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Here is a chance to play a fractions version of the classic Countdown Game.
It would be nice to have a strategy for disentangling any tangled ropes...
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.
Can you see how to build a harmonic triangle? Can you work out the next two rows?
An environment which simulates working with Cuisenaire rods.
Can you find the pairs that represent the same amount of money?
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
What do you notice about these families of recurring decimals?
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?
Can you use the given image to say something about the sum of an infinite series?
What does the empirical formula of this mixture of iron oxides tell you about its consituents?
Can you work out the parentage of the ancient hero Gilgamesh?
This article extends and investigates the ideas in the problem "Stretching Fractions".
Which dilutions can you make using only 10ml pipettes?
I need a figure for the fish population in a lake. How does it help to catch and mark 40 fish?
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.
The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.
The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.
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?
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.
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
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 meet at the start again? If so, after how many circuits?
When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
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.
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?
Relate these algebraic expressions to geometrical diagrams.
Which of these continued fractions is bigger and why?
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 paper.
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
What fractions can you find between the square roots of 65 and 67?