Solve (3-1/4):(14/5-2)/(8-frac{2{3}):(4-5/4)}

$$\frac { ( 3 - \frac { 1 } { 4 } ) : ( \frac { 14 } { 5 } - 2 ) } { ( 8 - \frac { 2 } { 3 } ) : ( 4 - \frac { 5 } { 4 } ) }$$

Evaluate

$$\frac{165}{128}=1.2890625$$

Solution Steps

Divide \frac{3-\frac{1}{4}}{\frac{14}{5}-2} by \frac{8-\frac{2}{3}}{4-\frac{5}{4}} by multiplying \frac{3-\frac{1}{4}}{\frac{14}{5}-2} by the reciprocal of \frac{8-\frac{2}{3}}{4-\frac{5}{4}}.

$$\frac{\left(3-\frac{1}{4}\right)\left(4-\frac{5}{4}\right)}{\left(\frac{14}{5}-2\right)\left(8-\frac{2}{3}\right)}$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{\left(\frac{12}{4}-\frac{1}{4}\right)\left(4-\frac{5}{4}\right)}{\left(\frac{14}{5}-2\right)\left(8-\frac{2}{3}\right)}$$

Since \frac{12}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{12-1}{4}\left(4-\frac{5}{4}\right)}{\left(\frac{14}{5}-2\right)\left(8-\frac{2}{3}\right)}$$

Subtract 1 from 12 to get 11.

$$\frac{\frac{11}{4}\left(4-\frac{5}{4}\right)}{\left(\frac{14}{5}-2\right)\left(8-\frac{2}{3}\right)}$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{\frac{11}{4}\left(\frac{16}{4}-\frac{5}{4}\right)}{\left(\frac{14}{5}-2\right)\left(8-\frac{2}{3}\right)}$$

Since \frac{16}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{4}\times \frac{16-5}{4}}{\left(\frac{14}{5}-2\right)\left(8-\frac{2}{3}\right)}$$

Subtract 5 from 16 to get 11.

$$\frac{\frac{11}{4}\times \frac{11}{4}}{\left(\frac{14}{5}-2\right)\left(8-\frac{2}{3}\right)}$$

Multiply \frac{11}{4} times \frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{11\times 11}{4\times 4}}{\left(\frac{14}{5}-2\right)\left(8-\frac{2}{3}\right)}$$

Do the multiplications in the fraction \frac{11\times 11}{4\times 4}.

$$\frac{\frac{121}{16}}{\left(\frac{14}{5}-2\right)\left(8-\frac{2}{3}\right)}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{\frac{121}{16}}{\left(\frac{14}{5}-\frac{10}{5}\right)\left(8-\frac{2}{3}\right)}$$

Since \frac{14}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{121}{16}}{\frac{14-10}{5}\left(8-\frac{2}{3}\right)}$$

Subtract 10 from 14 to get 4.

$$\frac{\frac{121}{16}}{\frac{4}{5}\left(8-\frac{2}{3}\right)}$$

Convert 8 to fraction \frac{24}{3}.

$$\frac{\frac{121}{16}}{\frac{4}{5}\left(\frac{24}{3}-\frac{2}{3}\right)}$$

Since \frac{24}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{121}{16}}{\frac{4}{5}\times \frac{24-2}{3}}$$

Subtract 2 from 24 to get 22.

$$\frac{\frac{121}{16}}{\frac{4}{5}\times \frac{22}{3}}$$

Multiply \frac{4}{5} times \frac{22}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{121}{16}}{\frac{4\times 22}{5\times 3}}$$

Do the multiplications in the fraction \frac{4\times 22}{5\times 3}.

$$\frac{\frac{121}{16}}{\frac{88}{15}}$$

Divide \frac{121}{16} by \frac{88}{15} by multiplying \frac{121}{16} by the reciprocal of \frac{88}{15}.

$$\frac{121}{16}\times \frac{15}{88}$$

Multiply \frac{121}{16} times \frac{15}{88} by multiplying numerator times numerator and denominator times denominator.

$$\frac{121\times 15}{16\times 88}$$

Do the multiplications in the fraction \frac{121\times 15}{16\times 88}.

$$\frac{1815}{1408}$$

Reduce the fraction \frac{1815}{1408} to lowest terms by extracting and canceling out 11.

$$\frac{165}{128}$$

Factor

$$\frac{3 \cdot 5 \cdot 11}{2 ^ {7}} = 1\frac{37}{128} = 1.2890625$$