Solve 90(1+2%)(1-2%div11%)

$$90(1+2 \% )(1-2 \% \div 11 \% )$$

Evaluate

$$\frac{4131}{55}\approx 75.109090909$$

Solution Steps

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

$$90\left(1+\frac{1}{50}\right)\left(1-\frac{\frac{2}{100}}{\frac{11}{100}}\right)$$

Convert 1 to fraction \frac{50}{50}.

$$90\left(\frac{50}{50}+\frac{1}{50}\right)\left(1-\frac{\frac{2}{100}}{\frac{11}{100}}\right)$$

Since \frac{50}{50} and \frac{1}{50} have the same denominator, add them by adding their numerators.

$$90\times \frac{50+1}{50}\left(1-\frac{\frac{2}{100}}{\frac{11}{100}}\right)$$

Add 50 and 1 to get 51.

$$90\times \frac{51}{50}\left(1-\frac{\frac{2}{100}}{\frac{11}{100}}\right)$$

Express 90\times \frac{51}{50} as a single fraction.

$$\frac{90\times 51}{50}\left(1-\frac{\frac{2}{100}}{\frac{11}{100}}\right)$$

Multiply 90 and 51 to get 4590.

$$\frac{4590}{50}\left(1-\frac{\frac{2}{100}}{\frac{11}{100}}\right)$$

Reduce the fraction \frac{4590}{50} to lowest terms by extracting and canceling out 10.

$$\frac{459}{5}\left(1-\frac{\frac{2}{100}}{\frac{11}{100}}\right)$$

Divide \frac{2}{100} by \frac{11}{100} by multiplying \frac{2}{100} by the reciprocal of \frac{11}{100}.

$$\frac{459}{5}\left(1-\frac{2\times 100}{100\times 11}\right)$$

Cancel out 2\times 50 in both numerator and denominator.

$$\frac{459}{5}\left(1-\frac{2}{11}\right)$$

Convert 1 to fraction \frac{11}{11}.

$$\frac{459}{5}\left(\frac{11}{11}-\frac{2}{11}\right)$$

Since \frac{11}{11} and \frac{2}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{459}{5}\times \frac{11-2}{11}$$

Subtract 2 from 11 to get 9.

$$\frac{459}{5}\times \frac{9}{11}$$

Multiply \frac{459}{5} times \frac{9}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{459\times 9}{5\times 11}$$

Do the multiplications in the fraction \frac{459\times 9}{5\times 11}.

$$\frac{4131}{55}$$

Factor

$$\frac{3 ^ {5} \cdot 17}{5 \cdot 11} = 75\frac{6}{55} = 75.10909090909091$$