Getting your questions ready
Getting your questions ready
Beat the crowd
10 questions No timer
40 free Fractions trivia questions with answers — trivia quiz, new questions added Aug 2026.
Fractions are the first piece of maths most people remember finding hard, and the last one they keep using: halving a recipe, reading a tape measure, working out what a sale really costs. They also hide some of the best stories in arithmetic, from a hamburger that flopped because customers misread a fraction to a stock market that priced shares the way pirates split coins. These 40 questions mix worked problems with the ideas behind them: equivalent fractions and lowest terms, adding and subtracting over a common denominator, multiplication and division, converting between fractions, decimals and percentages, and comparing and ordering. Alongside them sit the vocabulary of fraction notation and the history of who wrote fractions how, from ancient scribes to the booklet that sold Europe on decimals. It suits a maths classroom starter, a revision session before a test, or a pub-quiz round where everyone thinks they know the answer and half the room gets it wrong.
30 of 40 questions with answers and explanations. Play the quiz
Q 01Which patty size did A&W pitch against McDonald's Quarter Pounder, only for customers to judge it smaller?
1/3 lb
A&W's 1/3 lb Third Pounder lost to the Quarter Pounder because diners read 3 as less than 4 and assumed a third was less meat than a quarter. It beat the rival in taste tests and was cheaper by weight.
Q 02What share of an 18-karat gold ring is actually gold, on a scale where 24 karat means pure?
75%
18-karat gold is 75% gold, because karats count parts per 24 and 18/24 reduces to three quarters. The rest is copper, silver or other metals that make the ring harder.
Q 03In which fraction of a dollar did the NYSE quote prices until 1997, a habit from Spanish coins chopped into 'bits'?
Eighths
Eighths ruled Wall Street because the Spanish dollar was literally cut into eight 'bits', and that 1/8 tick lasted until the New York Stock Exchange went to sixteenths in 1997 and to decimals in 2001.
Q 04What does a '2×4' board actually measure in inches, once the rough-sawn plank has been dried and planed smooth?
1 1/2 × 3 1/2 in
A '2×4' is really 1 1/2 × 3 1/2 in (38 by 89 mm), because the name describes the rough green board before kiln drying shrinks it and planing takes off the faces. By the same rule a '2×2' ends up 1 1/2 in square.
Q 05Which Roman punishment, 'destruction of a tenth' in Latin, killed every tenth man of a unit that had shown cowardice?
Decimation
Decimation chose its victims by lot, and the nine men spared in each group of ten had to club their condemned comrade to death. The survivors were then put on barley rations and made to camp outside the walls.
Q 06Which church levy, from the Old English for 'tenth', took one part in ten of a farmer's produce?
Tithe
A tithe is a tenth, and Genesis has Abraham paying one to Melchizedek from the spoils of battle, the precedent churches cited for centuries of compulsory giving.
Q 07Which graphic, first drawn by William Playfair in 1801, shows fractions of a whole as wedges of a circle?
Pie chart
The pie chart first appeared in Playfair's Statistical Breviary of 1801, and Florence Nightingale later reshaped it into her polar area diagram to show what was killing soldiers in the military hospital she ran.
Q 08What do British musicians call the note Americans know as a quarter note, worth a quarter of a semibreve?
Crotchet
A crotchet is the British quarter note, half as long as a minim and twice as long as a quaver, with the whole note itself going by the name semibreve.
Q 09What fraction of an hour is a 15-minute coffee break plus a 10-minute one, the sum 1/4 + 1/6?
5/12
1/4 + 1/6 = 5/12, because quarters and sixths only line up over 12: 3/12 + 2/12. In minutes that is 15 + 10 = 25 of the 60.
Q 10Which name does 2 1/2 go by, the form tape measures and recipes prefer to the top-heavy 5/2?
Mixed number
A mixed number pairs a whole number with a proper fraction, and any top-heavy fraction can be turned into one by dividing: 5/2 is two with a half left over.
Q 11What is 5/3 called in relation to 3/5, the partner every fraction has whose product with it is exactly 1?
Reciprocal
The reciprocal flips a fraction over, and dividing by a fraction means you multiply by it instead: 5/3 × 3/5 = 1, so dividing by 3/5 is the same as scaling up by 5/3.
Q 12What is 5/6 − 1/4, the difference found by rewriting both fractions over the common denominator 12?
7/12
5/6 − 1/4 = 7/12, since 5/6 is 10/12 and 1/4 is 3/12, and 10 − 3 = 7. Subtracting tops and bottoms separately would give the nonsense answer 4/2.
Q 13What is 4/5 × 5/6, the product that simplifies the moment the two fives cancel each other?
2/3
4/5 × 5/6 = 2/3, because going straight across gives 20/30 and both parts divide by 10. Adding tops and bottoms to get 9/11 is the classic mistake.
Q 21How many 1/8-cup scoops of flour fill a 5/8-cup measure, a division done by flipping the divisor to multiply instead?
5
Five scoops, because 5/8 ÷ 1/8 = 5/8 × 8/1 = 40/8 = 5, since both amounts are counted in the same size of slice.
Q 22Which of these denominators gives a decimal that stops rather than repeats, having no prime factor other than 2 and 5?
16
1/16 = 0.0625 and stops, because 16 is a pure power of 2, while 7, 9 and 12 each carry a factor of 3 or 7 and so their decimals repeat forever.
Q 23Which shortcut tests whether 3/4 and 9/12 are equal by checking that 3 × 12 matches 4 × 9?
Cross-multiplying
Cross-multiplying works because two fractions are equal exactly when the diagonal products agree, and 3 × 12 and 4 × 9 both come to 36.
Q 14Which symbol, a % with an extra zero in the divisor, is the usual unit for seawater salinity?
Per mille
Per mille (‰) means 'in each thousand', so a salinity written as 35‰ is 35 parts of salt in every thousand of seawater, a scale ten times finer than a percentage.
Q 15Which mathematician's 1585 booklet De Thiende told surveyors and tradesmen to calculate in decimal fractions?
Simon Stevin
Simon Stevin's De Thiende ('the art of tenths') sold Europe on decimal fractions, though he did not invent them: al-Uqlidisi had used them in 952 and al-Kashi systematised them in 1427.
Q 16Which 12th-century mathematician first wrote fractions with a bar between top and bottom, as Fibonacci soon did too?
Al-Hassar
Al-Hassar, working in 12th-century Morocco, gave fractions the bar we still use, and Fibonacci carried the notation into Europe in the 13th century.
Q 17What fraction of a Roman pound was the uncia, a unit whose name survives in both the ounce and the inch?
One-twelfth
The uncia was one-twelfth of both the Roman pound and the Roman foot, and it lives on as the ounce, the fluid ounce and the inch.
Q 18What is the bar over the repeating digits of a decimal like 0.1666… called, from the Latin for 'fetter' or 'chain'?
Vinculum
A vinculum is the overline that marks a repetend, and the same horizontal 'chain' was once drawn over groups of terms to tie them together, a job parentheses mostly do today.
Q 19Which formal name for the slash in 3/4 recalls the mark's old use as the shilling mark in British prices?
Solidus
Solidus is the slash's formal name because pre-decimal Britain used the stroke to write shillings, and by the early 20th century 'shilling mark' and 'solidus' were interchangeable.
Q 20What do older textbooks call the ÷ symbol, a word that also names a dagger mark flagging dubious lines in manuscripts?
Obelus
Obelus was the ancient editors' mark beside lines they thought spurious, and the same name passed to the ÷ symbol once it was borrowed for division.
Q 24What are fractions like 11/32, with a power of two on the bottom, called, the only kind an inch ruler marks?
Dyadic
Dyadic rationals are the halves, quarters and sixteenths of a tape measure, and they are also what a computer's floating-point numbers are built from: an integer times a power of two.
Q 25Which camera setting, written like f/8, is literally focal length divided by the width of the hole admitting light?
Aperture
Aperture is what f/8 sets, and because that figure is focal length over the pupil's diameter, a bigger figure means a smaller hole and less light reaching the sensor.
Q 26Which of these fractions is equal to 3/5, found by scaling top and bottom by the same factor?
9/15
9/15 is 3/5 with both parts tripled, and scaling top and bottom alike never changes a fraction's value, which is why 6/15, with only the top doubled, is a different amount.
Q 27What is 28/36 in lowest terms, the form reached once top and bottom are both divided by 4?
7/9
28/36 reduces to 7/9 because 4 divides both 28 and 36 and no larger factor does, so 7/9 cannot be simplified any further.
Q 28What is 7/8 as a decimal, the figure reached by adding three steps of 0.125 to 0.5?
0.875
7/8 = 0.875, since 1/8 is 0.125 and seven of them make 0.875, which is exactly what dividing 7 by 8 on a calculator shows.
Q 29A recipe's 3/4 cup of butter is cut to half for a small batch; how much butter goes in?
3/8 cup
Half of 3/4 cup is 3/8 cup, because halving a fraction doubles the bottom: 3/4 × 1/2 = 3/8. Tripling the batch instead would call for 2 1/4 cups.
Q 30What percentage is 7 right answers out of 20, the fraction 7/20 scaled up to a denominator of 100?
35%
7 out of 20 is 35%, because scaling top and bottom by 5 gives 35/100, and 'per cent' literally means 'per hundred'.