Solve 100-80/frac{-20%{80%-2%}}

$$100- \frac{ 80 }{ \frac{ -20 \% }{ 80 \% -2 \% } }$$

Evaluate

$$412$$

Solution Steps

Divide 80 by \frac{-\frac{20}{100}}{\frac{80}{100}-\frac{2}{100}} by multiplying 80 by the reciprocal of \frac{-\frac{20}{100}}{\frac{80}{100}-\frac{2}{100}}.

$$100-\frac{80\left(\frac{80}{100}-\frac{2}{100}\right)}{-\frac{20}{100}}$$

Reduce the fraction \frac{80}{100} to lowest terms by extracting and canceling out 20.

$$100-\frac{80\left(\frac{4}{5}-\frac{2}{100}\right)}{-\frac{20}{100}}$$

Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$100-\frac{80\left(\frac{4}{5}-\frac{1}{50}\right)}{-\frac{20}{100}}$$

Least common multiple of 5 and 50 is 50. Convert \frac{4}{5} and \frac{1}{50} to fractions with denominator 50.

$$100-\frac{80\left(\frac{40}{50}-\frac{1}{50}\right)}{-\frac{20}{100}}$$

Since \frac{40}{50} and \frac{1}{50} have the same denominator, subtract them by subtracting their numerators.

$$100-\frac{80\times \frac{40-1}{50}}{-\frac{20}{100}}$$

Subtract 1 from 40 to get 39.

$$100-\frac{80\times \frac{39}{50}}{-\frac{20}{100}}$$

Express 80\times \frac{39}{50} as a single fraction.

$$100-\frac{\frac{80\times 39}{50}}{-\frac{20}{100}}$$

Multiply 80 and 39 to get 3120.

$$100-\frac{\frac{3120}{50}}{-\frac{20}{100}}$$

Reduce the fraction \frac{3120}{50} to lowest terms by extracting and canceling out 10.

$$100-\frac{\frac{312}{5}}{-\frac{20}{100}}$$

Reduce the fraction \frac{20}{100} to lowest terms by extracting and canceling out 20.

$$100-\frac{\frac{312}{5}}{-\frac{1}{5}}$$

Divide \frac{312}{5} by -\frac{1}{5} by multiplying \frac{312}{5} by the reciprocal of -\frac{1}{5}.

$$100-\frac{312}{5}\left(-5\right)$$

Express \frac{312}{5}\left(-5\right) as a single fraction.

$$100-\frac{312\left(-5\right)}{5}$$

Multiply 312 and -5 to get -1560.

$$100-\frac{-1560}{5}$$

Divide -1560 by 5 to get -312.

$$100-\left(-312\right)$$

The opposite of -312 is 312.

$$100+312$$

Add 100 and 312 to get 412.

$$412$$

Factor

$$2^{2}\times 103$$