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\frac{8}{4\left(1\times 8+7\right)}
Divide \frac{1}{4} by \frac{1\times 8+7}{8} by multiplying \frac{1}{4} by the reciprocal of \frac{1\times 8+7}{8}.
\frac{8}{4\left(8+7\right)}
Multiply 1 and 8 to get 8.
\frac{8}{4\times 15}
Add 8 and 7 to get 15.
\frac{8}{60}
Multiply 4 and 15 to get 60.
\frac{2}{15}
Reduce the fraction \frac{8}{60} to lowest terms by extracting and canceling out 4.