The value of `CMLXXXII + "CC"LIV` is _______ .

Options

A. CDLXV
B. MCCCLXV
C. MCCXXXVI
D. MCMXCVI

Answer

To solve the problem of finding the value of `CMLXXXII + CCLIV`, we will first convert the Roman numerals into their respective Arabic numeral values, perform the addition, and then convert the result back into Roman numerals if necessary.

### Step-by-Step Solution:

1. **Convert CMLXXXII to Arabic Numerals:**
- Break down the Roman numeral:
- C = 100
- M = 1000
- L = 50
- X = 10 (there are three X's, so 10 + 10 + 10 = 30)
- I = 1 (there are two I's, so 1 + 1 = 2)
- Now, calculate the total:
- M (1000) - C (100) = 900
- Add L (50) = 900 + 50 = 950
- Add XXX (30) = 950 + 30 = 980
- Add II (2) = 980 + 2 = 982
- Thus, CMLXXXII = 982.

2. **Convert CCLIV to Arabic Numerals:**
- Break down the Roman numeral:
- C = 100 (there are two C's, so 100 + 100 = 200)
- L = 50
- I = 1 (before V, so we subtract 1 from 5)
- Now, calculate the total:
- 200 + 50 = 250
- Subtract I from V (5): 5 - 1 = 4
- Thus, CCLIV = 254.

3. **Add the Two Values:**
- Now, we add the two Arabic numeral values:
- 982 + 254
- Perform the addition:
- 982 + 254 = 1236.

4. **Convert 1236 back to Roman Numerals:**
- Break down 1236:
- 1000 = M
- 200 = CC
- 30 = XXX
- 6 = VI
- Combine them:
- M + CC + XXX + VI = MCCXXXVI.

Thus, the value of `CMLXXXII + CCLIV` is **MCCXXXVI**.