Table Of Contents
Last updated on February 26th, 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 LXV.
Ancient Romans discovered that counting fingers could become cumbersome after 10. To overcome this complexity, the Roman numeric system was developed. This system 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. LXV in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., LXV = 65.
Let us learn more about the Roman numeral LXV, how we write it, 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 LXV 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 LXV,
Step 1: First, we break the Roman numerals. LXV = L + X + V
Step 2: Write the Roman Numerals for each part The Roman Numeral L is 50 The Roman Numeral X is 10 The Roman Numeral V is 5
Step 3: Combine all the numbers L + X + V = 50 + 10 + 5 = 65. Therefore, the Roman Numeral LXV is 65.
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 LXV.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are L, X, and V. The numeral for L is 50.
Step 2: Now we need to either add or subtract the smaller number, depending on its place. Here we add X and V to L, and we will get LXV. The Roman numeral X is 10, and V is 5. Therefore, the numeral of LXV is 65.
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
If a Roman artifact is inscribed with the numerals LXV and XL, what is the total value of the numerals combined? Write your answer in Roman numerals.
The total is CV
Convert both Roman numerals into their decimal forms:
LXV = 65
XL = 40
Now add both numbers: 65 + 40 = 105
Convert 105 into Roman numerals: 105 = 100 (C) + 5 (V) = CV
A scroll contains the numerals LXV and XXV. What is the difference when XXV is subtracted from LXV? Write the answer in Roman numerals.
The difference is XL
Convert the Roman numerals into their decimal forms:
LXV = 65
XXV = 25
Now subtract the numbers: 65 - 25 = 40
Convert 40 into Roman numerals: 40 = XL
A Roman sundial shows the numeral LXV. If the time is divided into 5 equal parts, what is the value of one part in Roman numerals?
XIII
Convert LXV into its decimal form:
LXV = 65
Divide by 5: 65 / 5 = 13
Write 13 in Roman numerals: 13 = 10 (X) + 3 (III) = XIII
A Roman shield is decorated with numerals. If the product of LXV and III is calculated, what is the resulting numeral?
CXCV
Convert LXV and III into numbers:
LXV = 65
III = 3
Multiply the numbers: 65 × 3 = 195
Convert 195 into Roman numerals: 195 = 100 (C) + 90 (XC) + 5 (V) = CXCV
Convert LXV into its decimal form.
In decimal form, LXV is 65
Break LXV into components: L = 50 X = 10 V = 5 Add the values: 50 + 10 + 5 = 65
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.