Rules of Roman Numeration

We will learn about Roman Numeration and its rules. We know that there are seven basic Roman Numerals. They are I, V, X, L, C, D and M. These numerals stand for the number 1, 5, 10, 50, 100, 500 and 1000 respectively. We already learned about the numerals I, V, X, L and C and now we will learn about the remaining two numerals.

Rules of Roman Numeration:

1. First Rule: Numerals of the same value are added.

When the same symbol is repeated, the value of the symbol is added to get the value of the numeral. I, X and C can be repeated only up to three times. i.e., We can use I, X, C and M only thrice in a combination.

Symbols V, L and D are never repeated.

Symbols V, L and D cannot be used more than once in a number. We write V for 5 but we cannot write VV for 10 or VVV for 15.

Similarly, we write L for 50 but we cannot write LL = 100 or LLL 150.

D can also not be repeated in any number. We write D for 500 but we cannot write DD for 1000 or DDD for 1500.

For example:

I  stands for 1

II  stands for 1 + 1 = 2

II stands for 1 + 1 + 1 = 3

X stands for 10

XX stands for 10 + 10 = 20

XXX stands for 10 + 10 + 10 = 30

C  stands for 100

CC  stands for 100 + 100 = 200

CCC stands for 100 + 100 + 100 = 300

M stands for 1000

MM stands for 1000 + 1000 = 2000

MMM stands for 1000 + 1000 + 1000 = 3000

But we cannot write IIII for 4, XXXX for 40, CCCC for 400 or MMMM for 4000.

Note:

(i) Symbols V, L and D are not repeated.

(ii) A symbol cannot be repeated more than three times.

2. Second Rule: A symbol of smaller value put on the right of greater value symbol is added to it.

The values of the symbols are added or subtracted to find the values of the Roman numerals. When the smaller numeral is written to the right of a greater numeral, the value of the smaller numeral is added to the greater numeral. 

I, X, C are the only symbols used for addition as well as subtraction. When we use them to the right of a number, they are added to the number.

For example:

VI stands for 5 + 1 = 6

XI stands for 5 + 1 = 6

LX = 50 + 10 = 60

CV = 100 + 5 = 105

CX = 100 + 10 = 110

CXX stands for 100 + 10 + 10 = 120

DC = 500 + 100 = 600

MC = 1000 + 100 = 1100

MCL stands for 1000 + 100 + 50 = 1150

Note: (i) We can add X to L and C only.

LX = 50 + 10 = 60

CX = 100 + 10 = 110

We cannot write MX for 1010

(ii) We can add C to D and M only.

For example,

DC = 500 + 100 = 600

MC = 1000 + 100 = 1100

3. Third Rule. A symbol of smaller value put on the left of greater value symbol is subtracted from it.

When the smaller numeral is written to the left of a greater numeral, the value of the smaller numeral is subtracted from the greater numeral.

I, X, C are the only symbols used for addition as well as subtraction. When we use them to the left of a number, they are subtracted from the number

The V, L and D are not subtracted. Only one number can be subtracted from another.

For example:

IV stands for 5 - 1 = 4

IX stands for 10 - 1 = 9

XL stands for 50 - 10 = 40

XC stands for 100 - 10 = 90

CD stands for 500 - 100 = 400

CM stands for 1000 - 100 = 900

Note:

(i) Symbol V, L and D are never subtracted.

(ii) Symbol I can be subtracted from V and X only.

(iii) Symbol X can be subtracted from L and C only as L and C are greater than X.

For example,

XL = 50 - 10 = 40

XC = 100 - 10 = 90

We cannot write XD for 490

(iv) Symbol C can be subtracted from D and M only.

For example,

CD = 500 - 100 = 400

CM = 1000 - 100 = 900

4. Fourth Rule. A symbol of smaller value, put between two symbols of greater value is subtracted from the symbol on its right.

When the symbols are combined to make a numeral, the value of the symbol between the two symbols is subtracted from the value of the symbol on its right.

For example:

XIV stands for 10 + 5 - 1 = 14

LIX stands for 50 + 10 - 1 = 59

XCIX stands for 90 + 10 - 1 = 99

XLIX stands for 40 + 10 - 1 = 49

Note:

(i) We never use I to the left or right of any number except V and X.

For example,

VI = 6

IV = 4

XI = 11

IX = 9

We cannot write LI = 51 or ID = 499

(ii) Bigger Roman numbers are also expressed in the same way as we express smaller Roman numbers.

For example, 2511 is expressed as MMDXI.

             (MMDXI = 1000 + 1000 + 500 + 10 + 31

5th Grade Math Problems

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