X VII XI V Thinking Skills Roman Numerals Level I I = 1; V = 5; X = 10; L = 50; C =100; D = 500; M = 1000 ROMAN NUMERALS LEVEL I Remember from your notes that the Romans built their numbers up by adding or subtracting. When small numbers followed big numbers they were all added together as will be the case in all Level 1 questions. Example I: LXVII = L + X + V + I + I Which = 50 + 10 + 5 + 1 + 1 = 67 Using the above principle, work out the following 1. XV = 2. XXIII = 3. XXXVII = 4. LXVIII = 5. LXXXV1 = 6. CLXXI = 7. CCCLVII = 8. DCCXXXV = 9. DCCCLXXIII = 10. MDCCLXXVII = 11. MCCCXX = 12. MMV = 13. MDCLXVII = 14. MCCLXXI = 15. DCCXXVIII = 16. DCVII = 17. MMDCCLVII = 18. MCLXV1 = 19. DCCLXXI = 20. MMII = The Edinburgh Techniques Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk X VII XI V Thinking Skills Roman Numerals Level I ANSWERS 1. = 15 (X + V = 10 + 5 = 15) 2. = 23 (X + X + I + I + I = 10 + 10 + 1 + 1 + 1 = 23) 3. = 37 4. = 68 (50 + 10 + 5 + 1 + 1 + 1 = 68) 5. = 86 (50 + 10 + 10 + 10 + 5 + 1 = 86) 6. = 171 (100 + 50 + 10 + 10 + 1 = 171) 7. = 357 (100 + 100 + 100 + 50 + 5 + 1 + 1 = 357) 8. = 735 (500 + 100 + 100 + 10 + 10 + 10 + 5 = 735) 9. = 873 (500 + 100 + 100 + 100 + 50 + 10 + 10 + 1 + 1 + 1 = 873) 10. = 1777 (1000 + 500 + 100 + 100 + 50 + 10 + 10 + 5 + 1 + 1 = 1777) 11. = 1320 (1000 + 300 + 20 = 1320 (DECLARATION of ARBROATH) 12. = 2005 (1000 + 1000 + 5 = 2005) 13. = 1667 (1000 + 600 + 67 = 1667) 14. = 1271 (1000 + 200 + 71 = 1271) 15. = 728 (700 + 20 + 8 = 728) 16. = 607 (600 + 0 + 7 = 607) 17. = 2757 (2000 + 700 + 50 + 7 = 2757) 18. = 1166 (1000 + 100 + 60 + 6 = 1166) 19. = 771 (700 + 70 + 1 = 771) 20. = 2002 (2000 + 2 = 2002) (X + X + X + V + I + I = 10 + 10 + 10 + 5 + 1 + 1 = 37) The Edinburgh Techniques Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk X VII XI V Thinking Skills Roman Numerals Level II I = 1; V = 5; X = 10; L = 50; C =100; D = 500; M = 1000 ROMAN NUMERALS LEVEL II As well as Adding numbers the Romans also Subtracted numbers IF small came BEFORE Big e.g. XL = (L - X) = (50 - 10) = 40 Example II: CDLIV = (D - C) + L + (V - I) Which = (500 – 100) + 50 + (5 - 1) = 454 Using the above principle, work out the following 1. XLIV = 2. XCVIII = 3. CDXLVII = 4. DCXLVIII = 5. DCCXLII = 6. CMLXIV = 7. MCCXLVII = 8. CDXXIV = 9. CMXXXIII = 10. MCDXLVII = 11. MCMXLV = 12. MCMLXXIV = 13. MDXLVII = 14. MCCCXIV = 15. MCMLXIII = 16. MCMIV = 17. MMCDIV = 18. MDCCLXXXIX = 19. MCMXVII = 20. MCMLXVIII = The Edinburgh Techniques Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk v X VII XI V Thinking Skills Roman Numerals ANSWERS 1. = 44 (X – L + V – 1 = 50 – 10 + 5 - 1 = 44) 2. = 98 (C - X + V + I + I + I = 100 - 10 + 5 +1 + 1 + 1 = 98) 3. = 447 (D - C + L - X + V + I + I = 500 - 100 + 50 -10 + 5 + 1 + 1 = 447) 4. = 648 (600 + 50 - 10 + V + 1 + 1 +1 = 648) 5. = 742 (700 + 50 - 10 + 1 + 1 = 742) 6. = 964 (1000 - 100 + 50 + 10 + 5 - 1 = 964) 7. = 1247 (1200 + 50 – 10 + 5 + 1 + 1 = 1247) 8. = 424 (500 - 100 + 20 + 5 – 1 = 424) 9. = 933 (1000 - 100 + 30 + 1 + 1 + 1 = 933) 10. = 1447 (1000 + 500 - 100 + 50 - 10 + 5 + 1 + 1 = 1447) 11. = 1945 (1000 + 1000 -100 + 40 + 5 = 1945 (WW11 ENDS) 12. = 1974 (1900 + 70 + 4 = 1974) 13. = 1547 (1500 + 40 + 7 = 1547) 14. = 1314 (1300 + 14 = 1314 (BANOCKBURN) 15. = 1963 (1900 + 60 + 3 = 1963 (JFK ASSASSINATION) 16. = 1904 (1900 + 4 = 1904 (Norway gains INDEPENDENCE) 17. = 2404 (2400 + 4 = 2404) 18. = 1789 (1700 + 80 + 9 = 1789 (FRENCH REVOLUTION) 19. = 1917 (1900 + 17 = 1917 (RUSSIAN REVOLUTION) 20. = 1968 (1900 + 60 + 8 = 1968 (RFK ASSASSINATION) The Edinburgh Techniques Level II Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk X VII XI V Thinking Skills Roman Numerals Level III I = 1; V = 5; X = 10; L = 50; C =100; D = 500; M = 1000 ROMAN NUMERALS LEVEL III This level takes us from Arabic numbers which we use, to Roman. Just build the numbers as you go along using the biggest number you can first, in this case, Ex 3, it’s 50 (L). Example 3: 68 = LXVIII If necessary see the Notes for full details 1. 22 = 2. 35 = 3. 87 = 4. 121 = 5. 177 = 6. 356 = 7. 578 = 8. 777 = 9. 1103 = 10. 1365 = 11. 1707 = 12. 2003 = 13. 2573 = 14. 1832 = 15. 1355 = 16. 1667 = 17. 1888 = 18. 1551 = 19. 2332 = 20. 2781 = The Edinburgh Techniques Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk X VII XI V Thinking Skills Roman Numerals ANSWERS 1. = XXII (20 (XX) + 2 (II) = 22) 2. = XXXV (30 (XXX) + 5 (V) = 35) 3. = LXXXVII (80 (LXXX) + 7(VII) = 87) 4. = CXXI (20 (XX) + 1 (I) = 121) 5. = CLXXVII (100 (C) + 70 (LXX) + 7 (VII) =177) 6. = CCCLVI (300 (CCC) + 50 (L) + 6 (VI) = 356) 7. = DLXXVIII (500 (D) + 70 (LXX) + 8 (VIII) = 578) 8. = DCCLXXVII (700 (DCC) + 70 (LXX) + 7 (VII) = 777) 9. = MCIII (1000 (M) + 100 (C) + 3 (III) = 1103) 10. = MCCCLXV (1000 (M) + 300 (CCC) + 60 (LX) + 5 (V) = 1365) 11. = MDCCVII (1700 (MDCC) + 7 (VII) = 1707) 12. = MMIII (2000 (MM) + 3 (III) = 2003) 13. = MMDLXXIII (2500 (MMD) + 70 (LXX) + 2 (II) = 2572) 14. = MDCCCXXXII (1800 (MDCCC) + 30 (XXX) + 2 (II) = 1832) 15. = MCCLV (1200 (MCC) + 50(L) + 5 (V) = 1255) 16. = MDCLXVII (1600 (MDC) + 60 (LX) + 7 (VII) = 1667) 17. = MDCCCLXXXVIII (1800 (MDCCC) + 80 (LXXX) + 8 (VIII) = 1888) 18. = MDLI (1500 (MD) + 51 (LI) = 1551) 19. = MMXXXII (2000 (MM) + 32 (XXXII) = 2332) 20. = MMDCCLXXXI (2700 (MMDCC) + 81 (LXXXI) = 2781) The Edinburgh Techniques Level III Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk X VII XI V Thinking Skills Roman Numerals Level IV I = 1; V = 5; X = 10; L = 50; C =100; D = 500; M = 1000 ROMAN NUMERALS LEVEL IV This level continues from Arabic to Roman but includes the minus calculations to get 4, 9, 90 etc Build the numbers as in Roman III Example 4: 99 = XCIX (XC = 90) (IX = 9) If necessary see the Notes for full details. Ok! Man the guns and knock out the following 20 questions. Anyone producing this for no 1: XXXXIIIIIII will be taken out and shot, hung, drawn and quartered AND sent to bed without any cocoa and chockie bickies….might manage a small milk and plain bickie……. but THAT’S IT!! 1. 47 = 2. 92 = 3. 114 = 4. 447 = 5. 797 = 6. 944 = 7. 1299 = 8. 1473 = 9. 1999 = 10. 1741 = 11. 2404 = 12. 3799 = 13. 3003 = 14. 1997 = 15. 1944 = 16. 989 = 17. 1111 = 18. 2221 = 19. 3553 = 20. 1479 = The Edinburgh Techniques Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk v X VII XI V Thinking Skills Roman Numerals ANSWERS 1. = XLVII (40 (XL) + 7 (VII) = 47) 2. = XCII (100 (C) – 10 (X) + 2 (II) = 92) 3. = CXIV (100 (C) + 10 (X) + 4 (IV) = 114) 4. = CDXLVII (400 (CD) + 40 (XL) + 7 (VII) = 447) 5. = DCCXCVII (700 (DCC) + 90 (XC) + 7 (VII) =797) 6. =CMXLIV (900 (CM) + 40 (XL) + 4 (IV) = 944) 7. = MCCXCIX (1200 (MCC) +90 (XC) + 9 (IX) = 1299) 8. = MCDLXXIII (1400 (MCD) + 70 (LXX) + 3 (III) = 1473) 9. = MCMXCIX (1900 (MCM) + 90 (XC) + 9 (IX) = 1999) 10. = MDCCXLI (1700 (MDCC) + 41 (XLI) = 1741) 11. = MMCDIV (2400 (MMCD) + 4 (IV) = 2404) 12. = MMMDCCXCIX (3700 (MMMDCC) + 99 (XCIX) = 3799) 13. = MMMIII (3000 (MMM) + 3 (III) = 3003) 14. = MCMXCVII (1900 (MCM) + 97 (XCVII) = 1997) 15. = MCMXLIV (1900 (MCM) + 44(XLIV) = 1944) 16. = CMLXXXIX (900 (CM) + 89 (LXXXIX) = 989) 17. = MCXI (1100 (MC)) + 11 (XI) = 1111) 18. = MMCCXXI (2200 (MMCC) + 21 (XXI) = 2221) 19. = MMMDLIII (3500 (MM) + 53 (LIII) = 3553) 20. = MCDLXXIX (1400 (MCD) + 79 (LXXIX = 1479) The Edinburgh Techniques Level IV Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk X VII XI V Thinking Skills Roman Numerals NOTES PARENT/ TEACHER/ STUDENT NOTES Introduction The Romans were a very smart group of people, with a very high level of sophistication for their time. For example, they had a form of central heating, as well as running hot water, steam rooms, thousands of miles of virtually straight roads and the most highly trained army in history, up to 2/3 centuries either side of the birth of Jesus Christ. However, their Numerical System, though good, was not as sophisticated as the Arabic system which we in the West use today. In fact they didn’t even use numbers as we know them. They used letters to represent numbers. Their system had simple, but effective rules. The first we will use in Level 1. THE NUMBERS….or should I say, Letters? 1, 2, 3, 4 = I, II, III, IIII Very straight forward, though later we will see a simpler way of writing 4. The Romans used letters to represent bigger Numbers: V = 5; X = 10; L = 50; C = 100; D = 500; M = 1000 The Romans built bigger numbers by adding smaller numbers together. But they had a very important RULE: Start with the highest number first and work your way down to the lowest, adding as you go. On the next page is an example of Level I Roman: The Edinburgh Techniques Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk X VII XI V Thinking Skills Roman Numerals NOTES LEVEL I; Example: XXVII is 27 = X+ X+V+ I+I = 10 + 10 + 5 + 1 + 1 SOUNDS LIKE: 10, 20, 5, 6, 7….. 27 But the Romans got some of their numbers by subtracting a smaller number from a BIGGER number e.g. 90 = XC which is C – X = 100 – 10 = 90 Look at this next example: LEVEL II Example: MCMXLV is 1945 (The end of World War II) M = 1000 but CM = M – C = 1000 - 100 = 900 MCM =1900 XL = L – X = 50 – 10 = 40 Now Add the V (5) Total: 1945 In stage III we move from our numbers (Arabic) to Roman, a bit more tricky but essentially the same principle. Let’s see the example on the page below: The Edinburgh Techniques Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk X VII XI V Thinking Skills Roman Numerals NOTES LEVEL III Example: First thing we do is look for the biggest whole ROMAN number we can find out of 578. That’s 500 (D) leaving us with 78. Next biggest whole ROMAN number is 50 (L) leaving 28, then come 2 tens (XX) followed by 5(V) and three 1s (III) Therefore 578 is DLXXVIII = D + L + X + X +V + I + I + I = 500 + 50 + 10 + 10 + 5 + 1 +1 + 1 = 578 SOUNDS LIKE: 5 50, 60, 70, 75, 6, 7, 8, 578 Get the idea? Couldn’t be simpler…….could it? Who said yes? This final level includes those pesky minus numbers again, as well as going from the tricky Arabic to Roman. Oooh, I can’t cope!! For God’s sake pull yourself together Mostyn..….you ARE the Headmaster!! Am I? Oh God! LEVEL IV Example: 1441 …….Oooh, nasty! The Edinburgh Techniques Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk X VII XI V Thinking Skills Roman Numerals NOTES Nonsense. What’s the biggest number? Correct, 1000 (M). Next? 400 Good. What’s the biggest ROMAN number nearest to 400? Correct: D (500) Remember the rule, small number before large means TAKE AWAY Therefore to get 400 (CD) we have to TAKE AWAY 100 from 500 = D – C = 500 – 100 = 400 add that to the thousand = MCD (1400) Next comes 40 (XL). Biggest ROMAN number to 40 is L (50), L –X = 50 -10 =40 Plus I = 41 Add it all together: M + CD + XL + I = 1000 + 400 + 40 + 1 = 1441 Sounds Like: 1000, 400 and 41 A piece of cake….what do you think Hercules? Eh, with you in a tick sir must finish my 10 lengths. The Edinburgh Techniques Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk X VII XI V Thinking Skills Roman Numerals NOTES Thank you Hercules, now then, moving swiftly along, let’s re-cap: Level I is simple addition: The numbers go in Descending order i.e. BIGGEST numbers first all the way down to the tiny I Level II is Addition and that naughty Taking Away which allows us to get numbers like 4, 9, 40, 90, 400 and 900. Here, if a small number comes Before a BIG number, we take the small number away from the BIG number then Add to the other numbers. Levels III and IV are trickier as they go from Arabic to Roman. The trick is to look for the biggest ROMAN number possible, all the way down to V (5). Not too difficult to understand now was it? Yes, well em ahem…Hercules, what do YOU think of it so far? Rubbish! Charmed I’m sure. Thank you Hercules, that will be all for today. Never work with animals and children…Oh I DO wish I had listened to mummy all those years ago. What idiot suggested using that bear anyway???? Erm….. That would be you sir…. Ah!! ….. Quite so Jeffries, quite so….and a jolly good idea it was too. The little……Rascals sir? Thank you Jeffries. Yes, they’ll love it……. The Edinburgh Techniques Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk X VII XI V Thinking Skills Roman Numerals NOTES FOOTNOTE C meaning 100 comes from a Century of men (100) in the Roman Army, which a Centurion was in charge of. We also get the word Century, for 100 years. Ah, Ollie. What did you think of it all? Oh I liked your talk sir, really interesting. I was just wondering. If the Romans used letters for numbers, what did they use for letters? Well I…what? Jeffries, get that ape out of here, far too smart. He’s an Orangutan sir. I don’t care if he’s a PhD, what with swimming bears and now smart apes. I need a stiff room, a dark compact and a cold, damp brandy, not necessarily in that order. Been dealing with idiots all day long. Indeed sir. I know the feeling well. Jeffries….!!? Ollie the Orangutan. Isn’t he lovely? He’s also quite clever, too clever to be caged in a zoo. Big guys like him and the other great Apes need to be free to wander in National Parks where they can thrive and where we can observe them in their natural habitat. Quick Thinking Point 1: The symbols you are reading are just meaningless lines to non English speakers, just as their symbols are to us. Why? Symbols (writing) and Sounds (speech) become associated with real objects or ideas, without which they would be meaningless. More on QTP1 at a later date, not to mention more QTPs. The Edinburgh Techniques Copyright © ECAL Educational Products 1986 - 2006 www.edinburghtechniques.co.uk