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\frac{1}{\frac{5}{\frac{5}{5\text{bmod}55}}}
Divide 1 by \frac{\frac{5}{\frac{5}{5\text{bmod}55}}}{1} by multiplying 1 by the reciprocal of \frac{\frac{5}{\frac{5}{5\text{bmod}55}}}{1}.
\frac{1}{\frac{5\left(5\text{bmod}55\right)}{5}}
Divide 5 by \frac{5}{5\text{bmod}55} by multiplying 5 by the reciprocal of \frac{5}{5\text{bmod}55}.
\frac{1}{5\text{bmod}55}
Cancel out 5 and 5.
\frac{1}{5}
Divide 5 by 55 to get the remainder 5.