11 plus Roman Numerals questions

What a Roman Numerals question looks like

Roman numerals sit in the number part of 11 plus maths, next to place value and rounding rather than off on their own. Across our own bank of questions they do four jobs, and it is worth knowing all four because a child who has only practised one is caught out by the others. Some questions give a numeral and ask for it in figures. Some give a number in figures and ask for the numeral. Some put a numeral into a setting, the year a film was made, a date in history, the numbers round a clock face, and ask what it means. The rest ask for a calculation, adding, multiplying or working backwards, with the numbers in the question and the answer both written in letters.

The values run from single figures up to a little past two thousand, so a child needs all seven letters but never a very large number. Every question offers five options, and the wrong ones are built from real reading slips rather than random numbers.

Two rules do almost all the work. Letters written in order from biggest to smallest are added, so XXXVI is 10 plus 10 plus 10 plus 5 plus 1, which is 36. When a smaller letter comes before a bigger one, it is taken away instead. There are only six of those pairs: IV is 4, IX is 9, XL is 40, XC is 90, CD is 400 and CM is 900.

Example one: turning a numeral into figures

What is XLIV in figures?

Go from the left and take the letters in chunks. The first two are X then L, a smaller letter before a bigger one, so that is a take-away pair: 50 take away 10, which is 40. The next two are I then V, another take-away pair: 5 take away 1, which is 4. Now add the chunks: 40 and 4.

The answer is 44.

The tempting wrong option is 64. A child who adds every letter instead of spotting the pair gets 10 plus 50 plus 4. That is careful working with the wrong rule. The other trap is 46, which comes from reading IV as VI.

Example two: a numeral inside a real setting

A film was made in the year MCMXC. What year is this in figures?

Chunk it from the left again. M on its own is 1000. Then comes CM, a smaller letter before a bigger one, so 1000 take away 100, which is 900. Then XC, which is 100 take away 10, or 90. Add them: 1000 plus 900 plus 90.

The answer is 1990.

Two wrong options are waiting. The first is 1910, from reading the XC as just the X and letting the C disappear. The second is 1980, from taking away the wrong way round in the XC and landing on 80. Both come from rushing the last chunk, which is why it pays to say each chunk out loud before adding.

Example three: a calculation in numerals

Work out XIV added to XXXVI. Give your answer in Roman numerals.

Convert both numbers first. XIV is X, then the pair IV, so 10 plus 4, which is 14. XXXVI is 10 plus 10 plus 10 plus 5 plus 1, which is 36. Now do the sum in ordinary figures: 14 plus 36 is 50. Turn 50 back into a numeral, and 50 is a single letter.

The answer is L.

The wrong option that catches most children is LI, which is 51. It comes from reading XIV as XV, worth 15, by letting the I slide to the wrong side of the V. There is also XXII, which is 22, from taking away instead of adding.

How to answer it

1. Read the instruction before the numeral, and note which way round the answer has to be. Some questions want figures, some want letters back, and a right number written in the wrong form scores nothing.
2. Split the numeral into chunks from the left, keeping any take-away pair together as one chunk.
3. Work out each chunk on its own, then add the chunks. Thousands first, then hundreds, then tens, then units.
4. For a calculation, convert everything into ordinary figures, do the maths in figures, and only then convert the answer back.
5. Check the other way round before choosing. Convert your answer back into the form the question started in and see whether you land on the number you were given.

Common mistakes

• Adding a take-away pair instead of taking away. XL read as 60, IX read as 11, XC read as 110. This is the most common single error, and every set of options in this topic has one of these sitting in it.
• Reversing a pair. IV read as VI, IX read as XI. The letters are the same and only the order tells you which is which.
• Losing or gaining a repeated letter. LXX is 70 and LXXX is 80, XXXVI is 36 and XXXV is 35. One letter is easy to miscount when three or four of them sit in a row.
• Getting the number right and writing it wrong. A child works out 473 correctly and then writes CDLXXXIII, which is 483. The last conversion needs as much care as the first.
• Inventing a shortcut. 349 is CCCXLIX, not CCCIL. Only I, X and C are ever taken away, and only from the next two sizes up, so IL is not a real numeral even though it looks tidy.
• Doing the wrong operation. A question saying multiplied gets added instead, so 21 and 4 come out as 25 rather than 84. Reading the instruction word is half the question.

How to practise 11 plus Roman Numerals questions

This is a topic that rewards little and often. The letters and the six take-away pairs need to be automatic, because a child who is still working out what XL means has nothing left over for the calculation on top, which is the pattern behind how much 11 plus practice a child needs each day. Real numerals are everywhere once you look: the year at the end of a film, a date on an old building, the face of a clock. Ask what they say, then ask for the answer back in figures, and you have covered both directions in a minute. 11+ Daily has a Roman Numerals project alongside the rest of the number work, on laptop, tablet or phone, and the full set is listed on our 11 plus maths practice page. Every question is original to 11+ Daily, nothing is a past paper and nothing is licensed from another publisher, and the bank is re-checked in rounds.

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