Roman numerals
Problem
Roman Numerals printable sheet
These symbols are the building blocks of Roman numerals:
I, V, X, L, C, D and M
Do you know the value of each letter? Click on 'Show' to check...
I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000
In our number system (the Arabic numeral system), there are ten different digits, (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the place of these digits in the number determines their value. For example, 2 on its own means 'two', but in 3240, the '2' now means "two hundred". In this way, any number can be written down, using only ten digits.
Roman numerals have a set of rules which allow you to write down any number:
1. If a smaller numeral comes after a larger numeral, add the smaller number to the larger number;
2. If a smaller numeral comes before a larger numeral, subtract the smaller number from the larger number;
3. Do not use the same symbol more than three times in a row.
Can you use these rules to construct and decipher Roman numerals?
Try converting the following Roman numerals into Arabic numerals:
III
IV
XVIII
XIX
MCMLXXVI
MMXXIII
MCMLXII
Now try converting the following into Roman numerals:
55
86
two thousand five hundred and ninety-two
913
Can you work out how to write '1984' in Roman numerals?
'1984' written in Roman numerals has more numerals than when it is written in Arabic numerals. However, this will not always be the case.
Can you find some examples when the number of Roman numerals is fewer than the number of Arabic numerals for the same number?
Getting Started
Here are some examples to help you follow the rules:
What number is "XII"?
Using rule number one, and breaking the number down into tens and units:
X= ten
II= two
The two comes after the ten, and so we add two to ten, and get the number 12.
What about "IX"?
This time, we use rule number two:
X=ten
I= one.
The one comes before the ten, and so we subtract one from ten, and get the number 9.
Student Solutions
Thank you to everybody who submitted a solution to this activity.
Erica, Sarah and Annie in Wenona, Australia sent in solutions to the first part of this activity:
These are the answers we got for Roman Numerals:
III = 3
IV = 4
XVIII = 18
XIX = 19
MCMLXXVI = 1976
MMXXIII = 2023
MCMLXII = 1962
55 = LV
86 = LXXXVI
2592 = MMDXCII
913 = CMXIII
1984 = MCMLXXXIV
We received similar solutions from Amy at Luckwell Primary School, Julia at BIS in South Korea, Stanley at Smithy Bridge, Alfie in the UK and Thomas at St Mary's Academy in the UK - thank you all for sending in your solutions.
Thomas also suggested that X, L, C, D and M would be examples of numbers where the number of Roman numerals is fewer than the number of Arabic numerals for the same number. Are these the only examples where the number is represented by just one Roman numeral?
Albert from St Matthew's Primary in the UK added a suggestion to this list:
In our number system 2000 has four digits but in Roman numerals it only has 2 digits MM
EH and FH from Shebbear Primary School in England sent in some more suggestions:
CM MC DL LD ML LM
These are good ideas, although there are some extra rules for writing numbers as Roman numerals which mean that LD and LM are not allowed - we would actually write those as CDL and CML.
Andrew at BIS in Vietnam said:
Can you find some examples when the number of Roman numerals is fewer than the number of Arabic numerals for the same number?
My ideas :
1200 = MCC
1510 = MDX
2500 = MMD etc
It looks like there might be a lot of possibilities! I wonder what Andrew means by 'etc'?
Teachers' Resources
Why do this problem?
This activity introduces children to Roman numerals. Comparing the number of numerals used in the two different systems makes an interesting context in which to practise interpreting and creating Roman numerals.
Possible approach
You could begin by inviting learners to share anything they know already about Roman numerals.
Challenge learners to decipher the Roman numerals given (perhaps in pairs) and use these examples to draw out the three rules. You could then invite pairs to create the Roman numerals for the numbers written in Arabic numerals in the problem, which will help them familiarise themselves with the rules.
The group can then work on the task of finding numbers which use fewer numerals in the Roman numeral system than the Arabic system.
Key questions
How did you work this one out?
What would you say are the differences between Roman numerals and the ways we write numbers now?
Possible extension
Learners might enjoy investigating which Roman numerals read the same backwards as forwards.