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.

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.

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.

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. . . .

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.

This challenge asks you to imagine a snake coiling on itself.

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

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

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?

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.

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

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .

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

Sometime during every hour the minute hand lies directly above the hour hand. At what time between 4 and 5 o'clock does this happen?

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

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

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...

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

My recipe is for 12 cakes - how do I change it if I want to make a different number of cakes?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Can you find combinations of strips of paper which equal the length of the black strip? If the length of the black is 1, how could you write the sum of the strips?

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

Can you find ways to make twenty-link chains from these smaller chains? This gives opportunities for different approaches.

This task offers opportunities to subtract fractions using A4 paper.

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!

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

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

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

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.

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

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?

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?

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.

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.

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?

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.

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Look carefully at the video of a tangle and explain what's happening.

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