Resources tagged with: Fractions

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There are 64 results

Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Fractions

Rod Fractions

Age 7 to 14
Challenge Level

Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?

Almost One

Age 11 to 14
Challenge Level

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

Fractions and Percentages Card Game

Age 11 to 16
Challenge Level

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

Mixing Lemonade

Age 11 to 14
Challenge Level

Can you work out which drink has the stronger flavour?

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.

Ratio Sudoku 3

Age 11 to 16
Challenge Level

A Sudoku with clues as ratios or fractions.

3388

Age 11 to 14
Challenge Level

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.

Repetitiously

Age 14 to 16
Challenge Level

Can you express every recurring decimal as a fraction?

Terminating or Not

Age 11 to 14
Challenge Level

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

What a Joke

Age 14 to 16
Challenge Level

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

History of Fractions

Age 7 to 14

Who first used fractions? Were they always written in the same way? How did fractions reach us here? These are the sorts of questions which this article will answer for you.

Farey Sequences

Age 11 to 14
Challenge Level

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

Peaches Today, Peaches Tomorrow...

Age 11 to 14
Challenge Level

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?

Ben's Game

Age 11 to 16
Challenge Level

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

As Easy as 1,2,3

Age 11 to 14
Challenge Level

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. . . .

Unit Fractions

Age 11 to 14
Challenge Level

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.

Matching Fractions, Decimals and Percentages

Age 7 to 14
Challenge Level

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

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?

The Genes of Gilgamesh

Age 14 to 16
Challenge Level

Can you work out the parentage of the ancient hero Gilgamesh?

Countdown Fractions

Age 11 to 16
Challenge Level

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

How Long Is the Cantor Set?

Age 11 to 14
Challenge Level

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?

Special Sums and Products

Age 11 to 14
Challenge Level

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.

Stretching Fractions

Age 14 to 16
Challenge Level

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?

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?

Water Lilies

Age 11 to 14
Challenge Level

There are some water lilies in a lake. The area that they cover doubles in size every day. After 17 days the whole lake is covered. How long did it take them to cover half the lake?

Counting Fish

Age 14 to 16
Challenge Level

I need a figure for the fish population in a lake. How does it help to catch and mark 40 fish?

Investigating the Dilution Series

Age 14 to 16
Challenge Level

Which dilutions can you make using only 10ml pipettes?

Keep it Simple

Age 11 to 14
Challenge Level

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

Teaching Fractions with Understanding: Part-whole Concept

Age 5 to 14

Written for teachers, this article describes four basic approaches children use in understanding fractions as equal parts of a whole.

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.

Circuit Training

Age 14 to 16
Challenge Level

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

Fractions Rectangle

Age 11 to 14
Challenge Level

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?

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 untangle the ropes.

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?

Sum Equals Product

Age 11 to 14
Challenge Level

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. . . .

Do Unto Caesar

Age 11 to 14
Challenge Level

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. . . .

Rationals Between...

Age 14 to 16
Challenge Level

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

Tangles

Age 11 to 16

A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?

Archimedes and Numerical Roots

Age 14 to 16
Challenge Level

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?

Tweedle Dum and Tweedle Dee

Age 11 to 14
Challenge Level

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...

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?

Equal Temperament

Age 14 to 16
Challenge Level

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.

Tiny Nines

Age 14 to 16
Challenge Level

What do you notice about these families of recurring decimals?

Lower Bound

Age 14 to 16
Challenge Level

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

Bull's Eye

Age 11 to 14
Challenge Level

What fractions of the largest circle are the two shaded regions?

F'arc'tion

Age 14 to 16 Short
Challenge Level

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. . . .

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?

Racing Odds

Age 11 to 14
Challenge Level

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

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.

Couples

Age 11 to 14
Challenge Level

In a certain community two thirds of the adult men are married to three quarters of the adult women. How many adults would there be in the smallest community of this type?