Solve {l}{21/3div1/4}{42/5div11/5}

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

Sort

$$\frac{11}{3},\frac{28}{3}$$

Solution Steps

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

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

Multiply 2 and 3 to get 6.

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

Add 6 and 1 to get 7.

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

Multiply 7 and 4 to get 28.

$$sort(\frac{28}{3},\frac{\frac{4\times 5+2}{5}}{\frac{1\times 5+1}{5}})$$

Divide \frac{4\times 5+2}{5} by \frac{1\times 5+1}{5} by multiplying \frac{4\times 5+2}{5} by the reciprocal of \frac{1\times 5+1}{5}.

$$sort(\frac{28}{3},\frac{\left(4\times 5+2\right)\times 5}{5\left(1\times 5+1\right)})$$

Cancel out 5 in both numerator and denominator.

$$sort(\frac{28}{3},\frac{2+4\times 5}{1+5})$$

Multiply 4 and 5 to get 20.

$$sort(\frac{28}{3},\frac{2+20}{1+5})$$

Add 2 and 20 to get 22.

$$sort(\frac{28}{3},\frac{22}{1+5})$$

Add 1 and 5 to get 6.

$$sort(\frac{28}{3},\frac{22}{6})$$

Reduce the fraction \frac{22}{6} to lowest terms by extracting and canceling out 2.

$$sort(\frac{28}{3},\frac{11}{3})$$

To sort the list, start from a single element \frac{28}{3}.

$$\frac{28}{3}$$

Insert \frac{11}{3} to the appropriate location in the new list.

$$\frac{11}{3},\frac{28}{3}$$

Evaluate

$$\frac{28}{3},\ \frac{11}{3}$$