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Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Calculating with fractions

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More Fraction Bars

Age 7 to 11 Challenge Level:

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

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A4 Fraction Subtraction

Age 7 to 11 Challenge Level:

This task offers opportunities to subtract fractions using A4 paper.

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A4 Fraction Addition

Age 7 to 11 Challenge Level:

Try adding fractions using A4 paper.

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Same Answer

Age 11 to 14 Challenge Level:

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

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Jumping

Age 7 to 11 Challenge Level:

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

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Ratios and Dilutions

Age 14 to 16 Challenge Level:

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

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Mixing Lemonade

Age 11 to 14 Challenge Level:

Can you work out which drink has the stronger flavour?

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Diminishing Returns

Age 11 to 14 Challenge Level:

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

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The Greedy Algorithm

Age 11 to 14 Challenge Level:

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.

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Keep it Simple

Age 11 to 14 Challenge Level:

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

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More Twisting and Turning

Age 11 to 14 Challenge Level:

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

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Twisting and Turning

Age 11 to 14 Challenge Level:

Take a look at the video and try to find a sequence of moves that will take you back to zero.

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Balance of Halves

Age 7 to 11 Challenge Level:

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?

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A Chance to Win?

Age 11 to 14 Challenge Level:

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

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Making Longer, Making Shorter

Age 5 to 7 Challenge Level:

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

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Fractions Jigsaw

Age 11 to 14 Challenge Level:

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

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Harmonic Triangle

Age 14 to 16 Challenge Level:

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

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Andy's Marbles

Age 7 to 11 Challenge Level:

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.

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Orange Drink

Age 7 to 11 Challenge Level:

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?

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Ben's Game

Age 11 to 14 Challenge Level:

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.

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Fair Feast

Age 5 to 11 Challenge Level:

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

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Peaches Today, Peaches Tomorrow...

Age 11 to 14 Challenge Level:

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?

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Egyptian Fractions

Age 11 to 14 Challenge Level:

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.

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Shopping Basket

Age 11 to 16 Challenge Level:

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

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Fractions in a Box

Age 7 to 11 Challenge Level:

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.

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Blue and White

Age 11 to 14 Challenge Level:

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

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Fair Shares?

Age 14 to 16 Challenge Level:

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?

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There's a Limit

Age 14 to 18 Challenge Level:

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?

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A Swiss Sum

Age 16 to 18 Challenge Level:

Can you use the given image to say something about the sum of an infinite series?

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Extending Fraction Bars

Age 7 to 11 Challenge Level:

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

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Linked Chains

Age 7 to 11 Challenge Level:

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

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Fraction Lengths

Age 7 to 11 Challenge Level:

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?

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Snake Coils

Age 7 to 11 Challenge Level:

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

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Tray Bake

Age 11 to 14 Challenge Level:

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

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Reductant Ratios

Age 16 to 18 Challenge Level:

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

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Countdown Fractions

Age 11 to 16 Challenge Level:

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

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Investigating the Dilution Series

Age 14 to 16 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

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Turning Tangles

Age 11 to 14 Challenge Level:

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

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All Tangled Up

Age 11 to 14 Challenge Level:

Can you tangle yourself up and reach any fraction?

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Magic Matrix

Age 7 to 11 Challenge Level:

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

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Once Upon a Time

Age 7 to 11 Challenge Level:

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?

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The Harmonic Triangle and Pascal's Triangle

Age 16 to 18

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

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Fractions Made Faster

Age 7 to 11 Challenge Level:

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

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Fracmax

Age 14 to 16 Challenge Level:

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.

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And So on - and on -and On

Age 16 to 18 Challenge Level:

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

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Hello Again

Age 11 to 14 Challenge Level:

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?

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Smaller and Smaller

Age 7 to 14 Challenge Level:

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?

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Hands Together

Age 11 to 14 Challenge Level:

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?

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Fun Time

Age 7 to 11 Challenge Level:

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.

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In the Money

Age 7 to 11 Challenge Level:

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