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There are **108** NRICH Mathematical resources connected to **Fractions**, you may find related items under Fractions, decimals, percentages, ratio and proportion.

Problem
Primary curriculum
Secondary curriculum
### Terminating or Not

Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Almost One

Choose some fractions and add them together. Can you get close to 1?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractions Rectangle

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Extending Fraction Bars

Can you compare these bars with each other and express their lengths as fractions of the black bar?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Fraction Bars

What fraction of the black bar are the other bars? Have a go at this challenging task!

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A4 Fraction Subtraction

This task offers opportunities to subtract fractions using A4 paper.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Same Answer

Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tangling and Untangling

Twisting and turning with ropes can be encoded mathematically using fractions. Can you find a way to get back to zero?

Problem
Primary curriculum
Secondary curriculum
### Jumping

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Diminishing Returns

How much of the square is coloured blue? How will the pattern continue?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Countdown Fractions

Here is a chance to play a fractions version of the classic Countdown Game.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Greedy Algorithm

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Keep it Simple

Can all unit fractions be written as the sum of two unit fractions?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Twisting and Turning

It would be nice to have a strategy for disentangling any tangled ropes...

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Twisting and Turning

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Chance to Win?

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Longer, Making Shorter

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Equal Temperament

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractions Jigsaw

A jigsaw where pieces only go together if the fractions are equivalent.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fraction Fascination

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Harmonic Triangle

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Age 14 to 16

Challenge Level

Interactive
Primary curriculum
Secondary curriculum
### Cuisenaire Environment

An environment which simulates working with Cuisenaire rods.

Age 5 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractions and Percentages Card Game

Can you find the pairs that represent the same amount of money?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Andy's Marbles

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Orange Drink

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ben's Game

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fair Feast

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Peaches Today, Peaches Tomorrow...

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tiny Nines

What do you notice about these families of recurring decimals?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Matching Fractions, Decimals and Percentages

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Egyptian Fractions

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractions in a Box

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rectangle Tangle

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fair Shares?

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### There's a Limit

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?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Bowl of Fruit

Can you work out how many apples there are in this fruit bowl if you know what fraction there are?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Do Unto Caesar

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### F'arc'tion

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.

Age 14 to 16

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### As Easy as 1,2,3

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Special Sums and Products

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sum Equals Product

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 ï¿½ 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Lower Bound

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tweedle Dum and Tweedle Dee

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...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rationals Between...

What fractions can you find between the square roots of 65 and 67?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pizza Portions

My friends and I love pizza. Can you help us share these pizzas equally?

Age 7 to 11

Challenge Level