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State Board · Class 5 · Mathematics

Lesson 1: Roman Numerals

5 concepts · 40 practice questions with answers · Free to read

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Roman numerals and their symbols

From daily life

Look at an old clock in a temple or a railway station. Instead of 1, 2, 3 it often shows I, II, III up to XII. These are Roman numerals.

Simple definition

In ancient Europe, Roman capital letters were used to write numbers, so they are called Roman numerals (रोमन अंक). The basic symbols are I = 1, V = 5, X = 10. There was no symbol for zero.

A clock face with the hours written in Roman numerals, I to XII.XIIIIIIIIIVVVIVIIVIIIIXXXI

In the figure : Roman numerals on a clock: I to XII show the hours.

Roman symbols and their values: I = 1, V = 5, X = 10.I1V5X10

In the figure : The three basic symbols: I = 1, V = 5 and X = 10.

Rule 1: Learn the three symbols — Use only I, V and X for the numbers 1 to 20.

  • Easy : I = 1, V = 5, X = 10.
  • Medium : The hour hand at 5 shows V; at 10 it shows X.
  • Exam-type : Which symbol is missing on Roman clocks for 0? There is none, because Roman numerals have no zero.
Live figure

Roman numerals and their symbols

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Remember

I, V and X are the three starting symbols. There is no zero in Roman numerals.

Common mistake

Taking V as 10 or X as 5. Remember: V is the smaller one, 5, and X is 10.

Shortcut

Memory clue: I-V-X = 1-5-10 — a V is like the open hand, one hand has 5 fingers; X is two Vs joined, 10.

Spot the difference

SymbolIVX
Value1510
Looks likeone fingerone handtwo hands

Practice questions

Easy
  1. 1What is the value of V?
  2. 2Write 10 in Roman numerals.
  3. 3Which symbol stands for 1?
Medium
  1. 4Is there a Roman symbol for zero?
  2. 5Which is bigger, V or X?
  3. 6The hour hand points at the symbol X. Which hour is it?
Challenging
  1. 7How many fingers are on two hands, and which symbol shows this?
  2. 8Rohit says V = 10 and X = 5. Correct him.
Show answers (try them yourself first)
  1. 15
  2. 2X
  3. 3I
  4. 4No.
  5. 5X (10) is bigger than V (5).
  6. 610 o'clock.
  7. 710 fingers; X.
  8. 8V = 5 and X = 10.

Repeating symbols and adding

From daily life

A shopkeeper keeps tally marks: | | | for three. Roman numerals do the same for small numbers: I, II, III.

Simple definition

When I or X is repeated, their values are added. When a smaller symbol is written on the right of a bigger one, it is added as well.

III is I + I + I = 3.I1+I1+I1=III3I may be repeated up to three times

In the figure : Repeating a symbol adds: III = 1 + 1 + 1 = 3.

Rule 1: Repeat and add — I and X can be repeated, but at most 3 times in a row. V is never repeated.

  • Easy : II = 1 + 1 = 2 and XX = 10 + 10 = 20.
  • Medium : XXX = 30 would be 10 + 10 + 10, but the problem only needs numbers up to 20, so XX is the biggest we use.
  • Exam-type : Why is VV wrong for 10? V is never repeated; 10 is written X.

Rule 2: Small on the right: add — A smaller symbol on the right of a bigger one is added to it.

VI is V + I = 5 + 1 = 6.V5+I1=VI6smaller symbol on the right: add

In the figure : A smaller symbol on the right of a bigger one is added: VI = 5 + 1 = 6.

  • Easy : VI = 5 + 1 = 6 and XI = 10 + 1 = 11.
  • Medium : VIII = 5 + 1 + 1 + 1 = 8 and XIII = 10 + 1 + 1 + 1 = 13.
  • Exam-type : XVII = 10 + 5 + 1 + 1 = 17. Check: V is not repeated and I is used 2 times.
Remember

I and X may appear at most 3 times in a row; V never repeats.

Common mistake

Writing IIII for 4. Four I's in a row are not allowed; 4 is written IV.

Shortcut

Memory clue: Big first, then small: add. VII = 5 then 1 + 1.

Spot the difference

NumberRomanWorking
3III1 + 1 + 1
6VI5 + 1
12XII10 + 1 + 1
16XVI10 + 5 + 1

Practice questions

Easy
  1. 1Write 2 in Roman numerals.
  2. 2Write 6 in Roman numerals.
  3. 3What number is XX?
Medium
  1. 4Write 8 in Roman numerals.
  2. 5What number is XIII?
  3. 6Write 17 in Roman numerals.
Challenging
  1. 7Why is VV not the Roman numeral for 10?
  2. 8Aman wrote IIII for 4 and VX for 5. What is wrong, and what are the correct forms?
Show answers (try them yourself first)
  1. 1II
  2. 2VI (5 + 1)
  3. 320
  4. 4VIII (5 + 1 + 1 + 1)
  5. 513
  6. 6XVII (10 + 5 + 1 + 1)
  7. 7V is never repeated. 10 is X.
  8. 8I cannot be written 4 times and V is not placed before X to mean 5. 4 = IV, 5 = V.

Subtracting: IV, IX, XIV and XIX

From daily life

A clock shows IX when the hour hand is one step before X. We can say, "one before ten". Roman numerals use the same idea.

Simple definition

When I is written on the left of V or X, its value is subtracted: IV = 5 − 1 = 4 and IX = 10 − 1 = 9. I is not used more than once before V or X, so 8 is not IIX.

IV is V − I = 5 − 1 = 4.V5−I1=IV4I written on the left of V: subtract

In the figure : A smaller symbol on the left of a bigger one is subtracted: IV = 5 − 1 = 4 and IX = 10 − 1 = 9.

Rule 1: Small on the left: subtract — Write I before V or X to subtract 1.

  • Easy : IV = 5 − 1 = 4.
  • Medium : IX = 10 − 1 = 9.
  • Exam-type : Compare IV and VI: IV = 5 − 1 = 4 but VI = 5 + 1 = 6. The side of I decides add or subtract.

Rule 2: 14 and 19 — Break the number into 10 + the rest.

  • Easy : 14 = 10 + 4 = X + IV = XIV.
  • Medium : 19 = 10 + 9 = X + IX = XIX.
  • Exam-type : Why is 14 not XIIII? Because I is not written four times; 4 becomes IV.
Remember

Left of a bigger symbol: subtract. Right of a bigger symbol: add.

Common mistake

Writing IIX for 8. 8 is VIII (5 + 1 + 1 + 1).

Shortcut

Memory clue: Small before big takes away (IV, IX). Small after big adds on (VI, XI).

Spot the difference

RomanIVVIIXXI
Side of Ileftrightleftright
Working5 − 15 + 110 − 110 + 1
Value46911

Practice questions

Easy
  1. 1What number is IV?
  2. 2Write 9 in Roman numerals.
  3. 3Is VI equal to IV?
Medium
  1. 4Write 14 in Roman numerals.
  2. 5Write 19 in Roman numerals.
  3. 6What number is XIV? Show the working.
Challenging
  1. 7Why is 8 written VIII and not IIX?
  2. 8Page numbers in a book are written XIX, XIV and XVIII. Write them in order from smallest to biggest as numbers.
Show answers (try them yourself first)
  1. 14
  2. 2IX
  3. 3No. VI = 6 and IV = 4.
  4. 4XIV (10 + 4)
  5. 5XIX (10 + 9)
  6. 6X = 10 and IV = 4, so 14.
  7. 7I is used only once before V or X to subtract; for 8 we add 1 three times after V.
  8. 814, 18, 19 (XIV, XVIII, XIX).

Writing the numbers 1 to 20

From daily life

A teacher marks the chapters of a book as I, II, III and so on. To write any number from 1 to 20 we need only I, V and X and the add-or-subtract rules.

Simple definition

To write a number, split it into groups of 10, 5 and 1 and apply the rules.

Roman numerals 1 to 20: 1 = I, 2 = II, 3 = III, 4 = IV, 5 = V, 6 = VI, 7 = VII, 8 = VIII, 9 = IX, 10 = X, 11 = XI, 12 = XII, 13 = XIII, 14 = XIV, 15 = XV, 16 = XVI, 17 = XVII, 18 = XVIII, 19 = XIX, 20 = XX.1I2II3III4IV5V6VI7VII8VIII9IX10X11XI12XII13XIII14XIV15XV16XVI17XVII18XVIII19XIX20XX

In the figure : Roman numerals from 1 to 20. The orange ones (IV, IX, XIV, XIX) use subtraction.

Rule 1: Split into 10, 5 and 1 — Take the 10s first, then the 5, then the 1s.

  • Easy : 12 = 10 + 1 + 1 = XII.
  • Medium : 18 = 10 + 5 + 1 + 1 + 1 = XVIII.
  • Exam-type : 15 = 10 + 5 = XV; and 20 = 10 + 10 = XX.

Rule 2: Use 4 and 9 where needed — For 4, 9, 14 and 19, use subtraction.

  • Easy : 4 = IV and 9 = IX.
  • Medium : 14 = X + IV = XIV and 19 = X + IX = XIX.
  • Exam-type : Write 1 to 20 in a list to check yourself: I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII, XIII, XIV, XV, XVI, XVII, XVIII, XIX, XX.
Remember

There are only 4 numbers from 1 to 20 that use subtraction: 4, 9, 14 and 19.

Common mistake

Writing 16 as XVI and then 17 as XVIIII. I is never written four times; 17 = XVII.

Shortcut

Memory clue: Tens, Five, Ones, then check 4 and 9.

Spot the difference

NumberSplitRoman
1110 + 1XI
1310 + 1 + 1 + 1XIII
1710 + 5 + 1 + 1XVII
1910 + 9XIX

Practice questions

Easy
  1. 1Write 11 in Roman numerals.
  2. 2Write 15 in Roman numerals.
  3. 3Write 20 in Roman numerals.
Medium
  1. 4Write 16 in Roman numerals.
  2. 5What number is XVIII?
  3. 6Which numbers from 1 to 20 use subtraction in their Roman form?
Challenging
  1. 7Write 12, 17 and 19 in Roman numerals.
  2. 8A book has XIV chapters and a second book has XVIII chapters. How many more chapters does the second book have?
Show answers (try them yourself first)
  1. 1XI
  2. 2XV
  3. 3XX
  4. 4XVI (10 + 5 + 1)
  5. 518
  6. 64, 9, 14 and 19.
  7. 7XII, XVII, XIX
  8. 818 − 14 = 4 chapters (IV).

L, C, D, M and the decimal system

From daily life

The number plate of an old coin or the year on a monument may be written like MCMXLVII. To read such numbers we need the bigger Roman symbols too.

Simple definition

Four more symbols are used: L = 50, C = 100, D = 500, M = 1000. Roman numerals are hard to use for calculation, so we use the decimal system (दशमान पद्धत) of ten digits 0 to 9, in which the value of a digit depends on its place. India's mathematicians invented it.

Roman symbols and their values: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000.I1V5X10L50C100D500M1000

In the figure : The seven Roman symbols: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000.

Rule 1: Know the big symbols — L = 50, C = 100, D = 500, M = 1000.

  • Easy : LX = 50 + 10 = 60.
  • Medium : CC = 100 + 100 = 200 and DC = 500 + 100 = 600.
  • Exam-type : MD = 1000 + 500 = 1500.

Rule 2: Why the decimal system wins — In the decimal system the same digit has a different value at a different place.

  • Easy : In 505, the first 5 means 500 and the last 5 means 5.
  • Medium : 40 in the decimal system uses two digits. In Roman numerals, 40 is XL.
  • Exam-type : Multiplying 24 × 12 is easy with decimal digits. With Roman numerals XXIV × XII it is very hard.
Remember

Roman numerals have no zero and no place value. The decimal system has both.

Common mistake

Taking C as 50 and L as 100. L is 50 and C is 100.

Shortcut

Memory clue: L C D M = 50, 100, 500, 1000 — "Lazy Cows Drink Milk".

Spot the difference

SymbolLCDM
Value501005001000
ExampleLV = 55CL = 150DX = 510MC = 1100

Practice questions

Easy
  1. 1What is the value of L?
  2. 2Which symbol stands for 1000?
  3. 3Write 100 in Roman numerals.
Medium
  1. 4What number is LX?
  2. 5What number is DC?
  3. 6Write 150 in Roman numerals.
Challenging
  1. 7Give two reasons why we prefer the decimal system.
  2. 8A monument shows MD. Which year number is this, and what is the sum of its two symbol values?
Show answers (try them yourself first)
  1. 150
  2. 2M
  3. 3C
  4. 460
  5. 5600
  6. 6CL (100 + 50)
  7. 7It has zero and place value, and calculations are easy.
  8. 8MD = 1000 + 500 = 1500.

Quick revision

  • I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000.
  • I, X: at most 3 times in a row; V: never repeated.
  • IV = 4, IX = 9, XIV = 14, XIX = 19.