Four identical glasses are shown below. One glass is empty, and the other 3 glasses are \(\dfrac{1}{4}\) full, \(\dfrac{1}{2}\) full, \(\dfrac{4}{5}\) full of water, respectively. If the water were redistributed equally among the 4 glasses, what fractional part of each glass would be filled?

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The total amount of water is the sum of each fractional value:

$$ \frac{1}{4}+\frac{1}{2}+\frac{4}{5} $$ $$ =\frac{5}{20}+\frac{10}{20}+\frac{16}{20} $$ $$ = \frac{31}{20} $$

Dividing this among four glasses:

$$ =\frac{31}{20} \div 4 $$ $$ = \frac{31}{20}\cdot \frac{1}{4} $$ $$ = \boxed{\frac{31}{80}} $$