Solve {l}{2-2/5/frac{4{5}}+3-1/3/frac{4{frac{4}{3}}}{frac{4}{3}}*(frac{7}{20}*frac{11}{2})}{frac{4-frac{1}{4}}{frac{1}{2}}+frac{5-frac{1}{5}}{24}}{frac{2*5-2}{5}+frac{3*3-1}{3}}

$$\left. \begin{array} { l } { \frac { 2 - \frac { 2 } { 5 } } { \frac { 4 } { 5 } } + \frac { 3 - \frac { 1 } { 3 } } { \frac { 4 } { \frac { 4 } { 3 } } } { \frac { 4 } { 3 } } \times ( \frac { 7 } { 20 } \times \frac { 11 } { 2 } ) } \\ { \frac { 4 - \frac { 1 } { 4 } } { \frac { 1 } { 2 } } + \frac { 5 - \frac { 1 } { 5 } } { 24 } } \\ { \frac { 2 \times 5 - 2 } { 5 } + \frac { 3 \times 3 - 1 } { 3 } } \end{array} \right.$$

Sort

$$\frac{64}{15},\frac{578}{135},\frac{77}{10}$$

Solution Steps

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

$$sort(\frac{\frac{10}{5}-\frac{2}{5}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{\frac{4}{3}}}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Since \frac{10}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{\frac{10-2}{5}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{\frac{4}{3}}}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Subtract 2 from 10 to get 8.

$$sort(\frac{\frac{8}{5}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{\frac{4}{3}}}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Divide \frac{8}{5} by \frac{4}{5} by multiplying \frac{8}{5} by the reciprocal of \frac{4}{5}.

$$sort(\frac{8}{5}\times \frac{5}{4}+\frac{3-\frac{1}{3}}{\frac{4}{\frac{4}{3}}}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Multiply \frac{8}{5} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{8\times 5}{5\times 4}+\frac{3-\frac{1}{3}}{\frac{4}{\frac{4}{3}}}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Cancel out 5 in both numerator and denominator.

$$sort(\frac{8}{4}+\frac{3-\frac{1}{3}}{\frac{4}{\frac{4}{3}}}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Divide 8 by 4 to get 2.

$$sort(2+\frac{3-\frac{1}{3}}{\frac{4}{\frac{4}{3}}}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Convert 3 to fraction \frac{9}{3}.

$$sort(2+\frac{\frac{9}{3}-\frac{1}{3}}{\frac{4}{\frac{4}{3}}}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$sort(2+\frac{\frac{9-1}{3}}{\frac{4}{\frac{4}{3}}}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Subtract 1 from 9 to get 8.

$$sort(2+\frac{\frac{8}{3}}{\frac{4}{\frac{4}{3}}}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Divide 4 by \frac{4}{3} by multiplying 4 by the reciprocal of \frac{4}{3}.

$$sort(2+\frac{\frac{8}{3}}{4\times \frac{3}{4}}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Cancel out 4 and 4.

$$sort(2+\frac{\frac{8}{3}}{3}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Express \frac{\frac{8}{3}}{3} as a single fraction.

$$sort(2+\frac{8}{3\times 3}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Multiply 3 and 3 to get 9.

$$sort(2+\frac{8}{9}\times \frac{4}{3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Multiply \frac{8}{9} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$sort(2+\frac{8\times 4}{9\times 3}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Do the multiplications in the fraction \frac{8\times 4}{9\times 3}.

$$sort(2+\frac{32}{27}\times \frac{7}{20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Multiply \frac{32}{27} times \frac{7}{20} by multiplying numerator times numerator and denominator times denominator.

$$sort(2+\frac{32\times 7}{27\times 20}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Do the multiplications in the fraction \frac{32\times 7}{27\times 20}.

$$sort(2+\frac{224}{540}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Reduce the fraction \frac{224}{540} to lowest terms by extracting and canceling out 4.

$$sort(2+\frac{56}{135}\times \frac{11}{2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Multiply \frac{56}{135} times \frac{11}{2} by multiplying numerator times numerator and denominator times denominator.

$$sort(2+\frac{56\times 11}{135\times 2},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Do the multiplications in the fraction \frac{56\times 11}{135\times 2}.

$$sort(2+\frac{616}{270},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Reduce the fraction \frac{616}{270} to lowest terms by extracting and canceling out 2.

$$sort(2+\frac{308}{135},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Convert 2 to fraction \frac{270}{135}.

$$sort(\frac{270}{135}+\frac{308}{135},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Since \frac{270}{135} and \frac{308}{135} have the same denominator, add them by adding their numerators.

$$sort(\frac{270+308}{135},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Add 270 and 308 to get 578.

$$sort(\frac{578}{135},\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

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

$$sort(\frac{578}{135},\frac{\frac{16}{4}-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Since \frac{16}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{578}{135},\frac{\frac{16-1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Subtract 1 from 16 to get 15.

$$sort(\frac{578}{135},\frac{\frac{15}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Divide \frac{15}{4} by \frac{1}{2} by multiplying \frac{15}{4} by the reciprocal of \frac{1}{2}.

$$sort(\frac{578}{135},\frac{15}{4}\times 2+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Express \frac{15}{4}\times 2 as a single fraction.

$$sort(\frac{578}{135},\frac{15\times 2}{4}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Multiply 15 and 2 to get 30.

$$sort(\frac{578}{135},\frac{30}{4}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$sort(\frac{578}{135},\frac{15}{2}+\frac{5-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Convert 5 to fraction \frac{25}{5}.

$$sort(\frac{578}{135},\frac{15}{2}+\frac{\frac{25}{5}-\frac{1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Since \frac{25}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{578}{135},\frac{15}{2}+\frac{\frac{25-1}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Subtract 1 from 25 to get 24.

$$sort(\frac{578}{135},\frac{15}{2}+\frac{\frac{24}{5}}{24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Express \frac{\frac{24}{5}}{24} as a single fraction.

$$sort(\frac{578}{135},\frac{15}{2}+\frac{24}{5\times 24},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Cancel out 24 in both numerator and denominator.

$$sort(\frac{578}{135},\frac{15}{2}+\frac{1}{5},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Least common multiple of 2 and 5 is 10. Convert \frac{15}{2} and \frac{1}{5} to fractions with denominator 10.

$$sort(\frac{578}{135},\frac{75}{10}+\frac{2}{10},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Since \frac{75}{10} and \frac{2}{10} have the same denominator, add them by adding their numerators.

$$sort(\frac{578}{135},\frac{75+2}{10},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Add 75 and 2 to get 77.

$$sort(\frac{578}{135},\frac{77}{10},\frac{2\times 5-2}{5}+\frac{3\times 3-1}{3})$$

Multiply 2 and 5 to get 10.

$$sort(\frac{578}{135},\frac{77}{10},\frac{10-2}{5}+\frac{3\times 3-1}{3})$$

Subtract 2 from 10 to get 8.

$$sort(\frac{578}{135},\frac{77}{10},\frac{8}{5}+\frac{3\times 3-1}{3})$$

Multiply 3 and 3 to get 9.

$$sort(\frac{578}{135},\frac{77}{10},\frac{8}{5}+\frac{9-1}{3})$$

Subtract 1 from 9 to get 8.

$$sort(\frac{578}{135},\frac{77}{10},\frac{8}{5}+\frac{8}{3})$$

Least common multiple of 5 and 3 is 15. Convert \frac{8}{5} and \frac{8}{3} to fractions with denominator 15.

$$sort(\frac{578}{135},\frac{77}{10},\frac{24}{15}+\frac{40}{15})$$

Since \frac{24}{15} and \frac{40}{15} have the same denominator, add them by adding their numerators.

$$sort(\frac{578}{135},\frac{77}{10},\frac{24+40}{15})$$

Add 24 and 40 to get 64.

$$sort(\frac{578}{135},\frac{77}{10},\frac{64}{15})$$

Least common denominator of the numbers in the list \frac{578}{135},\frac{77}{10},\frac{64}{15} is 270. Convert numbers in the list to fractions with denominator 270.

$$\frac{1156}{270},\frac{2079}{270},\frac{1152}{270}$$

To sort the list, start from a single element \frac{1156}{270}.

$$\frac{1156}{270}$$

Insert \frac{2079}{270} to the appropriate location in the new list.

$$\frac{1156}{270},\frac{2079}{270}$$

Insert \frac{1152}{270} to the appropriate location in the new list.

$$\frac{1152}{270},\frac{1156}{270},\frac{2079}{270}$$

Replace the obtained fractions with the initial values.

$$\frac{64}{15},\frac{578}{135},\frac{77}{10}$$

Evaluate

$$\frac{578}{135},\ \frac{77}{10},\ \frac{64}{15}$$