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\frac{\left(1\times 9+1\right)\times 11}{9\times 7}
Divide \frac{1\times 9+1}{9} by \frac{7}{11} by multiplying \frac{1\times 9+1}{9} by the reciprocal of \frac{7}{11}.
\frac{\left(9+1\right)\times 11}{9\times 7}
Multiply 1 and 9 to get 9.
\frac{10\times 11}{9\times 7}
Add 9 and 1 to get 10.
\frac{110}{9\times 7}
Multiply 10 and 11 to get 110.
\frac{110}{63}
Multiply 9 and 7 to get 63.