Solve ((-2/5+3/2):(+1/2+3/5)*(+frac{1}{4}+frac{1}{1}+frac{7}{20})]:[(-frac{2}{5}+frac{3}{4})*(+frac{1}{2}+frac{11}{10})]=

$$( ( - \frac { 2 } { 5 } + \frac { 3 } { 2 } ) : ( + \frac { 1 } { 2 } + \frac { 3 } { 5 } ) \cdot ( + \frac { 1 } { 4 } + \frac { 1 } { 1 } + \frac { 7 } { 20 } ) ] : [ ( - \frac { 2 } { 5 } + \frac { 3 } { 4 } ) \cdot ( + \frac { 1 } { 2 } + \frac { 11 } { 10 } ) ] =$$

Evaluate

$$\frac{20}{7}\approx 2.857142857$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{\frac{-\frac{2}{5}+\frac{3}{2}}{\frac{1}{2}+\frac{3}{5}}\left(\frac{1}{4}+1+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Least common multiple of 5 and 2 is 10. Convert -\frac{2}{5} and \frac{3}{2} to fractions with denominator 10.

$$\frac{\frac{-\frac{4}{10}+\frac{15}{10}}{\frac{1}{2}+\frac{3}{5}}\left(\frac{1}{4}+1+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Since -\frac{4}{10} and \frac{15}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{-4+15}{10}}{\frac{1}{2}+\frac{3}{5}}\left(\frac{1}{4}+1+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Add -4 and 15 to get 11.

$$\frac{\frac{\frac{11}{10}}{\frac{1}{2}+\frac{3}{5}}\left(\frac{1}{4}+1+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{3}{5} to fractions with denominator 10.

$$\frac{\frac{\frac{11}{10}}{\frac{5}{10}+\frac{6}{10}}\left(\frac{1}{4}+1+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Since \frac{5}{10} and \frac{6}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{11}{10}}{\frac{5+6}{10}}\left(\frac{1}{4}+1+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Add 5 and 6 to get 11.

$$\frac{\frac{\frac{11}{10}}{\frac{11}{10}}\left(\frac{1}{4}+1+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Divide \frac{11}{10} by \frac{11}{10} to get 1.

$$\frac{1\left(\frac{1}{4}+1+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{1\left(\frac{1}{4}+\frac{4}{4}+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Since \frac{1}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{1\left(\frac{1+4}{4}+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Add 1 and 4 to get 5.

$$\frac{1\left(\frac{5}{4}+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Least common multiple of 4 and 20 is 20. Convert \frac{5}{4} and \frac{7}{20} to fractions with denominator 20.

$$\frac{1\left(\frac{25}{20}+\frac{7}{20}\right)}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Since \frac{25}{20} and \frac{7}{20} have the same denominator, add them by adding their numerators.

$$\frac{1\times \frac{25+7}{20}}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Add 25 and 7 to get 32.

$$\frac{1\times \frac{32}{20}}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Reduce the fraction \frac{32}{20} to lowest terms by extracting and canceling out 4.

$$\frac{1\times \frac{8}{5}}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Multiply 1 and \frac{8}{5} to get \frac{8}{5}.

$$\frac{\frac{8}{5}}{\left(-\frac{2}{5}+\frac{3}{4}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Least common multiple of 5 and 4 is 20. Convert -\frac{2}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{\frac{8}{5}}{\left(-\frac{8}{20}+\frac{15}{20}\right)\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Since -\frac{8}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8}{5}}{\frac{-8+15}{20}\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Add -8 and 15 to get 7.

$$\frac{\frac{8}{5}}{\frac{7}{20}\left(\frac{1}{2}+\frac{11}{10}\right)}$$

Least common multiple of 2 and 10 is 10. Convert \frac{1}{2} and \frac{11}{10} to fractions with denominator 10.

$$\frac{\frac{8}{5}}{\frac{7}{20}\left(\frac{5}{10}+\frac{11}{10}\right)}$$

Since \frac{5}{10} and \frac{11}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8}{5}}{\frac{7}{20}\times \frac{5+11}{10}}$$

Add 5 and 11 to get 16.

$$\frac{\frac{8}{5}}{\frac{7}{20}\times \frac{16}{10}}$$

Reduce the fraction \frac{16}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{8}{5}}{\frac{7}{20}\times \frac{8}{5}}$$

Multiply \frac{7}{20} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{8}{5}}{\frac{7\times 8}{20\times 5}}$$

Do the multiplications in the fraction \frac{7\times 8}{20\times 5}.

$$\frac{\frac{8}{5}}{\frac{56}{100}}$$

Reduce the fraction \frac{56}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{8}{5}}{\frac{14}{25}}$$

Divide \frac{8}{5} by \frac{14}{25} by multiplying \frac{8}{5} by the reciprocal of \frac{14}{25}.

$$\frac{8}{5}\times \frac{25}{14}$$

Multiply \frac{8}{5} times \frac{25}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 25}{5\times 14}$$

Do the multiplications in the fraction \frac{8\times 25}{5\times 14}.

$$\frac{200}{70}$$

Reduce the fraction \frac{200}{70} to lowest terms by extracting and canceling out 10.

$$\frac{20}{7}$$

Factor

$$\frac{2 ^ {2} \cdot 5}{7} = 2\frac{6}{7} = 2.857142857142857$$