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\frac{\left(1\times 10+1\right)\times 7}{10\left(1\times 7+4\right)}
Divide \frac{1\times 10+1}{10} by \frac{1\times 7+4}{7} by multiplying \frac{1\times 10+1}{10} by the reciprocal of \frac{1\times 7+4}{7}.
\frac{\left(10+1\right)\times 7}{10\left(1\times 7+4\right)}
Multiply 1 and 10 to get 10.
\frac{11\times 7}{10\left(1\times 7+4\right)}
Add 10 and 1 to get 11.
\frac{77}{10\left(1\times 7+4\right)}
Multiply 11 and 7 to get 77.
\frac{77}{10\left(7+4\right)}
Multiply 1 and 7 to get 7.
\frac{77}{10\times 11}
Add 7 and 4 to get 11.
\frac{77}{110}
Multiply 10 and 11 to get 110.
\frac{7}{10}
Reduce the fraction \frac{77}{110} to lowest terms by extracting and canceling out 11.