Math material-roman numerals

The numbers, 1234567890, we use nowadays are called as “Arabic numerals”. It is easy to recognize the size among several numbers, and is also easy to write and read. However there is more than one numeral system in the world. Roman numerals that we still see often now is also a numeral system. Although it is troublesome to write, its rules are very interesting!

First we need to remember the following rules:

♦ Change from 1
♦ Left is minus
♦ right is plus
♦ Repeat times of letters means “multiples”, up to three*One line means a thousand times

It would be clearer to explain by examples:

Change from 1, 5

Only 1, 5, 10, 50, 100, 500, 1000 has their own single letters in Roman numerals. Other numbers are basically changed by these numbers.Then how to make changes? According to Alex’s own statement (yes, that’s me), I will divided the number by the “same level”. That is, one-digit and one-digit are in the same level, two-digit and two-digit are in the same level, and so on.

For example, 70 and 50 are at the same level, and 70 is greater than 50. So we use the “plus” method to make changes. 4 and 5 are at the same level, 4 is smaller than 5, so we use the “minus” method. And what is the way to make changes? We’ll talk about it later.

Left is minus, right is plus

Then how do these letter combine? Since there are few letters, it must to be added and subtracted. In a roman numerals, you can see some larger number will be with the small number before or after.

For example: \(VI\),the largest number is 5, and the right followed by one 1. According to “Left is minus, right is plus”, we have the number is 5+1=6.

Look at one more:The largest number is 50, and followed by a 10 on the left. According to “Left is minus, right is plus”, we know that this number is (-10)+50=40

The times we repeated are the times we multiple it. Three times at most

Like XXX means 10*3=30. The number nine, in the rule, must have the same level as 5. It should be written as \(9=5+4=XIIII\) . But there is a rule – Three times at most. So it would be written as 9=(-1)+10=\(IX\)

Notice that we would not write 8 as \(IIX\), because 8 can be written by the normal rule.

one line represents a thousand times

What if I want to write a larger number? Like three thousand or more? You can add a line above the letter, this number will be thousands of time.For example:I want to express 5000 by using roman numerals, but the biggest number one letter can show is 1000, and I can’t repeat it five times due to the rule.The only thing I need to do is to add a line on the top of V. Then we get \(\overline V\) =5*000=5000

If there is two line, then multiple the number \(1000^2\) times.

I will separate it into the sum of several digit:


100= \(C\)

90=(-10)+100= \(XC\)

4=(-1)+5= \(IV\)


take a larger number:1985


1000= \(M\)

900= (-100)+1000= \(CM\)

80= 50+(10*3)= \(LXXX\)

5= \(V\)


The content above is to teach you how to write. The next step is to teach you how to read.

Alex is walking on the letters and it’s nothing when encountered a number at the same level (or above). And separate it when encountered a smaller one.

Take \(MMMCLXIX\) fro example:

We started from M, and encountered 3M. Until we met a number smaller, separate it.

Keep walking and encounter L, L is smaller, separate it.

L and X are in the same level, nothing happen.

encounter I, smaller, separate it.

We’ll get


The sum of them is 3169.

try another one:

\({\overline V}MMMCDLXXII\)


\({\overline V}MMM\) / \(CD\) / \(LXX\) / \(II\)

8000+400+70+2 = 8472

Add some ingredients

There is no juice here, but don’t forget we have seasoned with Chinese!

Seasoned with Chinese

◊ roman numerals – 羅馬數字
◊ Arabic numerals – 阿拉伯數字

the feature picture is from  Pixabay (Author: TanteTati)
and other pictures is made by Alex

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