Solve (1div(60%-15%)*5%)div(1-1div(60%-15%)*5%*100%)

$$(1 \div (60 \% -15 \% ) \times 5 \% ) \div (1-1 \div (60 \% -15 \% ) \times 5 \% \times 100 \% )$$

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

Divide 100 by 100 to get 1.

$$\frac{\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}}{1-\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

Reduce the fraction \frac{60}{100} to lowest terms by extracting and canceling out 20.

$$\frac{\frac{1}{\frac{3}{5}-\frac{15}{100}}\times \frac{5}{100}}{1-\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

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

$$\frac{\frac{1}{\frac{3}{5}-\frac{3}{20}}\times \frac{5}{100}}{1-\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

Least common multiple of 5 and 20 is 20. Convert \frac{3}{5} and \frac{3}{20} to fractions with denominator 20.

$$\frac{\frac{1}{\frac{12}{20}-\frac{3}{20}}\times \frac{5}{100}}{1-\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

Since \frac{12}{20} and \frac{3}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{\frac{12-3}{20}}\times \frac{5}{100}}{1-\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

Subtract 3 from 12 to get 9.

$$\frac{\frac{1}{\frac{9}{20}}\times \frac{5}{100}}{1-\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

Divide 1 by \frac{9}{20} by multiplying 1 by the reciprocal of \frac{9}{20}.

$$\frac{1\times \frac{20}{9}\times \frac{5}{100}}{1-\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

Multiply 1 and \frac{20}{9} to get \frac{20}{9}.

$$\frac{\frac{20}{9}\times \frac{5}{100}}{1-\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

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

$$\frac{\frac{20}{9}\times \frac{1}{20}}{1-\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

Multiply \frac{20}{9} times \frac{1}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{20\times 1}{9\times 20}}{1-\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

Cancel out 20 in both numerator and denominator.

$$\frac{\frac{1}{9}}{1-\frac{1}{\frac{60}{100}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

Reduce the fraction \frac{60}{100} to lowest terms by extracting and canceling out 20.

$$\frac{\frac{1}{9}}{1-\frac{1}{\frac{3}{5}-\frac{15}{100}}\times \frac{5}{100}\times 1}$$

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

$$\frac{\frac{1}{9}}{1-\frac{1}{\frac{3}{5}-\frac{3}{20}}\times \frac{5}{100}\times 1}$$

Least common multiple of 5 and 20 is 20. Convert \frac{3}{5} and \frac{3}{20} to fractions with denominator 20.

$$\frac{\frac{1}{9}}{1-\frac{1}{\frac{12}{20}-\frac{3}{20}}\times \frac{5}{100}\times 1}$$

Since \frac{12}{20} and \frac{3}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{9}}{1-\frac{1}{\frac{12-3}{20}}\times \frac{5}{100}\times 1}$$

Subtract 3 from 12 to get 9.

$$\frac{\frac{1}{9}}{1-\frac{1}{\frac{9}{20}}\times \frac{5}{100}\times 1}$$

Divide 1 by \frac{9}{20} by multiplying 1 by the reciprocal of \frac{9}{20}.

$$\frac{\frac{1}{9}}{1-1\times \frac{20}{9}\times \frac{5}{100}\times 1}$$

Multiply 1 and \frac{20}{9} to get \frac{20}{9}.

$$\frac{\frac{1}{9}}{1-\frac{20}{9}\times \frac{5}{100}\times 1}$$

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

$$\frac{\frac{1}{9}}{1-\frac{20}{9}\times \frac{1}{20}\times 1}$$

Multiply \frac{20}{9} times \frac{1}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{9}}{1-\frac{20\times 1}{9\times 20}\times 1}$$

Cancel out 20 in both numerator and denominator.

$$\frac{\frac{1}{9}}{1-\frac{1}{9}\times 1}$$

Multiply \frac{1}{9} and 1 to get \frac{1}{9}.

$$\frac{\frac{1}{9}}{1-\frac{1}{9}}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{\frac{1}{9}}{\frac{9}{9}-\frac{1}{9}}$$

Since \frac{9}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{9}}{\frac{9-1}{9}}$$

Subtract 1 from 9 to get 8.

$$\frac{\frac{1}{9}}{\frac{8}{9}}$$

Divide \frac{1}{9} by \frac{8}{9} by multiplying \frac{1}{9} by the reciprocal of \frac{8}{9}.

$$\frac{1}{9}\times \frac{9}{8}$$

Multiply \frac{1}{9} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 9}{9\times 8}$$

Cancel out 9 in both numerator and denominator.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$