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. Symbols V, L and D are never repeated.
I I I stands for 1 + 1 + 1 = 3
XX = 10 + 10 = 20
X X X stands for 10 + 10 + 10 = 30
CC = 100 + 100 = 200
C C C stands for 100 + 100 + 100 = 300
M M M stands for 1000 + 1000 + 1000 = 3000
(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.
VI stands for 5 + 1 = 6
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
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. The V, L and D are not subtracted. Only one number can be subtracted from another.
IV stands for 5 - 1 = 4
IX stands for 10 - 1 = 9
XL stands for 50 - 10 = 40
XC stands for 100 - 10 = 90
DC stands for 500 - 100 = 400
(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.
(iv) Symbol C can be subtracted from D and M.
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.
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
5th Grade Math Problems
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