Arithmetic Chapter 4 Roman Number Up To One Hundred
Question 1. Write the following Roman Numbers in Hindu Arabic Numbers :
1. IV
2. VI
3. VII
4. VIII
5. IX
6. XI
7. XXVI
8. XXX
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9. XXXIX
10. XXXVI
11. XL
12. XLI
13. XLIX
14. LV
15. LIX
16. LX
17. XC
18. XCV
19. XLV
20. LXXV
21. LXXX
22. XCVI
23. XCII
24. LXXIX
25. XCIX
Solution :
1. IV = 5 – 1
= 4;
2. VI = 5 + 1
= 6;
3. VU = 5 + 1 + 1
= 7;
4. VIII = 5 + 1 + 1 + 1
= 8 ;
5. IX = 101
= 9;
6. XI = 10 + 1
= 11 ;
7. XXVI = 10 + 10 + 5 + 1
= 26;
8. XXX = 10 + 10 + 10
= 30 ;
9. XXXIX = 10+ 10 + 10 + (10 – 1)
= 10 + 10 + 10 + 9
= 39 ;
10. XXXVI = 10 + 10 + 10 + 5 + 1
= 36 ;
11. XL = 50 – 10
= 40 ;
12. XLI = (50 – 10) + 1
= 41 ;
13. XLIX = (50 – 10) + (10 – 1)
= 40 + 9 = 49 ;
14. LV = 50 + 5
= 55;
15. LIX = 50 + (10 – 1)
= 50 + 9
= 59 ;
16. LX = 50 + 10
= 60 ;
17. XC = 100 – 10
= 90
18. XCV = (100 – 10) + 5
= 90 + 5
= 95
19. XLV = (50 – 10) + 5
= 40 + 5
= 45;
20. LXXV = 50 + 10 + 10 + 5
= 75 ;
21. LXXX = 50 + 10 + 10 + 10
= 80 ;
22. XCVI = (100 – 10) + 5 + 1
= 90 + 5 + 1
= 96 ;
23. XCII = (100 – 10) + 1 + 1
= 90 + 2
= 92 ;
24. LXXIX = 50 + 10 + 10 + (10 – 1)
= 70 + 9
= 79 ;
25. XCIX = (100 – 10) + (10 – 1)
= 90 + 9
= 99
Question 2. Write the following numbers in Roman Numbers:
1. 4
2. 7
3. 9
4. 14
5. 25
6. 31
7. 36
8. 44
9. 54
10. 65
11. 89
12. 90
13. 93
14. 98
Solution:
1. 4 = IV;
2. 7 = VII;
3. 9 = IX;
4. 14 = XIV;
5. 25 = XXV;
6. 31 = XXXI;
7. 36 = XXXVI;
8. 44 = XLIV;
9. 54 = LIV ;
10. 65 = LXV;
11. 89 = LXXXIX;
12. 90 = XC;
13. 93 = XCIII;
14. 98 = XCVIII;
Question 3. Choose the correct answer to the following:
Solution :
1. 40 = XL;
2. 49 = XLIX;
3. 84 = LXXXIV;
4. 90 = XC;
Question 4. Put <, =, > signs in the boxes given below :
1. 5 
IV ;
2. 9 XI ;
3. XIV 14 ;
4. XIX XXI ;
5. 24 XXIV ;
6. LXXVI LXXIV.
Solution:
(i) 5 
IV ;
(ii) 9 
XI ;
(iii) XIV 
14 ;
(iv) XIX 
XXI ;
(v) 24 XXIV ;
(vi) LXXVI LXXIV
Example 5. Write the following numbers in Roman Numbers :
1. 105,
2. 400,
3. 600,
4. 650,
5. 700,
6. 900,
7. 1513,
8. 2323.
Solution :
1. 105 = CV ;
2. 400 = CD ;
3. 600 = DC ;
4. 650 = DCL ;
5. 700 = DCC ;
6. 900 = CM ;
7. 1513 = MDXIII ;
8. 2323 = MMCCCXXHI.
Question 6. Write the following Roman Numbers in Hindu Arabic Numbers :
1. \(\overline{X C}\)
2. \(\overline{\mathbf{M}}\)
3. \(\overline{\mathbf{X X I V}}\)
4. \(\overline{C M}\)
Solution :
1. \(\overline{X C}\) = XC x 1000
= (100 – 10) x 1000
= 90 x 1000
= 90000;
2. \(\overline{\mathbf{M}}\)= M x 1000
= 1000 x 1000
= 1000000 ;
3. \(\overline{\mathbf{X X I V}}\) = (XXIV) x 1000
= [10 + 10 + (5 – 1)] x 1000
= (10 + 10 + 4) x 1000
= 24000 ;
4. \(\overline{C M}\) = CM x 1000
= (1000 – 100) x 1000
= 900 x 1000
= 900000.
Question 7. Write the following numbers in Roman Numbers :
(1) 44000 ; (2) 99000 ; (3) 660000 ; (4) 2336000
Solution : (1) 44000 = 44 x 1000 = XLIV x 1000 = \(\overline{\text { XLIV }}\) ;
(2) 99000 = 99 x 1000 = (XCIX) x 1000 = \(\overline{\text { XCIX }}\) ;
(3) 660000 = 660 x 1000 = (DCLX) x 1000 = DCLX \(\overline{\text { DCLX }}\) ;
(4) 2336000 = 2336 x 1000 = (MMCCCXXXVI) x 1000 = \((\overline{\mathrm{MMCCCXXXVI}})\)
Question 8. Express the results of addition and subtraction of the following into Hindu Arabic Numbers and Roman Numbers :
1. CDXXXIX + CCCLXXVI ;
2. \(\overline{\text { MCCXXV }}+\overline{\text { MMDCLXXXIII }}\) ;
3. DCCCLXXIX -DCCXXXIX ;
4. \(\text { MCCCXXII }-\overline{\text { MCCLXXXIV }}\)
Solution :
1. CDXXXIX + CCCLXXVI .
= [(500 – 100) + 10 + 10 + 10 + (10 – 1)] + [ 100 + 100 + 100 + 50 + 10 + 10 + 5 + 1]
= (400 + 30 + 9) + (375 + 1) = 439 + 376 = 815
The required sum = 815 (in Hindu Arabic Numbers)
= DCCCXV (in Roman Number)
2. \(\overline{\text { MCCXXV }}+\overline{\text { MMDCLXXXIII }}\)
= (MCCXXV) x 1000 + (MMDCLXXXIII) x 1000 (1000 + 100 + 100 + 10 + 10 + 5) x 1000 + (1000 + 1000 + 500 + 100 + 50 + 10 + 10 + 10 + 1 + 1 + 1) x 1000
= (1000 + 200 + 20 + 5) x 1000 + (2000 + 600 + 80 + 3) x 1000.
= 1225 x 1000 + 2683 x 1000
= 1225000 + 2683000
= 3908000
The required sum = 39080000 (in Hindu Arabic Number)
= MMMCMVIII (in Roman Number)
3. DCCCLXXIX – DCCXXXIX
= [500 + 100 + 100 + 100 + 50 + 10 + 10 + (10 – 1)] – [500 + 100 + 100 + 10 + 10 + 10 + (10 – 1)]
= [500 + 300 + 70 + 9] – [500 + 200 + 30 + 9]
= 879 – 739
= 140
∴ The required result of subtraction = 140 (in Hindu Arabic Number)
= CXL (in Roman Number)
4. \(\text { MCCCXXII }-\overline{\text { MCCLXXXIV }}\)
= (MCCCXXII) x 1000 – (MCCLXXXIV) x 1000
= (1000 + 100 + 100 + 100 + 10 + 10 + 1 + 1) x 1000
– [1000 + 100 + 100 + 50 + 10 + 10 + 10 + (5 – 1)] x 1000
= (1000 + 300 + 20 + 2) x 1000 – (1000 + 200 + 50 + 30 + 4) x 1000
= 1322 x 1000 – 1284 x 1000
= 1322000 – 1284000
= 38000
∴ The required result of subtraction = 38000 (in Hindu Arabic Number)
= \(\overline{\text { XXXVIII }}\) (in Roman Number)