Our Roman Numerals Worksheet will help you in practicing and making you efficient in this topic. So our questions are based on roman numerations and rules that are used in solving them. In this Roman Numerals Comparison Worksheet, you will solve problems related to the comparison of two roman numerals, find the largest and smallest roman numeral among the given roman numbers. Look no further and begin practicing using our Worksheet on Comparing Roman Numerals.

Also, Read: Worksheet on Roman Numeration

## Rules for Converting Roman Numerals to Numbers

We have to follow certain rules while converting roman numbers into Hindi – Arabic numerals as mentioned below

- When a roman number is given we have initially split the given number into digit, double-digit, triple-digit, quadruple-digit symbols
- Find the largest Roman numeral by using the decimal value.
- Now if the largest numeral appears first then we have to count how many times it is repeated. Remember a number can’t be repeated more than three times.
- Now if the number is repeated, multiply its value by the number of times it is repeated.
- Now add the value of roman to the value of a decimal number.
- If in case largest numeral appears second then subtract the value of the number before its value.

### Rules for Converting Numbers to Roman Numerals

We have certain rules to covert Hindu-Arabic numbers into roman numerical as mentioned below.

- Each symbol can only be repeated three times.
- We have to split the given number into units form.
- Always remember if a smaller number is placed before a larger number, the number has the effect of addition. Which means the smaller number must be added to the larger number.
- And if a smaller number is placed after a larger number then we have to perform subtraction, which means we have to subtract a smaller number from a larger number

**1. Compare and find the largest Roman numeral. **

(i). MDCCCLXXIX, MDXXVI

(ii)CDXI, MDCCXI

(iii)MCMLX, DCCXLIII

(iv)CLVII, XXIV

(v)XXXVIII, XXV

## Solution:

To the largest numeral among given numerals, we have to initially convert those roman numerals into Hindu-Arabic numbers.

We have to repeat the above steps till we get our number.

Now let’s solve our problems.

(i) MDCCCLXXIX, MDXXVI

First let’s covert MDCCCLXXIX = M + D + 3(C) + L + 2(X) + IX

= 1000 + 500 + 3(100) + 50 + 2(10) + 9

= 1879

Now, MDXXVI = M + D + 2(X) + VI

= 1000 + 500 + 2(10) + 6

= 1526

Now that we know MDCCCLXXIX = 1879 & MDXXVI = 1526

Since 1879 is greater than 1526

**Answer**: MDCCCLXXIX is larger than MDXXVI

(ii) CDXI, MDCCXI

First let’s covert CDXI = CD + XI

= (1000-100) + 10 + 1

= 911

Now, MDCCXI = M + D + 2(C) + X + I

= 1000 + 500 + 2(100) + 10 + 1

= 1711

Now that we know CDXI = 911 & MDCCXI = 1711

Since 1711 is greater than 911

**Answer**: MDCCXI is larger than CDXI

(iii). MCMLX, DCCXLIII

First let’s covert MCMLX = M + CM + L + X

= 1000 + (1000- 100) + 50 + 10

= 1960

Now, DCCXLIII = D + 2(C) + XL + 3(I)

= 500 + 2(100) + (50-10) + 3(1)

= 743

Now that we know MCMLX = 1960 & DCCXLIII = 743

Since 1960 is greater than 743

**Answer**: MCMLX is larger than DCCXLIII

(iv). CLVII, XXIV

First let’s covert CLVII = C + L + V + I + I

= 100 + 50 + 5 + 1 +1

= 157

Now XXIV = X + X + IV

= 10 + 10 + 4

= 24.

Now that we know CLVII = 157 & XXIV = 24

Since 157 is greater than 24

**Answer**: CLVII is larger than XXIV

(v). XXXVIII, XXV

First let’s covert: CLVII = 3(X) + V +3( I)

= 30 + 5 + 3

= 38

XXV = 2(V)

= 10 + 10 + 5

= 25.

Now that we know CLVII = 38 & XXV = 25

Since 38 is greater than 22

**Answer**: CLVII is larger than XXV

**2. Compare and find the smallest Roman numeral. **

(i). CMLVI, DLXXII

(ii). LXXXVI, XI

(iii). CXXV, XXV

(iv). CC, VI

(v). CCL, XXVI

## Solution:

Now let’s solve our problems.

To the smallest numeral among given numerals, we have to initially convert those roman numerals into Hindu-Arabic numbers.

(i). CMLVI, DLXXII

First let’s covert CMLVI = CM + L + V + I

= 900+ 50 + 5 + 1

= 956

Now, DLXXII = D+ L + 2(X) + 2(I)

= 500 + 50 +2(10) + 2(1)

= 572

Now that we know CMLVI = 956 & DLXXII = 572

Since 572is smaller than 956

**Answer**: DLXXII is smaller than CMLVI

(ii). LXXXVI, XI

First let’s covert LXXXVI = L + 3(X) + V + I

= 50 + 30 + 5 + 1

= 86

Now, XI = X + I

= 10 + 1

= 11

Now that we know LXXXVI = 86 & XI = 11

Since 11 is smaller than 86

**Answer**: XI is smaller than LXXXVI

(iii). CXXV, XXV.

First let’s covert CXXV = C + 2(X) + V

= 100+ 2(10) + 5

= 125

Now XXV = 2(X) + V

= 2(10) + 5

= 25

Now that we know CXXV = 125 & XXV = 25

Since 25 is smaller than 125

**Answer**: XXV is smaller than CXXV

(iv). CC, VI.

First let’s covert CC = 2(C)

= 2(100)

= 200

Now LLVI = 2(L) + V + I

= 2(50) + 5 + 1

= 106

Now that we know CC = 200 & LLVI = 106

Since 106 is smaller than 200

**Answer**: LLVI is smaller than CC

(v). CCL, XXVI

First let’s covert CCL = 2(C) + L

= 2(100) + 50

= 250

Now, XXVI = 2(X) + V + I

= 2(10) + 5 + 1

= 26

Now that we know CCL = 250 & XXVI = 26

Since 26 is smaller than 250

**3.Compare and fill in the blank with correct sign (<, >, =)**

(i). MMVI ____ MLIX

(ii) XXVIII ____ LV

(iii) 105 ___ CV

(iv) CLXV ___ 165

(v) CLXXXIX ___ MCXXIV

## Solution:

To compare any two Roman numerical or any two Hindu-Arabic numbers first we need to find decimal value for those numbers.

**(i) MMMVI____ MLIX**

First let’s covert MMMVI = 3(M) + V + I

= 3(1000) + 5 + 1

= 3006

MLIX = M + L + IX

= 1000 + 50 + (10 – 1)

= 1059

Now that we know MMMVI = 3006 & MLIX = 1059

As we know 3006 is greater than 1059.

So MMMVI is greater than MLIX

**Answer**: MMXVI **>** MLIX

**(ii) XXVIII____ LV**

First let’s covert XXVIII = 2(X) + V + 3(I)

= 2(10) + 5 + 3(1)

= 28

LV = L + V

= 50 + 5

= 55

Now that we know XXVIII = 28 & LX = 55

As we know 28 is smaller than 55.

So XXVIII is smaller than LX

**Answer**: MMXVI **<** MLIX

(iii) 105___ CV

To compare any two digits they have to be in the same format, so let’s covert Hindu-Arabic number 105 into roman numerals.

So 105 = 100 + 5

= CV

**Answer**: 105 **=** CV

(iv). CLXV ___ 165

To compare any two digits they have to be in same format, so let’s convert roman numerical CLXV into -Arabic number.

As we already know steps to convert any given roman numerical to Hindu-Arabic digit let’s follow those steps and find out.

Let’s covert CLXV = C + L + V + X

= 100 + 50 + 10 + 5

= 165

**Answer**: CLXV **=** 165

(v). CLXXXIX____ MCXXIV

Following above mentioned steps and rules

First let’s covert CLXXXIX = C + L + 3(X) + IV

= 100 + 50 + 3(10) + (5-1)

= 189

MCXXIV = M + C + 2(X) + IV

= 1000 + 100 + 2 (10) + (5 – 1)

= 1124

Now that we know CLXXXIX = 189 & MCXXIV = 1124

As we know 189 is smaller than 1124.

So CLXXXIX is smaller than MCXXIV

**Answer**: CLXXXIX **<** MCXXIV