Roman Numerals Worksheet for Practice and Learning

Problem Analysis:

The worksheet involves converting Roman numerals to Arabic numbers, matching them correctly, and performing basic arithmetic operations with Roman numerals. Let's solve each section step by step.

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Section 1: Match the Roman numerals to the correct numbers

#### Step 1: Convert each Roman numeral to its Arabic equivalent.
- XXV:
\( X = 10 \), \( V = 5 \)
\( XX = 10 + 10 = 20 \)
\( XXV = 20 + 5 = 25 \)
Matches with 25.

- CLVI:
\( C = 100 \), \( L = 50 \), \( V = 5 \), \( I = 1 \)
\( CL = 100 + 50 = 150 \)
\( VI = 5 + 1 = 6 \)
\( CLVI = 150 + 6 = 156 \)
Matches with 156.

- XXXVII:
\( X = 10 \), \( V = 5 \), \( I = 1 \)
\( XXX = 10 + 10 + 10 = 30 \)
\( VII = 5 + 1 + 1 = 7 \)
\( XXXVII = 30 + 7 = 37 \)
Matches with 37.

- CCCXXI:
\( C = 100 \), \( X = 10 \), \( I = 1 \)
\( CCC = 100 + 100 + 100 = 300 \)
\( XX = 10 + 10 = 20 \)
\( I = 1 \)
\( CCCXXI = 300 + 20 + 1 = 321 \)
Matches with 321.

- XCIV:
\( X = 10 \), \( C = 100 \), \( I = 1 \), \( V = 5 \)
\( XC = 100 - 10 = 90 \)
\( IV = 5 - 1 = 4 \)
\( XCIV = 90 + 4 = 94 \)
Matches with 94.

#### Final Matches:
1. XXV → 25
2. CLVI → 156
3. XXXVII → 37
4. CCCXXI → 321
5. XCIV → 94

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Section 2: Choose the correct answer

#### Step 2: Convert each Roman numeral to its Arabic equivalent.
- CVIII:
\( C = 100 \), \( V = 5 \), \( I = 1 \)
\( VIII = 5 + 1 + 1 + 1 = 8 \)
\( CVIII = 100 + 8 = 108 \)
Not listed in the options.

- LXV:
\( L = 50 \), \( X = 10 \), \( V = 5 \)
\( LX = 50 + 10 = 60 \)
\( LXV = 60 + 5 = 65 \)
Not listed in the options.

- XXXIX:
\( X = 10 \), \( I = 1 \), \( X = 10 \)
\( XXX = 10 + 10 + 10 = 30 \)
\( IX = 10 - 1 = 9 \)
\( XXXIX = 30 + 9 = 39 \)
Not listed in the options.

- MMXXI:
\( M = 1000 \), \( X = 10 \), \( I = 1 \)
\( MM = 1000 + 1000 = 2000 \)
\( XX = 10 + 10 = 20 \)
\( I = 1 \)
\( MMXXI = 2000 + 20 + 1 = 2021 \)
Not listed in the options.

- CLXVI:
\( C = 100 \), \( L = 50 \), \( X = 10 \), \( V = 5 \), \( I = 1 \)
\( CL = 100 + 50 = 150 \)
\( XVI = 10 + 5 + 1 = 16 \)
\( CLXVI = 150 + 16 = 166 \)
Not listed in the options.

- 2010:
Convert to Roman numerals:
\( 2010 = MMX \)
Not listed in the options.

- 130:
Convert to Roman numerals:
\( 130 = CXXX \)
Not listed in the options.

#### Step 3: Identify the correct answers from the given options.
- 260:
Convert to Roman numerals:
\( 260 = CCLX \)
Not listed in the options.

- 350:
Convert to Roman numerals:
\( 350 = CCCL \)
Not listed in the options.

- 73:
Convert to Roman numerals:
\( 73 = LXXIII \)
Not listed in the options.

#### Final Answers:
This section seems to have a mismatch between the provided Roman numerals and the Arabic numbers. None of the conversions directly match the given options. However, based on the structure, the closest matches are:
- CVIII: Not listed.
- LXV: Not listed.
- XXXIX: Not listed.
- MMXXI: Not listed.
- CLXVI: Not listed.
- 2010: Not listed.
- 130: Not listed.
- 260: Not listed.
- 350: Not listed.
- 73: Not listed.

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Section 3: Perform arithmetic operations with Roman numerals

#### Step 4: Solve each arithmetic operation.
1. VI + IV:
\( VI = 6 \), \( IV = 4 \)
\( VI + IV = 6 + 4 = 10 \)
Convert 10 to Roman numerals:
\( 10 = X \)
Answer: X.

2. III + VII:
\( III = 3 \), \( VII = 7 \)
\( III + VII = 3 + 7 = 10 \)
Convert 10 to Roman numerals:
\( 10 = X \)
Answer: X.

3. X - V:
\( X = 10 \), \( V = 5 \)
\( X - V = 10 - 5 = 5 \)
Convert 5 to Roman numerals:
\( 5 = V \)
Answer: V.

4. XX - XI:
\( XX = 20 \), \( XI = 11 \)
\( XX - XI = 20 - 11 = 9 \)
Convert 9 to Roman numerals:
\( 9 = IX \)
Answer: IX.

5. L + XXX:
\( L = 50 \), \( XXX = 30 \)
\( L + XXX = 50 + 30 = 80 \)
Convert 80 to Roman numerals:
\( 80 = LXXX \)
Answer: LXXX.

#### Final Answers:
16. VI + IV = X
17. III + VII = X
18. X - V = V
19. XX - XI = IX
20. L + XXX = LXXX

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Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Section 1:} \\
1. \text{XXV} \rightarrow 25 \\
2. \text{CLVI} \rightarrow 156 \\
3. \text{XXXVII} \rightarrow 37 \\
4. \text{CCCXXI} \rightarrow 321 \\
5. \text{XCIV} \rightarrow 94 \\
\\
\text{Section 2:} \\
\text{(No direct matches in the options)} \\
\\
\text{Section 3:} \\
16. \text{VI + IV = X} \\
17. \text{III + VII = X} \\
18. \text{X - V = V} \\
19. \text{XX - XI = IX} \\
20. \text{L + XXX = LXXX}
\end{array}
}
\]