Roman numerals
Roman numerals (via the clock I–XII, then I–C).
Roman numerals are the number symbols the ancient Romans used — letters like I, V and X that we still meet today on clock faces, book chapters and building dates.
What it means
Our everyday numbers (0, 1, 2, 3, …) are called place-value numbers: the position of a digit tells you its worth, so the 3 in 30 means thirty. Roman numerals work in a completely different way. They use a small set of letters, each with a fixed value, and you add the values up.
The letters you need are:
| Letter | Value |
|---|---|
I | 1 |
V | 5 |
X | 10 |
L | 50 |
C | 100 |
Two rules turn these letters into any number:
- Adding. Write letters from largest to smallest and add them.
VIIis 5 + 1 + 1 = 7.XVis 10 + 5 = 15. - Subtracting. To avoid four of the same letter in a row, a smaller letter placed before a larger one is subtracted.
IVis 5 − 1 = 4, andIXis 10 − 1 = 9. In the same wayXLis 40 andXCis 90.
There is no symbol for zero, and you never repeat a letter more than three times. A good first home for all of this is the clock: the hours run I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII — every rule above appears on a single familiar face.
Worked examples
- Read
XXVII. Break it into pieces:X+X+V+I+I= 10 + 10 + 5 + 1 + 1 = 27. - Read
XLIX. Two subtraction pairs:XL= 40 andIX= 9, so 40 + 9 = 49. - Write 88. 88 = 50 + 10 + 10 + 10 + 5 + 1 + 1 + 1 →
LXXXVIII= LXXXVIII. - Write 4 the right way. Not
IIII— the subtraction rule givesIV(5 − 1).
The generative-art connection
A number written as a Roman numeral is already a little drawing made of strokes — the Romans literally cut tally marks into wood and stone, and I, II, III are just one, two, three of those cuts. That makes counting something you can see rather than only recite.
The clearest artefact is the clock. Arrange the twelve hour-numerals evenly around a circle and you have turned a list of numbers into a piece of radial art: twelve labels, equal angles apart, with a rotational symmetry a child can feel. Build one in the Math Clock app, then reproduce the same twelve marks with our dot-multiplier tool, which multiplies a single dot into a symmetric starburst — one dot per hour. The maths of the numeral and the maths of the pattern (counting, equal spacing, radial symmetry) are the same maths.
Common misconceptions
- Repeating too far.
IIIIandVIIIIare wrong; use the subtraction pairsIVandIX. At most three identical letters in a row. - Order flips the meaning.
IVis 4 butVIis 6 — a smaller letter before a larger one subtracts, after it adds. - Expecting place value. In
XItheXis not “tens” and theI“ones”; each letter carries its whole value and you simply add or subtract. There is also no zero to hold a place.
What a learner should be able to solve
The benchmark for mastering this concept — the problems a child at this stage is expected to be able to work through.
-
Read this Roman numeral and write it as an everyday number: `XXXIV`.
Answer
`34`. Break it up: `XXX` = 10 + 10 + 10 = 30, and `IV` is a subtraction pair meaning 5 − 1 = 4. So 30 + 4 = 34.
Art hook Draw a horizontal number line from 0 to 40 with a moving marker. Type a numeral like XXXIV and a glowing dot slides to 34, leaving a coloured trail. Each letter drop (X, X, X, IV) animates a jump, so the value is built up visibly on the line.
-
Write the number `94` as a Roman numeral, using the shortest correct form.
Answer
`XCIV`. 94 = 90 + 4. Ninety is the subtraction pair `XC` (100 − 10) and four is `IV` (5 − 1), giving `XCIV`. (Not `LXXXXIV` — you never write four `X`s in a row; use the subtraction pair instead.)
Art hook Two side-by-side circular clock-style dials, one labelled in tens (XC) and one in ones (IV). Clicking builds 94 as two arcs sweeping from 0, and the two Roman chunks light up as the arcs land, showing 90 + 4.
-
Write the number `86` as a Roman numeral.
Answer
`LXXXVI`. 86 = 50 + 10 + 10 + 10 + 5 + 1 = `L` + `XXX` + `V` + `I` = `LXXXVI`. At most three `X`s in a row, which is allowed here.
Art hook A vertical stack of coloured bars: one tall bar for L (50), three medium bars for XXX (30), one bar for V (5), one small bar for I (1). Stacking them fills a jar to the 86 line, matching numeral to height.
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Spot the mistake: a friend writes forty as `XXXX`. Explain what is wrong and give the correct numeral.
Answer
You may never write four of the same letter in a row. Forty must use the subtraction pair `XL` (50 − 10). The correct numeral is `XL`.
Art hook A 'rule-checker' canvas: type any numeral and any run of four identical letters flashes red with a gentle shake, then a hint bubble suggests the subtraction pair. Correct numerals glow green.
-
Put these three Roman numerals in order from smallest to largest: `XIX`, `XC`, `LIV`.
Answer
`XIX` = 19, `LIV` = 54, `XC` = 90. In order: `XIX`, `LIV`, `XC` (19, 54, 90).
Art hook Three cards you drag along a 0–100 track. Each card, once dropped, snaps to its true value and a bar grows to that length. When all three are in the right order the bars form a neat staircase.
Training exercises
Practice problems, easier first, that build toward the bar above. Each doubles as a seed for an interactive artwork.
-
Match each letter to its value: `I`, `V`, `X`, `L`, `C`.
Answer
`I` = 1, `V` = 5, `X` = 10, `L` = 50, `C` = 100.
Art hook A colour-wheel of five slices, one per letter. Clicking a slice reveals its value and lights that many dots (capped visually) — the wheel becomes a legend you reuse in later art pieces.
-
Read these clock hours: `II`, `VII`, `XI`.
Answer
`II` = 2, `VII` = 5 + 1 + 1 = 7, `XI` = 10 + 1 = 11.
Art hook Place 12 dots evenly around a circle and label them I to XII. Click a numeral in a list and its dot pulses, teaching that the hours are equally spaced points on a ring (radial symmetry).
-
Write these small numbers as Roman numerals: `3`, `6`, `8`.
Answer
`3` = `III`, `6` = `VI` (5 + 1), `8` = `VIII` (5 + 1 + 1 + 1).
Art hook A tally-mark canvas: each I you add cuts a stroke into a wooden bar. After three strokes the next tap flips to V (a diagonal notch), echoing how Romans carved counts.
-
These four numbers use subtraction pairs. Read each one: `IV`, `IX`, `XL`, `XC`.
Answer
`IV` = 4 (5 − 1), `IX` = 9 (10 − 1), `XL` = 40 (50 − 10), `XC` = 90 (100 − 10).
Art hook For each pair, show two arcs on a dial: a big arc for the larger letter and a small arc drawn backwards for the smaller one, so the 'subtraction' is a literal step back around the circle.
-
Read `XXIII` and `XXXV`.
Answer
`XXIII` = 10 + 10 + 1 + 1 + 1 = 23. `XXXV` = 10 + 10 + 10 + 5 = 35.
Art hook A grid of 10×10 = 100 squares. Reading a numeral fills that many squares in reading order, so 23 and 35 become two coloured rectangles you can compare by size.
-
Write `27` and `44` as Roman numerals.
Answer
`27` = `XXVII` (10 + 10 + 5 + 1 + 1). `44` = `XLIV` (40 + 4 = `XL` + `IV`).
Art hook A builder canvas with letter buttons. Tapping letters appends strokes to a growing 'stone tablet'; the running total is shown so you can watch 44 assemble from XL then IV.
-
Spot the mistake: someone reads `IX` as 11. What went wrong, and what is the real value?
Answer
They added instead of subtracting. Because the smaller `I` comes before the larger `X`, you subtract: 10 − 1 = 9. `IX` = 9. (11 would be `XI`, with the `I` after.)
Art hook A flip toggle showing IX and XI side by side. Sliding the small I from before to after the X animates the value flipping between 9 and 11, making order matter visibly.
-
On a clock, which hour numeral comes right after `VIII`, and what number is it?
Answer
After `VIII` (8) comes `IX`, which is 9.
Art hook An animated clock hand that ticks from VIII to IX; as it moves, the destination numeral enlarges and a 9-dot cluster appears in the centre to confirm the count.
-
Read `LXVI` and `LXXIX`.
Answer
`LXVI` = 50 + 10 + 5 + 1 = 66. `LXXIX` = 50 + 10 + 10 + 9 (`IX`) = 79.
Art hook Two thermometers filling to 66 and 79 on a 0–100 scale as you decode each numeral chunk by chunk, colouring the L, X, and IX segments in different hues.
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Write `59` and `72` as Roman numerals.
Answer
`59` = `LIX` (50 + 9). `72` = `LXXII` (50 + 10 + 10 + 1 + 1).
Art hook A radial 'petal' builder: each letter value adds petals of a set size around a centre (L = one big petal, X = medium, I = tiny). 59 and 72 bloom into two different symmetric flowers.
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Put these in order from smallest to largest: `XL`, `IV`, `XC`, `XIV`.
Answer
`IV` = 4, `XIV` = 14, `XL` = 40, `XC` = 90. In order: `IV`, `XIV`, `XL`, `XC`.
Art hook Four dots placed on a 0–100 circle by value. Connect them in order smallest to largest and the line sweeps around the ring, showing the ordering as a growing spiral arc.
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Stretch challenge: the year a building opened is carved as `MCMXCIX`, which uses one extra big letter, `M` = 1000. Using the very same add-and-subtract rules, work out the year. (Hint: `M` = 1000, `CM` = 900, `XC` = 90, `IX` = 9.)
Answer
`1999`. `M` = 1000, `CM` = 900, `XC` = 90, `IX` = 9, so 1000 + 900 + 90 + 9 = 1999. It shows the same two rules (add largest-to-smallest, subtract a smaller letter placed before a larger one) stretching to bigger letters — this goes beyond the usual I–C range as a bonus.
Art hook A 'date stone' generator: type any year and the canvas engraves it as a Roman numeral on a stone slab, animating each subtraction pair as a carved notch — a keepsake plaque of a birth year or the current year.