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

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

Evaluate

$$\frac{75}{4}=18.75$$

Solution Steps

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

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

Cancel out 5 in both numerator and denominator.

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

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

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

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

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

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

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

Add 3 and 2 to get 5.

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

Multiply \frac{2}{3} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 7}{3\times 5}.

$$\frac{\frac{5}{4}}{1-\frac{14}{15}}$$

Convert 1 to fraction \frac{15}{15}.

$$\frac{\frac{5}{4}}{\frac{15}{15}-\frac{14}{15}}$$

Since \frac{15}{15} and \frac{14}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{4}}{\frac{15-14}{15}}$$

Subtract 14 from 15 to get 1.

$$\frac{\frac{5}{4}}{\frac{1}{15}}$$

Divide \frac{5}{4} by \frac{1}{15} by multiplying \frac{5}{4} by the reciprocal of \frac{1}{15}.

$$\frac{5}{4}\times 15$$

Express \frac{5}{4}\times 15 as a single fraction.

$$\frac{5\times 15}{4}$$

Multiply 5 and 15 to get 75.

$$\frac{75}{4}$$

Factor

$$\frac{3 \cdot 5 ^ {2}}{2 ^ {2}} = 18\frac{3}{4} = 18.75$$