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Farey Sequences printable worksheet
If I gave you a list of decimals, you might find it quite straightforward to put them in order of size. But what about ordering fractions?
A man called John Farey investigated sequences of fractions in order of size - they are called Farey Sequences.
The third Farey Sequence, F_3, looks like this:
\frac01 \qquad \frac13 \qquad \frac12 \qquad \frac23 \qquad \frac11
Now that you've got the hang of it, write F_5.
Which extra fractions are in F_5 which weren't in F_4?
Which extra fractions will be in F_6 which aren't in F_5?
Where will they appear in the sequence?
There are lots of questions you could explore about Farey Sequences. Here are just a few that we thought of:
Send us your solutions to these and any other questions you decide to explore!
There is a curious link between the mediant of two fractions and Farey Sequences. See the problem Mediant Madness to learn more about mediants, and Farey Neighbours to apply it to Farey Sequences. Finally, the problem Ford
Circles shows the relationship between these fractions and some beautiful geometrical patterns.
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...
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 for any whole numbers?
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.