Solve (3/4-2/5)/(2-frac{1{5})}

$$\frac { ( \frac { 3 } { 4 } - \frac { 2 } { 5 } ) } { ( 2 - \frac { 1 } { 5 } ) }$$

Evaluate

$$\frac{7}{36}\approx 0.194444444$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{2}{5} to fractions with denominator 20.

$$\frac{\frac{15}{20}-\frac{8}{20}}{2-\frac{1}{5}}$$

Since \frac{15}{20} and \frac{8}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-8}{20}}{2-\frac{1}{5}}$$

Subtract 8 from 15 to get 7.

$$\frac{\frac{7}{20}}{2-\frac{1}{5}}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{\frac{7}{20}}{\frac{10}{5}-\frac{1}{5}}$$

Since \frac{10}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{20}}{\frac{10-1}{5}}$$

Subtract 1 from 10 to get 9.

$$\frac{\frac{7}{20}}{\frac{9}{5}}$$

Divide \frac{7}{20} by \frac{9}{5} by multiplying \frac{7}{20} by the reciprocal of \frac{9}{5}.

$$\frac{7}{20}\times \frac{5}{9}$$

Multiply \frac{7}{20} times \frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 5}{20\times 9}$$

Do the multiplications in the fraction \frac{7\times 5}{20\times 9}.

$$\frac{35}{180}$$

Reduce the fraction \frac{35}{180} to lowest terms by extracting and canceling out 5.

$$\frac{7}{36}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3 ^ {2}} = 0.19444444444444445$$