No 15

¹/₇ = 0.142857142857142857142...with repeating cycle (142857).

Suppose the cycle is reversed to give 0.758241758241758241758... or .(758241)

What fraction is this? It is ⁶⁹/₉₁. But ¹/₇ can be written ¹³/₉₁.

¹/₁₃ = 0.(076923) so what fraction is 0.(329670) ? It's ³⁰/₉₁. But ¹/₁₃ = ⁷/₉₁.

This amazing pattern is worth exploring further! For example:

¹/₉₁= ? Now reverse the cycle to get ^?/₉₁

²/₉₁= ? Now reverse the cycle to get ^?/₉₁

and so on ...

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E-mail us at madrascollege.maths@fife.gov.uk

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