Solve {l}{31/5div8/5*21/10}{1div1/2divfrac{4}{3}*frac{1}{6}}

$$\left. \begin{array} { l } { 3 \frac { 1 } { 5 } \div \frac { 8 } { 5 } \times 2 \frac { 1 } { 10 } } \\ { 1 \div \frac { 1 } { 2 } \div \frac { 4 } { 3 } \times \frac { 1 } { 6 } } \end{array} \right.$$

Sort

$$\frac{1}{4},\frac{21}{5}$$

Solution Steps

Divide \frac{3\times 5+1}{5} by \frac{8}{5} by multiplying \frac{3\times 5+1}{5} by the reciprocal of \frac{8}{5}.

$$sort(\frac{\left(3\times 5+1\right)\times 5}{5\times 8}\times \frac{2\times 10+1}{10},\frac{\frac{1}{\frac{1}{2}}}{\frac{4}{3}}\times \frac{1}{6})$$

Cancel out 5 in both numerator and denominator.

$$sort(\frac{1+3\times 5}{8}\times \frac{2\times 10+1}{10},\frac{\frac{1}{\frac{1}{2}}}{\frac{4}{3}}\times \frac{1}{6})$$

Multiply 3 and 5 to get 15.

$$sort(\frac{1+15}{8}\times \frac{2\times 10+1}{10},\frac{\frac{1}{\frac{1}{2}}}{\frac{4}{3}}\times \frac{1}{6})$$

Add 1 and 15 to get 16.

$$sort(\frac{16}{8}\times \frac{2\times 10+1}{10},\frac{\frac{1}{\frac{1}{2}}}{\frac{4}{3}}\times \frac{1}{6})$$

Divide 16 by 8 to get 2.

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

Multiply 2 and 10 to get 20.

$$sort(2\times \frac{20+1}{10},\frac{\frac{1}{\frac{1}{2}}}{\frac{4}{3}}\times \frac{1}{6})$$

Add 20 and 1 to get 21.

$$sort(2\times \frac{21}{10},\frac{\frac{1}{\frac{1}{2}}}{\frac{4}{3}}\times \frac{1}{6})$$

Express 2\times \frac{21}{10} as a single fraction.

$$sort(\frac{2\times 21}{10},\frac{\frac{1}{\frac{1}{2}}}{\frac{4}{3}}\times \frac{1}{6})$$

Multiply 2 and 21 to get 42.

$$sort(\frac{42}{10},\frac{\frac{1}{\frac{1}{2}}}{\frac{4}{3}}\times \frac{1}{6})$$

Reduce the fraction \frac{42}{10} to lowest terms by extracting and canceling out 2.

$$sort(\frac{21}{5},\frac{\frac{1}{\frac{1}{2}}}{\frac{4}{3}}\times \frac{1}{6})$$

Divide \frac{1}{\frac{1}{2}} by \frac{4}{3} by multiplying \frac{1}{\frac{1}{2}} by the reciprocal of \frac{4}{3}.

$$sort(\frac{21}{5},\frac{3}{\frac{1}{2}\times 4}\times \frac{1}{6})$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$sort(\frac{21}{5},\frac{3}{\frac{4}{2}}\times \frac{1}{6})$$

Divide 4 by 2 to get 2.

$$sort(\frac{21}{5},\frac{3}{2}\times \frac{1}{6})$$

Multiply \frac{3}{2} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{21}{5},\frac{3\times 1}{2\times 6})$$

Do the multiplications in the fraction \frac{3\times 1}{2\times 6}.

$$sort(\frac{21}{5},\frac{3}{12})$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$sort(\frac{21}{5},\frac{1}{4})$$

Least common denominator of the numbers in the list \frac{21}{5},\frac{1}{4} is 20. Convert numbers in the list to fractions with denominator 20.

$$\frac{84}{20},\frac{5}{20}$$

To sort the list, start from a single element \frac{84}{20}.

$$\frac{84}{20}$$

Insert \frac{5}{20} to the appropriate location in the new list.

$$\frac{5}{20},\frac{84}{20}$$

Replace the obtained fractions with the initial values.

$$\frac{1}{4},\frac{21}{5}$$

Evaluate

$$\frac{21}{5},\ \frac{1}{4}$$