to perform the same processes when performing addition or subtraction within the multiplication operation. Step 3 reduces the number if iterations remaining for the addition operation in Step 2 by decreasing the value of the multiplier. Step 5 reintroduces subtractive notation transforming the result back into a positional number.

Division

dividend / divisor = quotient

Example

CXXI / V = ?

Solution: CXXI / V = XXIV remainder I

Discussion

Step 1 decodes the positional data in the terms and replaces it with primitive counts. Step 2 subtracts the divisor from the dividend. Since subtractive notation has been removed in Step 1 and is later encoded in Step 5, there is no longer a requirement to perform the same processes when performing addition or subtraction within the division operation. Step 3 increases the counter used for the quotient if remaining count of the dividend is greater than the divisor. Step 5 reintroduces subtractive notation transforming the result back into a positional number.