Page 27 - Start Up Mathematics_4

Also, CDI = (CD) + 1

= (500 – 100) + 1

= 400 + 1 = 401

Conversion of Hindu-Arabic Numeral to Roman Numeral
Numbers 1, 2, 3 are written in Roman numerals as I, II and III, respectively. Now 4 cannot be
written as IIII since the symbol I can be repeated only three times in a row.

As, 4 < 5 and 4 = 5 – 1 = V – I

Therefore, 4 = IV.
Numbers 6, 7, 8 are written as VI, VII and VIII.

But 9 cannot be written as VIIII as I cannot be repeated more than three times.
As, 9 < 10 and 9 = 10 – 1 = X – I

Therefore, 9 = IX.

Similarly, 40 = 50 – 10 = L – X = XL and 90 = 100 – 10 = C – X = XC
To convert a large Hindu-Arabic numeral to a Roman numeral, convert each digit separately
and then combine the letters.
A Challenge!
Example 1: Convert 752 into Roman numeral.
Write 999 in Roman
Solution: 752 = 700 + 50 + 2 = DCC + L + II = DCCLII numerals.

Addition and Subtraction of Roman Numerals

To add or subtract Roman numerals, follow these steps.
• Change the number into Hindu–Arabic numbers.
• Add or subtract accordingly.

• Convert the answer into Roman numeral.

Example 2: XLV + LXIII Mental Maths
Solution: XLV = 45 Find the sum.

LXIII = 63 (a) MIX + I =
45 + 63 = 108 = CVIII (b) MIX – I =
Therefore, XLV + LXIII = CVIII

Example 3: CCXCVI – CLXXIV

Solution: CCXCVI = 296

CLXXIV = 174
296 – 174 = 122 = CXXII
Therefore, CCXCVI – CLXXIV = CXXII

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