Solve (13/4*7/2)div(2/5*(2-3/4))

$$( \frac { 13 } { 4 } \times \frac { 7 } { 2 } ) \div ( \frac { 2 } { 5 } \times ( 2 - \frac { 3 } { 4 } ) )$$

Evaluate

$$\frac{91}{4}=22.75$$

Solution Steps

Multiply \frac{13}{4} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13\times 7}{4\times 2}}{\frac{2}{5}\left(2-\frac{3}{4}\right)}$$

Do the multiplications in the fraction \frac{13\times 7}{4\times 2}.

$$\frac{\frac{91}{8}}{\frac{2}{5}\left(2-\frac{3}{4}\right)}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{\frac{91}{8}}{\frac{2}{5}\left(\frac{8}{4}-\frac{3}{4}\right)}$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{91}{8}}{\frac{2}{5}\times \frac{8-3}{4}}$$

Subtract 3 from 8 to get 5.

$$\frac{\frac{91}{8}}{\frac{2}{5}\times \frac{5}{4}}$$

Multiply \frac{2}{5} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{91}{8}}{\frac{2\times 5}{5\times 4}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{91}{8}}{\frac{2}{4}}$$

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

$$\frac{\frac{91}{8}}{\frac{1}{2}}$$

Divide \frac{91}{8} by \frac{1}{2} by multiplying \frac{91}{8} by the reciprocal of \frac{1}{2}.

$$\frac{91}{8}\times 2$$

Express \frac{91}{8}\times 2 as a single fraction.

$$\frac{91\times 2}{8}$$

Multiply 91 and 2 to get 182.

$$\frac{182}{8}$$

Reduce the fraction \frac{182}{8} to lowest terms by extracting and canceling out 2.

$$\frac{91}{4}$$

Factor

$$\frac{7 \cdot 13}{2 ^ {2}} = 22\frac{3}{4} = 22.75$$