Solve (5000div2000*15%*100div500)div(1-5000div2000*15%*100div500)

$$(5000 \div 2000 \times 15 \% \times 100 \div 500) \div (1-5000 \div 2000 \times 15 \% \times 100 \div 500)$$

Evaluate

$$\frac{3}{37}\approx 0.081081081$$

Solution Steps

Reduce the fraction \frac{5000}{2000} to lowest terms by extracting and canceling out 1000.

$$\frac{\frac{\frac{5}{2}\times \frac{15}{100}\times 100}{500}}{1-\frac{\frac{5000}{2000}\times \frac{15}{100}\times 100}{500}}$$

Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{\frac{5}{2}\times \frac{3}{20}\times 100}{500}}{1-\frac{\frac{5000}{2000}\times \frac{15}{100}\times 100}{500}}$$

Multiply \frac{5}{2} times \frac{3}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{5\times 3}{2\times 20}\times 100}{500}}{1-\frac{\frac{5000}{2000}\times \frac{15}{100}\times 100}{500}}$$

Do the multiplications in the fraction \frac{5\times 3}{2\times 20}.

$$\frac{\frac{\frac{15}{40}\times 100}{500}}{1-\frac{\frac{5000}{2000}\times \frac{15}{100}\times 100}{500}}$$

Reduce the fraction \frac{15}{40} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{\frac{3}{8}\times 100}{500}}{1-\frac{\frac{5000}{2000}\times \frac{15}{100}\times 100}{500}}$$

Express \frac{3}{8}\times 100 as a single fraction.

$$\frac{\frac{\frac{3\times 100}{8}}{500}}{1-\frac{\frac{5000}{2000}\times \frac{15}{100}\times 100}{500}}$$

Multiply 3 and 100 to get 300.

$$\frac{\frac{\frac{300}{8}}{500}}{1-\frac{\frac{5000}{2000}\times \frac{15}{100}\times 100}{500}}$$

Reduce the fraction \frac{300}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{\frac{75}{2}}{500}}{1-\frac{\frac{5000}{2000}\times \frac{15}{100}\times 100}{500}}$$

Express \frac{\frac{75}{2}}{500} as a single fraction.

$$\frac{\frac{75}{2\times 500}}{1-\frac{\frac{5000}{2000}\times \frac{15}{100}\times 100}{500}}$$

Multiply 2 and 500 to get 1000.

$$\frac{\frac{75}{1000}}{1-\frac{\frac{5000}{2000}\times \frac{15}{100}\times 100}{500}}$$

Reduce the fraction \frac{75}{1000} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{3}{40}}{1-\frac{\frac{5000}{2000}\times \frac{15}{100}\times 100}{500}}$$

Reduce the fraction \frac{5000}{2000} to lowest terms by extracting and canceling out 1000.

$$\frac{\frac{3}{40}}{1-\frac{\frac{5}{2}\times \frac{15}{100}\times 100}{500}}$$

Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{3}{40}}{1-\frac{\frac{5}{2}\times \frac{3}{20}\times 100}{500}}$$

Multiply \frac{5}{2} times \frac{3}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{40}}{1-\frac{\frac{5\times 3}{2\times 20}\times 100}{500}}$$

Do the multiplications in the fraction \frac{5\times 3}{2\times 20}.

$$\frac{\frac{3}{40}}{1-\frac{\frac{15}{40}\times 100}{500}}$$

Reduce the fraction \frac{15}{40} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{3}{40}}{1-\frac{\frac{3}{8}\times 100}{500}}$$

Express \frac{3}{8}\times 100 as a single fraction.

$$\frac{\frac{3}{40}}{1-\frac{\frac{3\times 100}{8}}{500}}$$

Multiply 3 and 100 to get 300.

$$\frac{\frac{3}{40}}{1-\frac{\frac{300}{8}}{500}}$$

Reduce the fraction \frac{300}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{3}{40}}{1-\frac{\frac{75}{2}}{500}}$$

Express \frac{\frac{75}{2}}{500} as a single fraction.

$$\frac{\frac{3}{40}}{1-\frac{75}{2\times 500}}$$

Multiply 2 and 500 to get 1000.

$$\frac{\frac{3}{40}}{1-\frac{75}{1000}}$$

Reduce the fraction \frac{75}{1000} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{3}{40}}{1-\frac{3}{40}}$$

Convert 1 to fraction \frac{40}{40}.

$$\frac{\frac{3}{40}}{\frac{40}{40}-\frac{3}{40}}$$

Since \frac{40}{40} and \frac{3}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{40}}{\frac{40-3}{40}}$$

Subtract 3 from 40 to get 37.

$$\frac{\frac{3}{40}}{\frac{37}{40}}$$

Divide \frac{3}{40} by \frac{37}{40} by multiplying \frac{3}{40} by the reciprocal of \frac{37}{40}.

$$\frac{3}{40}\times \frac{40}{37}$$

Multiply \frac{3}{40} times \frac{40}{37} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 40}{40\times 37}$$

Cancel out 40 in both numerator and denominator.

$$\frac{3}{37}$$

Factor

$$\frac{3}{37} = 0.08108108108108109$$