Solve 6,(32/3-0.6+21/3)div(53/4div1/4+2frac{2}{5}*1frac{2}{3})

$$6 , ( 3 \frac { 2 } { 3 } - 0.6 + 2 \frac { 1 } { 3 } ) \div ( 5 \frac { 3 } { 4 } \div \frac { 1 } { 4 } + 2 \frac { 2 } { 5 } \times 1 \frac { 2 } { 3 } )$$

Sort

$$0.2,6$$

Solution Steps

Multiply 3 and 3 to get 9.

$$sort(6,\frac{\frac{9+2}{3}-0.6+\frac{2\times 3+1}{3}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Add 9 and 2 to get 11.

$$sort(6,\frac{\frac{11}{3}-0.6+\frac{2\times 3+1}{3}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$sort(6,\frac{\frac{11}{3}-\frac{3}{5}+\frac{2\times 3+1}{3}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Least common multiple of 3 and 5 is 15. Convert \frac{11}{3} and \frac{3}{5} to fractions with denominator 15.

$$sort(6,\frac{\frac{55}{15}-\frac{9}{15}+\frac{2\times 3+1}{3}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Since \frac{55}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$sort(6,\frac{\frac{55-9}{15}+\frac{2\times 3+1}{3}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Subtract 9 from 55 to get 46.

$$sort(6,\frac{\frac{46}{15}+\frac{2\times 3+1}{3}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Multiply 2 and 3 to get 6.

$$sort(6,\frac{\frac{46}{15}+\frac{6+1}{3}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Add 6 and 1 to get 7.

$$sort(6,\frac{\frac{46}{15}+\frac{7}{3}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Least common multiple of 15 and 3 is 15. Convert \frac{46}{15} and \frac{7}{3} to fractions with denominator 15.

$$sort(6,\frac{\frac{46}{15}+\frac{35}{15}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Since \frac{46}{15} and \frac{35}{15} have the same denominator, add them by adding their numerators.

$$sort(6,\frac{\frac{46+35}{15}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Add 46 and 35 to get 81.

$$sort(6,\frac{\frac{81}{15}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Reduce the fraction \frac{81}{15} to lowest terms by extracting and canceling out 3.

$$sort(6,\frac{\frac{27}{5}}{\frac{\frac{5\times 4+3}{4}}{\frac{1}{4}}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Divide \frac{5\times 4+3}{4} by \frac{1}{4} by multiplying \frac{5\times 4+3}{4} by the reciprocal of \frac{1}{4}.

$$sort(6,\frac{\frac{27}{5}}{\frac{\left(5\times 4+3\right)\times 4}{4}+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Cancel out 4 and 4.

$$sort(6,\frac{\frac{27}{5}}{5\times 4+3+\frac{2\times 5+2}{5}\times \frac{1\times 3+2}{3}})$$

Multiply 2 and 5 to get 10.

$$sort(6,\frac{\frac{27}{5}}{5\times 4+3+\frac{10+2}{5}\times \frac{1\times 3+2}{3}})$$

Add 10 and 2 to get 12.

$$sort(6,\frac{\frac{27}{5}}{5\times 4+3+\frac{12}{5}\times \frac{1\times 3+2}{3}})$$

Multiply 1 and 3 to get 3.

$$sort(6,\frac{\frac{27}{5}}{5\times 4+3+\frac{12}{5}\times \frac{3+2}{3}})$$

Add 3 and 2 to get 5.

$$sort(6,\frac{\frac{27}{5}}{5\times 4+3+\frac{12}{5}\times \frac{5}{3}})$$

Multiply \frac{12}{5} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$sort(6,\frac{\frac{27}{5}}{5\times 4+3+\frac{12\times 5}{5\times 3}})$$

Cancel out 5 in both numerator and denominator.

$$sort(6,\frac{\frac{27}{5}}{5\times 4+3+\frac{12}{3}})$$

Divide 12 by 3 to get 4.

$$sort(6,\frac{\frac{27}{5}}{5\times 4+3+4})$$

Combine 5\times 4 and 4 to get 6\times 4.

$$sort(6,\frac{\frac{27}{5}}{6\times 4+3})$$

Multiply 6 and 4 to get 24.

$$sort(6,\frac{\frac{27}{5}}{24+3})$$

Add 24 and 3 to get 27.

$$sort(6,\frac{\frac{27}{5}}{27})$$

Express \frac{\frac{27}{5}}{27} as a single fraction.

$$sort(6,\frac{27}{5\times 27})$$

Cancel out 27 in both numerator and denominator.

$$sort(6,\frac{1}{5})$$

Convert decimal numbers in the list 6,\frac{1}{5} to fractions.

$$6,\frac{1}{5}$$

To sort the list, start from a single element 6.

$$6$$

Insert \frac{1}{5} to the appropriate location in the new list.

$$\frac{1}{5},6$$

Evaluate

$$6,0.2$$