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\frac{1}{5}-\frac{2}{5}\times 9
Divide \frac{2}{5} by \frac{1}{9} by multiplying \frac{2}{5} by the reciprocal of \frac{1}{9}.
\frac{1}{5}-\frac{2\times 9}{5}
Express \frac{2}{5}\times 9 as a single fraction.
\frac{1}{5}-\frac{18}{5}
Multiply 2 and 9 to get 18.
\frac{1-18}{5}
Since \frac{1}{5} and \frac{18}{5} have the same denominator, subtract them by subtracting their numerators.
-\frac{17}{5}
Subtract 18 from 1 to get -17.