Solve {1/5-80/51[(1-7/25):27/20-frac{1}{4}]}:[frac{3}{5}-frac{25}{14}(frac{7}{30}-frac{1}{6}):frac{10}{40}]:frac{55}{9}

$$\{ \frac { 1 } { 5 } - \frac { 80 } { 51 } [ ( 1 - \frac { 7 } { 25 } ) : \frac { 27 } { 20 } - \frac { 1 } { 4 } ] \} : [ \frac { 3 } { 5 } - \frac { 25 } { 14 } ( \frac { 7 } { 30 } - \frac { 1 } { 6 } ) : \frac { 10 } { 40 } ] : \frac { 55 } { 9 }$$

Evaluate

$$-\frac{21}{65}\approx -0.323076923$$

Solution Steps

Divide \frac{\frac{1}{5}-\frac{80}{51}\left(\frac{1-\frac{7}{25}}{\frac{27}{20}}-\frac{1}{4}\right)}{\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}} by \frac{55}{9} by multiplying \frac{\frac{1}{5}-\frac{80}{51}\left(\frac{1-\frac{7}{25}}{\frac{27}{20}}-\frac{1}{4}\right)}{\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}} by the reciprocal of \frac{55}{9}.

$$\frac{\left(\frac{1}{5}-\frac{80}{51}\left(\frac{1-\frac{7}{25}}{\frac{27}{20}}-\frac{1}{4}\right)\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Convert 1 to fraction \frac{25}{25}.

$$\frac{\left(\frac{1}{5}-\frac{80}{51}\left(\frac{\frac{25}{25}-\frac{7}{25}}{\frac{27}{20}}-\frac{1}{4}\right)\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Since \frac{25}{25} and \frac{7}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{1}{5}-\frac{80}{51}\left(\frac{\frac{25-7}{25}}{\frac{27}{20}}-\frac{1}{4}\right)\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Subtract 7 from 25 to get 18.

$$\frac{\left(\frac{1}{5}-\frac{80}{51}\left(\frac{\frac{18}{25}}{\frac{27}{20}}-\frac{1}{4}\right)\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Divide \frac{18}{25} by \frac{27}{20} by multiplying \frac{18}{25} by the reciprocal of \frac{27}{20}.

$$\frac{\left(\frac{1}{5}-\frac{80}{51}\left(\frac{18}{25}\times \frac{20}{27}-\frac{1}{4}\right)\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Multiply \frac{18}{25} times \frac{20}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\frac{1}{5}-\frac{80}{51}\left(\frac{18\times 20}{25\times 27}-\frac{1}{4}\right)\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Do the multiplications in the fraction \frac{18\times 20}{25\times 27}.

$$\frac{\left(\frac{1}{5}-\frac{80}{51}\left(\frac{360}{675}-\frac{1}{4}\right)\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Reduce the fraction \frac{360}{675} to lowest terms by extracting and canceling out 45.

$$\frac{\left(\frac{1}{5}-\frac{80}{51}\left(\frac{8}{15}-\frac{1}{4}\right)\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Least common multiple of 15 and 4 is 60. Convert \frac{8}{15} and \frac{1}{4} to fractions with denominator 60.

$$\frac{\left(\frac{1}{5}-\frac{80}{51}\left(\frac{32}{60}-\frac{15}{60}\right)\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Since \frac{32}{60} and \frac{15}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{1}{5}-\frac{80}{51}\times \frac{32-15}{60}\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Subtract 15 from 32 to get 17.

$$\frac{\left(\frac{1}{5}-\frac{80}{51}\times \frac{17}{60}\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Multiply \frac{80}{51} times \frac{17}{60} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\frac{1}{5}-\frac{80\times 17}{51\times 60}\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Do the multiplications in the fraction \frac{80\times 17}{51\times 60}.

$$\frac{\left(\frac{1}{5}-\frac{1360}{3060}\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Reduce the fraction \frac{1360}{3060} to lowest terms by extracting and canceling out 340.

$$\frac{\left(\frac{1}{5}-\frac{4}{9}\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Least common multiple of 5 and 9 is 45. Convert \frac{1}{5} and \frac{4}{9} to fractions with denominator 45.

$$\frac{\left(\frac{9}{45}-\frac{20}{45}\right)\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Since \frac{9}{45} and \frac{20}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-20}{45}\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Subtract 20 from 9 to get -11.

$$\frac{-\frac{11}{45}\times 9}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Express -\frac{11}{45}\times 9 as a single fraction.

$$\frac{\frac{-11\times 9}{45}}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Multiply -11 and 9 to get -99.

$$\frac{\frac{-99}{45}}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Reduce the fraction \frac{-99}{45} to lowest terms by extracting and canceling out 9.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{1}{6}\right)}{\frac{10}{40}}\right)\times 55}$$

Least common multiple of 30 and 6 is 30. Convert \frac{7}{30} and \frac{1}{6} to fractions with denominator 30.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{\frac{25}{14}\left(\frac{7}{30}-\frac{5}{30}\right)}{\frac{10}{40}}\right)\times 55}$$

Since \frac{7}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{\frac{25}{14}\times \frac{7-5}{30}}{\frac{10}{40}}\right)\times 55}$$

Subtract 5 from 7 to get 2.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{\frac{25}{14}\times \frac{2}{30}}{\frac{10}{40}}\right)\times 55}$$

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{\frac{25}{14}\times \frac{1}{15}}{\frac{10}{40}}\right)\times 55}$$

Multiply \frac{25}{14} times \frac{1}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{\frac{25\times 1}{14\times 15}}{\frac{10}{40}}\right)\times 55}$$

Do the multiplications in the fraction \frac{25\times 1}{14\times 15}.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{\frac{25}{210}}{\frac{10}{40}}\right)\times 55}$$

Reduce the fraction \frac{25}{210} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{\frac{5}{42}}{\frac{10}{40}}\right)\times 55}$$

Reduce the fraction \frac{10}{40} to lowest terms by extracting and canceling out 10.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{\frac{5}{42}}{\frac{1}{4}}\right)\times 55}$$

Divide \frac{5}{42} by \frac{1}{4} by multiplying \frac{5}{42} by the reciprocal of \frac{1}{4}.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{5}{42}\times 4\right)\times 55}$$

Express \frac{5}{42}\times 4 as a single fraction.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{5\times 4}{42}\right)\times 55}$$

Multiply 5 and 4 to get 20.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{20}{42}\right)\times 55}$$

Reduce the fraction \frac{20}{42} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{11}{5}}{\left(\frac{3}{5}-\frac{10}{21}\right)\times 55}$$

Least common multiple of 5 and 21 is 105. Convert \frac{3}{5} and \frac{10}{21} to fractions with denominator 105.

$$\frac{-\frac{11}{5}}{\left(\frac{63}{105}-\frac{50}{105}\right)\times 55}$$

Since \frac{63}{105} and \frac{50}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{11}{5}}{\frac{63-50}{105}\times 55}$$

Subtract 50 from 63 to get 13.

$$\frac{-\frac{11}{5}}{\frac{13}{105}\times 55}$$

Express \frac{13}{105}\times 55 as a single fraction.

$$\frac{-\frac{11}{5}}{\frac{13\times 55}{105}}$$

Multiply 13 and 55 to get 715.

$$\frac{-\frac{11}{5}}{\frac{715}{105}}$$

Reduce the fraction \frac{715}{105} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{11}{5}}{\frac{143}{21}}$$

Divide -\frac{11}{5} by \frac{143}{21} by multiplying -\frac{11}{5} by the reciprocal of \frac{143}{21}.

$$-\frac{11}{5}\times \frac{21}{143}$$

Multiply -\frac{11}{5} times \frac{21}{143} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-11\times 21}{5\times 143}$$

Do the multiplications in the fraction \frac{-11\times 21}{5\times 143}.

$$\frac{-231}{715}$$

Reduce the fraction \frac{-231}{715} to lowest terms by extracting and canceling out 11.

$$-\frac{21}{65}$$

Factor

$$-\frac{21}{65} = -0.3230769230769231$$