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.
Problem one was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?
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. . . .
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?
There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?
A jigsaw where pieces only go together if the fractions are equivalent.
Can you work out which drink has the stronger flavour?
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?
My recipe is for 12 cakes - how do I change it if I want to make a different number of cakes?
Take a look at the video and try to find a sequence of moves that will take you back to zero.
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!
Can you tangle yourself up and reach any fraction?
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.
It would be nice to have a strategy for disentangling any tangled ropes...
Look carefully at the video of a tangle and explain what's happening.
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 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?
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.
This challenge asks you to imagine a snake coiling on itself.
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?
Can you find ways to make twenty-link chains from these smaller chains? This gives opportunities for different approaches.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
In this problem, we have created a pattern from smaller and smaller squares. If we carried on the pattern forever, what proportion of the image would be coloured blue?
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.
Here is a chance to play a fractions version of the classic Countdown Game.
Can all unit fractions be written as the sum of two unit fractions?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
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?
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
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.
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?
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
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. . . .
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 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 disc. Use the information to find out how many discs of each colour there are in the box.
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
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.
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?