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There are 74 NRICH Mathematical resources connected to Fractions, you may find related items under Fractions, decimals, percentages, ratio and proportion.
Broad Topics > Fractions, decimals, percentages, ratio and proportion > FractionsIs there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
Choose some fractions and add them together. Can you get close to 1?
The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?
Can you compare these bars with each other and express their lengths as fractions of the black bar?
What fraction of the black bar are the other bars? Have a go at this challenging task!
This task offers opportunities to subtract fractions using A4 paper.
Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
How much of the square is coloured blue? How will the pattern continue?
Here is a chance to play a fractions version of the classic Countdown Game.
The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.
Can all unit fractions be written as the sum of two unit fractions?
It would be nice to have a strategy for disentangling any tangled ropes...
Take a look at the video and try to find a sequence of moves that will untangle the ropes.
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
A jigsaw where pieces only go together if the fractions are equivalent.
This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
An environment which simulates working with Cuisenaire rods.
Can you find the pairs that represent the same amount of money?
Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.
A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
There are lots of ideas to explore in these sequences of ordered fractions.
Can you match pairs of fractions, decimals and percentages, and beat your previous scores?
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?
This is a game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
On Saturday, Asha and Kishan's grandad took them to a Theme Park. Use the information to work out how long were they in the theme park.
One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?
Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?
In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?
Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.
What fractions of the largest circle are the two shaded regions?
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?
At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type 'TWO' it returns 2, and so on.
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?
Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...
My friends and I love pizza. Can you help us share these pizzas equally?