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Last updated on February 27th, 2025
To meet their daily commerce and administration needs, the ancient Romans developed Roman Numerals. It used a combination of seven symbols — I, V, X, L, C, D, and M to represent numbers. Roman numerals were used to record transactions, keep track of data, and label military units. In this topic, we are going to learn about the Roman numeral XXXI.
Ancient Romans discovered that counting fingers could get very complicated after 10. So to overcome the complexity, the Roman numeric system was developed. This was widely used throughout Europe as a standard writing system until the late Middle Ages.
Seven symbols are used to represent numbers in the Roman numeric system — I, V, X, L, C, D, and M. The numerals are made up of different combinations of these symbols. XXXI in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., XXXI = 31.
Let us learn more about the Roman numeral XXXI, how we write them, the mistakes we usually make, and ways to avoid these mistakes.
When writing Roman numerals, there are a few rules that we need to follow based on the Roman numerals we are trying to write. In this section, we will learn about the rules when writing Roman numerals and how to represent them.
When a larger symbol is followed by a smaller symbol, we add the numerals to each other. For example, in VIII, we have 5+3=8.
A symbol that is repeated three times in continuation increases the value of the numeral. For example, XXX=30.
We use the subtraction method when a larger symbol follows a smaller symbol. For example, XL=40 (which is 50–10).
Symbols cannot be repeated more than three times, and some symbols, such as V, L, and D, cannot be repeated more than once. For example, 10 is represented as X and not VV.
Let us learn about how to write XXXI in Roman numerals. There are two methods that we can use to write Roman numerals:
The breaking down of Roman numerals into parts and then converting them into numerals is what we call the expansion method. The expansion method is the breaking down of Roman numerals into numerical form and adding them to get the final number.
Step 1: Break the Roman numerals into parts.
Step 2: Now write each of the Roman numerals with its numerical digit in the place value.
Step 3: Add the numerals together.
For XXXI,
Step 1: First, we break the Roman numerals. XXXI = X + X + X + I
Step 2: Write the Roman Numerals for each part. The Roman Numeral X is 10. The Roman Numeral I is 1.
Step 3: Combine all the numbers. X + X + X + I = 10 + 10 + 10 + 1 = 31. Therefore, the Roman Numeral XXXI is 31.
Using subtraction and addition rules, we will apply the grouping method. This means we break the Roman numerals into smaller groups, which makes it easier to work with. This method groups the Roman numerals logically, and then we write the numbers for each group.
Step 1: Take the largest number and write the number for that Roman numeral.
Step 2: Write the Roman numeral using the subtraction and addition rules.
Example: Let’s take the Roman numeral XXXI.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are XXX and I. The numeral for XXX is 30.
Step 2: Now we need to either add or subtract the smaller number, depending on its place. Here we add I to XXX, and we will get XXXI. The Roman numeral I is 1. Therefore, the numeral of XXXI is 31.
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
What is the result of adding XXXI and IX? Write the answer in Roman numerals.
The result is XL
Convert both Roman numerals into their decimal form:
XXXI = 31
IX = 9
Now add both numbers: 31 + 9 = 40
Now convert the number into its Roman numeral: 40 = XL
Subtract XIV from XXXI and express the result in Roman numerals.
The result is XVII
Convert the Roman numerals into their decimal form:
XXXI = 31
XIV = 14
Now subtract the numbers: 31 - 14 = 17
Convert the number into its Roman numeral: 17 = 10 + 5 + 1 + 1 = XVII
Divide LXII by 2 and write the answer in Roman numerals.
XXXI
Convert LXII into its decimal form:
LXII = 62
Divide by 2: 62 / 2 = 31
Write 31 in Roman numerals: 31 = 30 + 1 = XXXI
What is the product of XXXI and III? Provide your answer in Roman numerals.
XCIII is the product of XXXI and III.
Write XXXI and III in numbers:
XXXI = 31
III = 3
Multiply the numbers: 31 × 3 = 93
Convert 93 into its Roman numerals: 90 (XC) + 3 (III) = XCIII
Convert XXXI into its decimal form.
In decimal form, XXXI is 31
Break XXXI into components:
XXX = 30 (X + X + X)
I = 1
Add values: 30 + 1 = 31
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.