Solve (3/25-1/50)div(9/10-9/20)

$$( \frac { 3 } { 25 } - \frac { 1 } { 50 } ) \div ( \frac { 9 } { 10 } - \frac { 9 } { 20 } )$$

Evaluate

$$\frac{2}{9}\approx 0.222222222$$

Solution Steps

Least common multiple of 25 and 50 is 50. Convert \frac{3}{25} and \frac{1}{50} to fractions with denominator 50.

$$\frac{\frac{6}{50}-\frac{1}{50}}{\frac{9}{10}-\frac{9}{20}}$$

Since \frac{6}{50} and \frac{1}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6-1}{50}}{\frac{9}{10}-\frac{9}{20}}$$

Subtract 1 from 6 to get 5.

$$\frac{\frac{5}{50}}{\frac{9}{10}-\frac{9}{20}}$$

Reduce the fraction \frac{5}{50} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{1}{10}}{\frac{9}{10}-\frac{9}{20}}$$

Least common multiple of 10 and 20 is 20. Convert \frac{9}{10} and \frac{9}{20} to fractions with denominator 20.

$$\frac{\frac{1}{10}}{\frac{18}{20}-\frac{9}{20}}$$

Since \frac{18}{20} and \frac{9}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{10}}{\frac{18-9}{20}}$$

Subtract 9 from 18 to get 9.

$$\frac{\frac{1}{10}}{\frac{9}{20}}$$

Divide \frac{1}{10} by \frac{9}{20} by multiplying \frac{1}{10} by the reciprocal of \frac{9}{20}.

$$\frac{1}{10}\times \frac{20}{9}$$

Multiply \frac{1}{10} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 20}{10\times 9}$$

Do the multiplications in the fraction \frac{1\times 20}{10\times 9}.

$$\frac{20}{90}$$

Reduce the fraction \frac{20}{90} to lowest terms by extracting and canceling out 10.

$$\frac{2}{9}$$

Factor

$$\frac{2}{3 ^ {2}} = 0.2222222222222222$$