A reciprocal of something like 2/3 would be 3/2. Zero as a fraction could be 0 over any other number such as 0/1, 0/5. So their reciprocals would be 1/0 or 5/0. Dividing by zero is mathematically impossible.
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No, there is no reciprocal of 0.
Every number does not. 0 is a number and it does not have a reciprocal.
7/0 does not exist, but its reciprocal would be 0
No
Only 0 doesn't have a reciprocal