Word Problems: Roman Numerals

Q1: Write the Roman numeral for 349.
Ans: CCCXLIX

Sol: 
Step 1: Break down the number into largest tens and ones according to roman numerals that fits into that number
349 can be broken down into:  349 = 300+40+9 
Step 2: Write Each Part as Roman Numerals 
300 = CCC
40= XL
9 = IX
Step 3: Combine the Roman Numerals After combining, we get 
=CCC + XL + IX  
=CCCXLIX

Q2: Add the Roman numerals XLIII and XVII.
Ans: LX

Sol: 
Step 1 :Let's find the values of XLIII and XVII
1. XLIII = 43
XL = 40
III = 3
So, XLIII = 40 + 3 = 43

2. XVII = 17
X = 10
V = 5
II = 2
So, XVII = 10 + 5 + 2 = 17
Step 2: Now, add the two
43 + 17 = 60
Step 3: Convert 60 back into Roman numerals
LX=60.
As,
L = 50
X = 10
So, L + X = 60
Therefore, XLIII + XVII = LX.

Q 3: Subtract the Roman numeral XXIV from LVI.
Ans: XXXII

Sol: 
Step 1:To subtract XXIV from LVI, Lets calculate the respective values
1. LVI = 50 + 5 + 1 = 56
2. XXIV = 10 + 10 + (5 - 1) = 24
Step 2: Subtract:
56-24 = 32$56\; -\; 24\; =\; 32$
Step 3: Now, let's convert 32 back into Roman numerals
30 is written as XXX.
2 is written as II.
So, 32 in Roman numerals is XXXII.

Q 4: Express the Hindu-Arabic number 789 in Roman numerals.
Ans: DCCLXXXIX

Sol: 
Step 1: We break it down into its components
789 = 700+80+9
Step 2: Write each part in Roman Numerals
1. 700 = DCC (D = 500, CC = 200)
2. 80 = LXXX (L = 50, XXX = 30)
3. 9 = IX (10 - 1)
Step 2: Now, combine these components

DCC + LXXX + IX = DCCLXXXIX

Q 5: Choose the Roman representation for 56.

a. LVI

b. XLVI

c. XVII

d. LXVI

Ans: Option 'a' is correct

Sol: 
The Hindu-Arabic number 56 is represented in Roman numerals as LVI.
L = 50
V = 5
I = 1
So, 56 = L + V + I = LVI.

Q 6: Add the Roman numerals CD and XC.
Ans: CDXC

Sol: 
Step 1: Convert them to their numeric values
CD = 400 (C = 100, D = 500; CD means 500 - 100)
XC = 90 (X = 10, C = 100; XC means 100 - 10)
Step 2:Add the values together
400+90=490
Step 3:Convert 490 back into Roman numerals
400 is written as CD.
90 is written as XC.
So after combining, 490 in Roman numerals is CDXC.

Q 7: Subtract the Roman numeral IX from XXV.
Ans: XVI

Sol: 
Step 1: Convert them into their numeric values
XXV = 10 + 10 + 5 = 25
IX = 10 - 1 = 9
Step 2: Now, subtract
25-9=16
Step 3: Convert 16 back into Roman numerals
10 is represented as X.
5 is represented as V.
1 is represented as I.
So, 16 in Roman numerals is XVI.

Q 8: Write the Roman numeral for the year 1776.
Ans: MDCCLXXVI

Sol: 
Step 1: break it down into its components
1. 1000 = M (for 1000)
2. 700 = DCC (D = 500, CC = 200)
3. 70 = LXX (L = 50, XX = 20)
4. 6 = VI (5 + 1)
Step 2: Now, combine these components
M + DCC + LXX + VI = MDCCLXXVI

Q 9: Convert the Roman numeral LXXXIV to a Hindu-Arabic number.
Ans: 84

Sol: 
Step 1: Break it down as follows
L = 50
XXX = 30 (10 + 10 + 10)
IV = 4 (5 - 1)
Step 2: Now, add these values together
= 50+30+4
=84

Q 10: Add the Roman numerals DCCC and CC.
Ans: M

Sol: 
Step 1: Convert them to their numeric values
DCCC = 800 (D = 500, CCC = 300)
CC = 200 (C = 100, C = 100)
Step 2: Now, add the values together
800+200=1000
Step 3: Convert 1000 back into Roman numerals
1000 is represented as M.