70 lines
3.5 KiB
Plaintext
70 lines
3.5 KiB
Plaintext
''There is a fine line between numerator and denominator.'' ''─── anonymous''
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A method to "reduce" some reducible fractions is to ''cross out'' <u>a</u> digit from the
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numerator and the denominator. An example is:
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<big>16</big> <big>1<b><strike>6</strike></b></big>
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──── and then (simply) cross─out the sixes: ────
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<big>64</big> <big><b><strike>6</strike></b>4</big>
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resulting in:
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<big>1</big>
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───
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<big>4</big>
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Naturally, this "method" of reduction must reduce to the proper value (shown as a fraction).
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This "method" is also known as ''anomalous cancellation'' and also ''accidental cancellation''.
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(Of course, this "method" shouldn't be taught to impressionable or gullible minds.) <big><big><big> 😇 </big></big></big>
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;Task:
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Find and show some fractions that can be reduced by the above "method".
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:* show 2-digit fractions found (like the example shown above)
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:* show 3-digit fractions
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:* show 4-digit fractions
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:* show 5-digit fractions (and higher) ''(optional)''
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:* show each (above) n-digit fractions separately from other different n-sized fractions, don't mix different "sizes" together
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:* for each "size" fraction, only show a dozen examples (the 1<sup>st</sup> twelve found)
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:* (it's recognized that not every programming solution will have the same generation algorithm)
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:* for each "size" fraction:
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:::* show a count of how many reducible fractions were found. The example (above) is size '''2'''
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:::* show a count of which digits were crossed out (one line for each different digit)
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:* for each "size" fraction, show a count of how many were found. The example (above) is size '''2'''
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:* show each n-digit example (to be shown on one line):
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:::* show each n-digit fraction
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:::* show each reduced n-digit fraction
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:::* show what digit was crossed out for the numerator and the denominator
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;Task requirements/restrictions:
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:* only proper fractions and their reductions (the result) are to be used (no vulgar fractions)
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:* only positive fractions are to be used (no negative signs anywhere)
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:* only base ten integers are to be used for the numerator and denominator
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:* no zeros (decimal digit) can be used within the numerator or the denominator
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:* the numerator and denominator should be composed of the same number of digits
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:* no digit can be repeated in the numerator
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:* no digit can be repeated in the denominator
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:* (naturally) there should be a shared decimal digit in the numerator ''and'' the denominator
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:* fractions can be shown as 16/64 (for example)
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Show all output here, on this page.
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;Somewhat related task:
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:* [https://rosettacode.org/wiki/Farey_sequence Farey sequence] (It concerns fractions.)
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;References:
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:* Wikipedia entry: [https://en.wikipedia.org/wiki/Fraction_(mathematics)#Proper_and_improper_fractions proper and improper fractions].
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:* Wikipedia entry: [https://en.wikipedia.org/wiki/Anomalous_cancellation anomalous cancellation and/or accidental cancellation].
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<br><br>
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