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\frac{8\times \frac{9}{4}}{15\times 6}
Divide \frac{8}{15} by \frac{6}{\frac{9}{4}} by multiplying \frac{8}{15} by the reciprocal of \frac{6}{\frac{9}{4}}.
\frac{\frac{9}{4}\times 4}{3\times 15}
Cancel out 2 in both numerator and denominator.
\frac{9}{3\times 15}
Cancel out 4 and 4.
\frac{9}{45}
Multiply 3 and 15 to get 45.
\frac{1}{5}
Reduce the fraction \frac{9}{45} to lowest terms by extracting and canceling out 9.