Roman Numerals up to MM

Primary Seven Mathematics — Term I, Topic 2

Uganda National Curriculum Development Centre

What You Will Learn in This Lesson

By the end of this lesson you will be able to:

1. Read and write Roman numerals from I to MM (1 to 2000)
2. Convert Hindu-Arabic numbers to Roman using decomposition
3. Convert Roman numerals to Hindu-Arabic using left-to-right parsing
4. Recognise Roman numerals in everyday contexts

What You Already Know from P6

Roman numerals use a small set of symbols with fixed values.

You learned up to M = 1000 in P6.

In P7 we go further: up to MM = 2000

Write down every Roman symbol you remember — then check against the table on the next slide.

The Seven Roman Numeral Symbols

Seven symbols — all else is combinations of these.

The P7 Extension: Numbers up to MM

• One more M symbol allowed — M can appear up to twice
• MM = 1000 + 1000 = 2000
• Numbers 1001–1999 use M + further symbols

Rule 1: Additive — Largest to Smallest

Symbols from largest to smallest → add their values.

MDCL = 1000 + 500 + 100 + 50 = 1650

MCCXV = 1000 + 100 + 100 + 10 + 5 = 1215

Rule: I, X, C, M may repeat up to 3 times each. V, L, D: never.

Rule 2: Subtractive — Only Six Valid Pairs

Constraint: only I before V/X; only X before L/C; only C before D/M.

Reading Three Examples Using Both Rules

Converting Hindu-Arabic Numbers to Roman

Decomposition Method — largest symbol down:

Check this order: M → CM → D → CD → C → XC → L → XL → X → IX → V → IV → I

If the remainder reaches a value: write the symbol, subtract, continue.

Worked Example: Converting 1994 → MCMXCIV

Result: MCMXCIV

Verify the Result: MCMXCIV → 1994

Parsing MCMXCIV back:

Always verify by converting in the opposite direction.

Second Worked Example: 1648 → MDCXLVIII

Result: MDCXLVIII — 1000+500+100+40+5+3 = 1648 ✓

Practise: Convert These Numbers to Roman

Convert these numbers — show your decomposition steps:

a) 1776
b) 1492
c) 2000

Answers: a) MDCCLXXVI   b) MCDXCII   c) MM

Converting Roman Numerals to Hindu-Arabic

Parsing Rule — left to right with look-ahead:

Before adding a symbol's value, check the next symbol.
If next symbol is larger → subtract the current symbol.
Otherwise → add it.

Write the running total after each symbol.

Worked Example: Parsing MCMXCIX → 1999

Practise: Convert These Roman Numerals

Convert these Roman numerals — show your running total:

a) MDCCXLII
b) MCMXCVII
c) MMXVII

Answers: a) 1742   b) 1997   c) 2017

Roman Numerals in Real Life

Where you will see them:

• Film credits: copyright year — e.g., MCMXCIX = 1999
• Building cornerstones: year of construction
• Chapter headings: Chapter XXIV (24), Chapter XII (12)
• Clock faces: I through XII (1 to 12)

Find one Roman numeral near you and convert it.

Uganda Connection: Independence Year 1962

Uganda's independence year: 1962 = MCMLXII

Decomposition:

• M = 1000
• CM = 900
• L = 50
• X = 10
• II = 2

Misconception 1: Invalid Subtraction Pairs

Wrong: IC for 99 — I can only precede V or X

Correct: XCIX = (XC=90) + (IX=9) = 99

Valid pairs only:

If your subtraction pair is not in this list — it is illegal.

Misconception 2: Repeating V, L, or D

Wrong: VV = 10 → Correct: X
Wrong: LL = 100 → Correct: C

Only I, X, C, M may repeat (max 3 times). V, L, D: never.

Misconception 3: Reading Pairs Backwards

Wrong direction: reading IX as 1+10 = 11
Correct: I before X → subtract → 10 − 1 = 9

Rule: smaller before larger = subtract.

Exit Question: Apply Both Methods

Exit task:

• Convert 1789 to Roman numerals
• Convert MDCCXCVIII to Hindu-Arabic

Answers and Summary of Both Methods

Answers:

• 1789 → MDCCLXXXIX   (1000+500+200+80+9)
• MDCCXCVIII → 1798   (1000+500+200+90+5+3)

Two methods to remember:

1. Decompose (largest symbol down) for Hindu-Arabic → Roman
2. Parse left to right with look-ahead for Roman → Hindu-Arabic