Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

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 take you back to zero.

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.

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

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 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.

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

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?

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.

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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.

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?

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?

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

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?

What does the empirical formula of this mixture of iron oxides tell you about its consituents?

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

Which dilutions can you make using only 10ml pipettes?

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

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?

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

The resources in this trail aim to enrich the experiences of children who are just being introduced to fractions.

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

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 harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.

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

Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.

Can you find the value of this function involving algebraic fractions for x=2000?

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?

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?

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?

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.

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?

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?

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. . . .

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

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

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?