Do you mean three and one fifth (3 1/5)?
If so, convert the mixed number to an improper fraction and then turn it upside down:
3 1/5 = 16/5
=> reciprocal of 3 1/5 = 5/16.
If you mean thirty one fifths (31/5), just turn it upside down => 5/31.
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5/21
eight over thirty one
1/3 its reciprocal is 3/1 or just '3'. The reciprocal of '3' is '1/3'. This rule applies to any number.
0.666666667
The reciprocal is a flipped fraction, 3 is 3 over 1, so, The reciprocal of 3 is 1 over 3, which is one third.