Solve 1/4+2/5/frac{3{5}-1/2}=

$$\frac { \frac { 1 } { 4 } + \frac { 2 } { 5 } } { \frac { 3 } { 5 } - \frac { 1 } { 2 } } =$$

Evaluate

$$\frac{13}{2}=6.5$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{2}{5} to fractions with denominator 20.

$$\frac{\frac{5}{20}+\frac{8}{20}}{\frac{3}{5}-\frac{1}{2}}$$

Since \frac{5}{20} and \frac{8}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+8}{20}}{\frac{3}{5}-\frac{1}{2}}$$

Add 5 and 8 to get 13.

$$\frac{\frac{13}{20}}{\frac{3}{5}-\frac{1}{2}}$$

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

$$\frac{\frac{13}{20}}{\frac{6}{10}-\frac{5}{10}}$$

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

$$\frac{\frac{13}{20}}{\frac{6-5}{10}}$$

Subtract 5 from 6 to get 1.

$$\frac{\frac{13}{20}}{\frac{1}{10}}$$

Divide \frac{13}{20} by \frac{1}{10} by multiplying \frac{13}{20} by the reciprocal of \frac{1}{10}.

$$\frac{13}{20}\times 10$$

Express \frac{13}{20}\times 10 as a single fraction.

$$\frac{13\times 10}{20}$$

Multiply 13 and 10 to get 130.

$$\frac{130}{20}$$

Reduce the fraction \frac{130}{20} to lowest terms by extracting and canceling out 10.

$$\frac{13}{2}$$

Factor

$$\frac{13}{2} = 6\frac{1}{2} = 6.5$$