Solve 2/3-2/5/frac{3{5}-1/2}

$$\frac { \frac { 2 } { 3 } - \frac { 2 } { 5 } } { \frac { 3 } { 5 } - \frac { 1 } { 2 } }$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{\frac{10}{15}-\frac{6}{15}}{\frac{3}{5}-\frac{1}{2}}$$

Since \frac{10}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-6}{15}}{\frac{3}{5}-\frac{1}{2}}$$

Subtract 6 from 10 to get 4.

$$\frac{\frac{4}{15}}{\frac{3}{5}-\frac{1}{2}}$$

Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{\frac{4}{15}}{\frac{6}{10}-\frac{5}{10}}$$

Since \frac{6}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{15}}{\frac{6-5}{10}}$$

Subtract 5 from 6 to get 1.

$$\frac{\frac{4}{15}}{\frac{1}{10}}$$

Divide \frac{4}{15} by \frac{1}{10} by multiplying \frac{4}{15} by the reciprocal of \frac{1}{10}.

$$\frac{4}{15}\times 10$$

Express \frac{4}{15}\times 10 as a single fraction.

$$\frac{4\times 10}{15}$$

Multiply 4 and 10 to get 40.

$$\frac{40}{15}$$

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

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$