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\frac{\frac{5}{2}\sqrt{2}\times 10}{9}
Divide \frac{5}{2}\sqrt{2} by \frac{9}{10} by multiplying \frac{5}{2}\sqrt{2} by the reciprocal of \frac{9}{10}.
\frac{\frac{5\times 10}{2}\sqrt{2}}{9}
Express \frac{5}{2}\times 10 as a single fraction.
\frac{\frac{50}{2}\sqrt{2}}{9}
Multiply 5 and 10 to get 50.
\frac{25\sqrt{2}}{9}
Divide 50 by 2 to get 25.