Std 5 Mathematics · Chapter 1

1. Roman Numerals

Solutions to Problem Set 1, with the rules for writing Roman numerals. Maharashtra State Board (Balbharati), Grade Five Mathematics, Part One.

Rules at a Glance

Symbols: I = 1, V = 5, X = 10. There is no symbol for zero, and a symbol keeps the same value wherever it is placed.

Rule 1 — Repeat and add: I or X written two or three times in a row are added. II = 2, III = 3, XX = 20.

Rule 2 — Limit on repeating: I and X may be repeated at most three times in a row. V is never repeated.

Rule 3 — Smaller on the right, add: I or V written to the right of a bigger symbol is added to it. VI = 6, XV = 15, XVI = 16.

Rule 4 — I on the left, subtract: I written to the left of V or X is subtracted from it, and only one I may be placed there. IV = 4, IX = 9.

Method: Break the number into tens, fives and ones, then apply the rules. For 4 or 9 in the ones place, use IV or IX instead of four I's. Example: 19 = 10 + 9 = X + IX = XIX.

Problem Set 1

1Write all the numbers from 1 to 20 using Roman numerals.

2II

3III

4IV

6VI

7VII

8VIII

9IX

10X

11XI

12XII

13XIII

14XIV

15XV

16XVI

17XVII

18XVIII

19XIX

20XX

Notice that 4, 9, 14 and 19 use subtraction (IV, IX). Every other number is built only by adding symbols.

2Write the following numbers using international numerals.

V = 5
VII = 5 + 1 + 1 = 7
X = 10
XIII = 10 + 1 + 1 + 1 = 13
XIV = 10 + (5 − 1) = 14
XVI = 10 + 5 + 1 = 16
XVIII = 10 + 5 + 1 + 1 + 1 = 18
IX = 10 − 1 = 9

3Fill in the empty boxes.

Number	Roman numeral
Three	III
Eight	VIII
Six	VI
Twelve	XII
Fifteen	XV
Nineteen	XIX

The textbook table runs across the page; it is shown here column by column. Answers filled in are in bold.

4Write the numbers using Roman numerals.

9 = 10 − 1 = IX
2 = 1 + 1 = II
17 = 10 + 5 + 2 = XVII
4 = 5 − 1 = IV
11 = 10 + 1 = XI
18 = 10 + 5 + 3 = XVIII

5In the table below, each given number is written in international numerals and then again in Roman numerals. If it is written correctly in Roman numerals, put ‘✓’ in the box under it. If not, put ‘✗’ and correct it.

International numeral	Given Roman numeral	Right / Wrong	Correct numeral
4	IIII	✗ Wrong	IV
6	VI	✓ Right	—
8	IIX	✗ Wrong	VIII
16	XVI	✓ Right	—
15	VVV	✗ Wrong	XV

Why the wrong ones are wrong:

IIII repeats I four times, but I can be repeated at most three times (Rule 2). So 4 is written as 5 − 1 = IV.
IIX places two I's before X, but only one I may be written on the left of V or X (Rule 4). So 8 is written as 5 + 3 = VIII.
VVV repeats V, which is never allowed (Rule 2). So 15 is written as 10 + 5 = XV.

Something More

AL, C, D and M are also used as Roman numerals.

Roman numeral	I	V	X	L	C	D	M
Number	1	5	10	50	100	500	1000

BActivity: Apart from clocks and watches, where else do we see Roman numerals?

Roman numerals are still used in many places, mostly for numbering things in order. Some common examples are:

Books: chapter or part numbers (Part I, Part II), and the page numbers of the preface or introduction (i, ii, iii…).
School: class or standard numbers (Std V, Std X), and question numbers or sections in exam papers.
Names of kings and queens: for example, Queen Elizabeth II or King George V.
Events and sequels: numbered events, sports tournaments and film or book sequels (Part II, Part III).
Buildings and monuments: the year of construction carved on foundation stones or gateways.
Lists and outlines: headings and sub-points in reports, forms and certificates.

This is an open activity. Students may add any other place where they have seen Roman numerals, such as floor numbers in lifts or numbers on a calendar.

The decimal system: Roman numerals are hard to read and write, and they make calculations difficult. The system we use today writes every number with the ten digits 0 to 9, and the value of a digit depends on its place in the number. This is called the decimal system. It was invented by mathematicians of ancient India and was later adopted all over the world because it is simple and convenient.

2. Number Work →