There are 108 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 > Fractions
Is 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?
Twisting and turning with ropes can be encoded mathematically using fractions. Can you find a way to get back to zero?
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...
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.
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.
Can you see how to build a harmonic triangle? Can you work out the next two rows?
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.
What do you notice about these families of recurring decimals?
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?
A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
Can you work out how many apples there are in this fruit bowl if you know what fraction there are?
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?
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.
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?
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
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...
What fractions can you find between the square roots of 65 and 67?
My friends and I love pizza. Can you help us share these pizzas equally?