1. Subtract only the values of letters I, X and C. Values of V, L and D cannot be subtracted. Consider the numeral = XLV [(50 10) + 5]

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1 2 ROMAN NUMERALS Let s recall... Roman numeral system was developed by the ancient Romans. t is based on seven letters of the alphabet. All the numbers are written using either one letter or a combination of letters. However, there is no letter representing zero. The seven letters used in the Roman numeral system and their corresponding values in HinduArabic numeral system are given in the following table. Roman Numeral L C D M Hindu-Arabic Numeral ,000 Let s learn further... n modern Roman numeral system, for large numbers a bar is placed above the base numeral indicating multiplication by 1,000, although the ancient Romans themselves often just used M for it. Five thousand Ten thousand L Fifty thousand C One hundred thousand D Five hundred thousand M One million Rules for Subtracting alues in Roman Numerals 1. Subtract only the values of letters, and C. alues of, L and D cannot be subtracted. Consider the numeral = L [(50 10) + 5] 45 L (50 5) 2. Subtract the value of only a single smaller numeral from a single bigger numeral. n other words, you can subtract only once from a numeral. Consider the numeral 8. 8 = (5 + 3) 8 (10 1 1) 3. Do not subtract a numeral from another numeral which is more than 10 times greater, i.e., can be subtracted from and but not from L, C, D and M. Similarly, can be subtracted from L and C but not from D, M and so on... Conversion of Roman Numeral to Hindu-Arabic Numeral 1. f a smaller number is to the left of a larger number, subtract the value of the smaller number from the larger number. 16

2 Consider the number. Since <, 10 1 = 9. Therefore, = 9. Also, in L, < L. Therefore, L = = f a smaller number is to the right of a larger number, add the value of the smaller number to the larger number. Consider the number. Since > l, = 11. Therefore, = f the number has more than two letters, add the value of each letter to find the number. Consider the number L. L = = 68. Also, CD = (CD) + 1 = ( ) + 1 = = 401. Remember Conversion of Hindu-Arabic Numeral to Roman Numeral Numbers 1, 2, 3 are written in Roman numerals as, and, respectively. Now 4 cannot be written as since the To subtract, the smaller symbol is placed before symbol can be repeated only three times in a row. Let s learn how to write 4 in Roman numerals. 4 < 5 and 4 = 5 1 = Therefore, 4 =. Now let s learn how to write 6 in Roman numerals. the bigger symbol. To add, the smaller symbol is placed after the bigger symbol. 6 > 5 and 6 = = + Therefore, 6 =. Similarly, 7 = = and 8 = =. But 9 cannot be written as as cannot be repeated more than three times. Let s learn how to write 9 in Roman numerals. 9 < 10 and 9 = 10 1 = Therefore, 9 =. Also, 11 > 10 and 11 = = +,, C and M can be repeated only three times in a row., L and D cannot be repeated at all. Therefore, 11 =. Similarly, 40 = = L = L And, 90 = = C = C To convert a large Hindu-Arabic numeral to a Roman numeral, convert each digit separately and then combine the letters. Example 1: Convert 752 into Roman numeral. Solution: 752 = = DCC + L + = DCCL Try this! Write 999 in Roman numerals. 17

3 Roman Numerals up to Hundred L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L C C C C C C C C C C C 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: L + L Solution: L = 45 L = 63 Example 3: = 108 = C Therefore, L + L = C CCC CL Solution: CCC = 296 CL = = 122 = C Therefore, CCC CL = C Try these! Find the sum. (a) M + = (b) M = Maths Fun How can half of be 7? 18

4 Modern Usage Roman numerals were commonly used until 14th century. Since they were not enough to write large numbers, they were replaced by Hindu-Arabic numbers. However, we still see them being used in certain places in modern times. Some of them are given below. Names of Monarchs and Popes like, Elizabeth and Benedict Hour marks on clock faces and timepieces Recurring grand event such as Olympic games Sometimes page numbering and chapter numbering LET S EALUATE 1. Convert the following Hindu-Arabic numbers to Roman numerals. (a) 15 = (b) 49 = (c) 103 = (d) 305 = (e) 228 = (f) 450 = (g) 637 = (h) 989 = (i) 354 = (j) 509 = (k) 83 = (l) 179 = 2. Convert the following Roman numerals to Hindu-Arabic numbers. (a) = (b) L = (c) C = (d) CCC = (e) CD = (f) CML = (g) DCC = (h) CM = (i) CD = (j) L = (k) L = (l) DC = 3. Find the value of the following Roman numerals. (a) L + (b) C + L (c) CCC C (d) DL CD (e) L + (f) + (g) L (h) C (i) 4. What comes before or after the given Roman numerals? (a), (b), C (c), (d) CCCC, (e), (f) L, (g), L (h), C (i), DL 5. Put the correct sign <, > or =. (a) 46 (b) CCL 245 (c) C C (d) CL 150 (e) L + 12 L (f) C Change the Hindu-Arabic numerals to Roman numerals and solve the following. Write the answer in Roman numerals. (a) (b) (c) (d) 29 9 (e) (f) (g) (h)

5 SCRATCH YOUR BRAN (HOTS) 1. There are seven letters used as Roman numerals,,, L, C, D and M. (a) Which is the biggest correctly formed Roman numeral using each numeral once? (b) Which is the smallest correctly formed Roman numeral using each numeral once? 2. Form two Roman numerals that are also words in English. For example, M is a Roman numeral and an English word. MATHS LAB ACTTES 1. Cut and paint a clock face from a cardboard sheet. Mark the hours in Roman numerals. 2. Using glue and matchsticks or toothpicks, design a birthday greeting with your birth date marked in Roman numerals. 3. Read the given riddle carefully. RAM SAENA GOES TO THE CHURCH ON THE STH OF MAY. n which year was he born? (Hint: Find all the Roman numerals and arrange correctly.) Answer: MCMC, i.e., 1999 Form groups, make more such riddles and have a class competition. HSTORY OF ROMAN NUMERALS Ancient Romans used only capital (upper case) letters to write numerals. However, during medieval age small (lower case) letters like i, ii, iii, etc. were developed and used. Further during the medieval age, practice of substituting j for the last numeral to end numbers was adopted. For example, iiij became 4 and viij became 8. This was done to prevent tempering after the numbers had been written. Also, earlier Romans made notch marks on wooden sticks to show numbers. Thus came from a vertical notch mark across the stick. Every fifth notch was double-cut like and every tenth notch was crosscut like. The notching pattern was.... This produced a positional system, 7 on a counting stick meant 7 notches which could be abbreviated as as the existence of implies 4 prior notches. Likewise, 16 was the 6th notch after ten which could be abbreviated as. So, the number 16 became. nterestingly, the Romans drew an extra stroke for every tenth or. The hundredth or were marked with a box or circle. And finally, 1000 was marked as circled or boxed. Another interesting fact you should know is that ancient Romans were smart enough to have a calculating machine like a modern calculator that could fit in a shirt s pocket. t was the Roman abacus which besides doing basic calculations could also do fractions. This Roman abacus was similar to the Chinese abacus Suanpan or the modern Japanese abacus Soroban. 20