116 LearnersLast updated on May 26th, 2025
CMLXIV in Roman Numerals
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 CMLXIV.
What is CMLXIV in Roman Numerals?
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. CMLXIV in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., CMLXIV = 964.
Let us learn more about the Roman numeral CMLXIV, how we write them, the mistakes we usually make, and ways to avoid these mistakes.
Basic Rules for CMLXIV in Roman Numerals
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.
Rule 1: Addition Method:
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.
Rule 2: Repetition Method:
A symbol that is repeated three times in continuation increases the value of the numeral. For example, XXX = 30.
Rule 3: Subtraction Method:
We use the subtraction method when a larger symbol follows a smaller symbol. For example, XL = 40 (which is 50 – 10).
Rule 4: Limitation Rule:
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.
How to Write CMLXIV in Roman Numerals?
Let us learn about how to write CMLXIV in Roman numerals. There are two methods that we can use to write Roman numerals:
- By Expansion Method
- By Grouping Method
CMLXIV in Roman Numeral by Expansion Method
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 CMLXIV,
Step 1: First we break the Roman numerals. CMLXIV = CM + LX + IV
Step 2: Write the Roman Numerals for each part The Roman Numeral CM is 900 The Roman Numeral LX is 60 The Roman Numeral IV is 4
Step 3: Combine all the numbers CM + LX + IV = 900 + 60 + 4 = 964. Therefore, the Roman Numeral CMLXIV is 964.
CMLXIV in Roman Numeral by Grouping Method
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 CMLXIV.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CM, LX, and IV. The numeral for CM is 900 The numeral for LX is 60
Step 2: Now we need to either add or subtract the smaller number, depending on its place.
Here we add LX and IV to CM and we will get CMLXIV. The Roman numeral IV is 4 Therefore, the numeral of CMLXIV is 964.
Numbers Related to CMLXIV in Roman Numerals
We follow a pattern when it comes to writing Roman numerals. In this section, we will write some numbers related to the Roman numeral CMLXIV:
| Roman Numeral | Number | Breakdown |
|---|---|---|
| CMLXIV | 964 | CM + LX + IV |
| CM | 900 | M - C |
| LX | 60 | L + X |
| IV | 4 | V - I |
Common Mistakes and How to Avoid Them in CMLXIV Roman Numerals
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
Mistake 1
Mistakes when applying the repetition method
It can be quite confusing for beginners to remember that Roman Numerals cannot be repeated more than three times. Another thing to keep in mind is that Roman Numerals such as V, L, and D cannot be repeated.
For example, writing LL as 100 is incorrect, the correct answer is C.
CMLXIV Roman Numerals Examples
Problem 1
Calculate the product of CMLXIV and II. Write the answer in Roman numerals.
The product is MCMXXVIII
Explanation
Convert CMLXIV into its decimal form:
CMLXIV = 964
Multiply by 2: 964 × 2 = 1928
Convert 1928 into Roman numerals: 1000 (M) + 900 (CM) + 20 (XX) + 8 (VIII) = MCMXXVIII
Problem 2
Find the difference between CMLXIV and CXLIV. Write the result in Roman numerals.
The difference is DCCCXX
Explanation
Convert the Roman numerals into decimal form:
CMLXIV = 964
CXLIV = 144
Subtract the numbers: 964 - 144 = 820
Convert 820 into Roman numerals: 800 (DCCC) + 20 (XX) = DCCCXX
Problem 3
Divide CMLXIV by VIII and write the answer in Roman numerals.
The result is CXX
Explanation
Convert CMLXIV into its decimal form:
CMLXIV = 964
Divide by 8: 964 ÷ 8 = 120.5
Since Roman numerals do not represent fractions, take the integer part: 120 = 100 (C) + 20 (XX) = CXX
Problem 4
Add CMLXIV and LXXXVI. Write the sum in Roman numerals.
The sum is M
Explanation
Convert the Roman numerals into decimal form:
CMLXIV = 964
LXXXVI = 86
Add the numbers: 964 + 86 = 1050
Convert 1050 into Roman numerals: 1000 (M) + 50 (L) = M
Problem 5
Convert CMLXIV into its decimal form.
In decimal form CMLXIV is 964
Explanation
Break CMLXIV into components:
CM = 900
LX = 60
IV = 4
Add values: 900 + 60 + 4 = 964
FAQs on CMLXIV in Roman Numerals
1.What is CLXIV in Roman numerals?
2.Is CMLXIV a prime number?
3.What is CMLXIV + CMLXIV?
4.What is MCMXLIV?
5.Subtract LXIV from CMLXIV
6.How can children in Bahrain use numbers in everyday life to understand CMLXIV in Roman Numerals?
7.What are some fun ways kids in Bahrain can practice CMLXIV in Roman Numerals with numbers?
8.What role do numbers and CMLXIV in Roman Numerals play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve CMLXIV in Roman Numerals skills?
Important Glossaries for CMLXIV in Roman Numerals
- Subtraction Method: When a smaller numeral precedes a larger numeral, it is subtracted. For example, IX is 9 (10 - 1).
- Addition Method: When a larger numeral precedes a smaller numeral, it is added. For example, VI is 6 (5 + 1).
- Limitation Rule: There are some symbols that cannot be repeated more than once (V, L, D). For example, VV for 10 is wrong, the correct answer is X.
- Numerical Value: The value assigned to a Roman numeral based on the symbols used, such as C = 100.
- Place Value: The position of a digit in a number, which determines its value. For example, the number 6 in 964 is in the tens place.
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
