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\frac{\frac{-1}{10\times 100}-\left(-\frac{1}{10}\right)^{2}}{\frac{1}{100}}
Multiply -\frac{1}{10} times \frac{1}{100} by multiplying numerator times numerator and denominator times denominator.
\frac{\frac{-1}{1000}-\left(-\frac{1}{10}\right)^{2}}{\frac{1}{100}}
Do the multiplications in the fraction \frac{-1}{10\times 100}.
\frac{-\frac{1}{1000}-\left(-\frac{1}{10}\right)^{2}}{\frac{1}{100}}
Fraction \frac{-1}{1000} can be rewritten as -\frac{1}{1000} by extracting the negative sign.
\frac{-\frac{1}{1000}-\frac{1}{100}}{\frac{1}{100}}
Calculate -\frac{1}{10} to the power of 2 and get \frac{1}{100}.
\frac{-\frac{1}{1000}-\frac{10}{1000}}{\frac{1}{100}}
Least common multiple of 1000 and 100 is 1000. Convert -\frac{1}{1000} and \frac{1}{100} to fractions with denominator 1000.
\frac{\frac{-1-10}{1000}}{\frac{1}{100}}
Since -\frac{1}{1000} and \frac{10}{1000} have the same denominator, subtract them by subtracting their numerators.
\frac{-\frac{11}{1000}}{\frac{1}{100}}
Subtract 10 from -1 to get -11.
-\frac{11}{1000}\times 100
Divide -\frac{11}{1000} by \frac{1}{100} by multiplying -\frac{11}{1000} by the reciprocal of \frac{1}{100}.
\frac{-11\times 100}{1000}
Express -\frac{11}{1000}\times 100 as a single fraction.
\frac{-1100}{1000}
Multiply -11 and 100 to get -1100.
-\frac{11}{10}
Reduce the fraction \frac{-1100}{1000} to lowest terms by extracting and canceling out 100.