Solve 3/4+5/6*3/5/frac{1{2}-frac{2}{7}*frac{7}{5}}

$$\frac { \frac { 3 } { 4 } + \frac { 5 } { 6 } \times \frac { 3 } { 5 } } { \frac { 1 } { 2 } - \frac { 2 } { 7 } \times \frac { 7 } { 5 } }$$

Evaluate

$$\frac{25}{2}=12.5$$

Solution Steps

Multiply \frac{5}{6} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{4}+\frac{5\times 3}{6\times 5}}{\frac{1}{2}-\frac{2}{7}\times \frac{7}{5}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{3}{4}+\frac{3}{6}}{\frac{1}{2}-\frac{2}{7}\times \frac{7}{5}}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{3}{4}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{7}\times \frac{7}{5}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{\frac{3}{4}+\frac{2}{4}}{\frac{1}{2}-\frac{2}{7}\times \frac{7}{5}}$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+2}{4}}{\frac{1}{2}-\frac{2}{7}\times \frac{7}{5}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{5}{4}}{\frac{1}{2}-\frac{2}{7}\times \frac{7}{5}}$$

Multiply \frac{2}{7} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{4}}{\frac{1}{2}-\frac{2\times 7}{7\times 5}}$$

Cancel out 7 in both numerator and denominator.

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

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

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

Since \frac{5}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 5 to get 1.

$$\frac{\frac{5}{4}}{\frac{1}{10}}$$

Divide \frac{5}{4} by \frac{1}{10} by multiplying \frac{5}{4} by the reciprocal of \frac{1}{10}.

$$\frac{5}{4}\times 10$$

Express \frac{5}{4}\times 10 as a single fraction.

$$\frac{5\times 10}{4}$$

Multiply 5 and 10 to get 50.

$$\frac{50}{4}$$

Reduce the fraction \frac{50}{4} to lowest terms by extracting and canceling out 2.

$$\frac{25}{2}$$

Factor

$$\frac{5 ^ {2}}{2} = 12\frac{1}{2} = 12.5$$