Fractions

problem

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?
problem

Modular Fractions

Age

16 to 18

Challenge level

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.
problem

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.
problem

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?
problem
Favourite

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.
problem

Fraction Card Game

Age

5 to 7

Challenge level

Can you match the halves in this interactive game?
problem
Favourite

A Bowl of Fruit

Age

5 to 7

Challenge level

Can you work out how many apples there are in this fruit bowl if you know what fraction there are?
problem
Favourite

Halving

Age

5 to 7

Challenge level

These pictures show squares split into halves. Can you find other ways?
problem
Favourite

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?
problem
Favourite

Happy Halving

Age

5 to 7

Challenge level

Can you split each of the shapes below in half so that the two parts are exactly the same?