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 =
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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)
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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 =
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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)
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Level II
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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 =
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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)
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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 =
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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)
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Level IV
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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:
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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:
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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!
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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.
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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…….
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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.
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