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1Place Value to Billions2Roman Numeral Arithmetic3Twin Primes & Co-primes4Divisibility Rules5Cryptarithm Puzzles6Estimation of Products7Division Cryptarithms

Concept 2 of 7

Roman Numeral Arithmetic

1

Today's big idea

Convert both numerals to ordinary numbers, do the arithmetic, then convert the answer back.

Only I, X and C are ever subtracted, so 95 is XCV and never VC.

2

How it works

👀 What's going on?

Two Roman numerals with a plus sign between them look impossible, until you notice that nobody adds them as letters. They take a detour through ordinary numbers.

💡 Here's the trick

Roman arithmetic in 3 stepsCDLXVII + CCXXXV⬇ convert to Arabic467 + 235 = 702⬇ convert back to RomanDCCIII=1 · V=5 · X=10 · L=50 · C=100 · D=500 · M=1000

Look at the pair above. The route out and back is the whole method. Turn each numeral into an ordinary number, do the arithmetic there where it is easy, then write the result back in letters.

🪄 How to do it

  1. 1.Convert each numeral in the pair above into an ordinary number.
  2. 2.Add or subtract those numbers as usual.
  3. 3.Convert the result back into Roman letters.

✍️ Try it

Work out XCIV + CLVI. Then: work out MMCDXV minus MDCCC.

XCIV is 94 and CLVI is 156, so the total is 250, written CCL. MMCDXV is 2415 and MDCCC is 1800, so the difference is 615, written DCXV.

⚠️ Watch out

You might be thinking any smaller letter can sit before a bigger one to subtract. Only I, X and C ever do that, and only before the next two symbols up. So 95 is XCV and never VC.

🌟 Why this matters

Clock faces, chapter numbers, film credits and the dates carved over old doorways all use these letters. Reading them is an ordinary skill you will keep long after this year, and writing them back is the half people skip.
Exam tip: Convert both numerals before you touch the operation.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“What is CCXLVI + CLXXV?”

  1. 1

    Convert each to Arabic

    CCXLVI = 246; CLXXV = 175.

  2. 2

    Add

    246 + 175 = 421

  3. 3

    Convert back to Roman

    421 = CD + XX + I = CDXXI.

  4. 4

    Answer ✓

    CDXXI

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

To add or subtract Roman numerals: convert each to a normal number, calculate, then convert back.

ROMAN · ROUND 1 OF 3

DCCLXIV + CXXV

5

Quick check

✅ VERIFICATION

Which of these is a correctly written Roman numeral?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Twin Primes & Co-primes

Twin = both prime, differ by 2. Co-prime = hcf is 1.

Concept 3 of 7 →