Solve {l}{31/12*21/4}{24/6*24/8}

$$\left. \begin{array} { l } { 3 \frac { 1 } { 12 } \times 2 \frac { 1 } { 4 } } \\ { 2 \frac { 4 } { 6 } \times 2 \frac { 4 } { 8 } } \end{array} \right.$$

Sort

$$\frac{20}{3},\frac{111}{16}$$

Solution Steps

Multiply 3 and 12 to get 36.

$$sort(\frac{36+1}{12}\times \frac{2\times 4+1}{4},\frac{2\times 6+4}{6}\times \frac{2\times 8+4}{8})$$

Add 36 and 1 to get 37.

$$sort(\frac{37}{12}\times \frac{2\times 4+1}{4},\frac{2\times 6+4}{6}\times \frac{2\times 8+4}{8})$$

Multiply 2 and 4 to get 8.

$$sort(\frac{37}{12}\times \frac{8+1}{4},\frac{2\times 6+4}{6}\times \frac{2\times 8+4}{8})$$

Add 8 and 1 to get 9.

$$sort(\frac{37}{12}\times \frac{9}{4},\frac{2\times 6+4}{6}\times \frac{2\times 8+4}{8})$$

Multiply \frac{37}{12} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{37\times 9}{12\times 4},\frac{2\times 6+4}{6}\times \frac{2\times 8+4}{8})$$

Do the multiplications in the fraction \frac{37\times 9}{12\times 4}.

$$sort(\frac{333}{48},\frac{2\times 6+4}{6}\times \frac{2\times 8+4}{8})$$

Reduce the fraction \frac{333}{48} to lowest terms by extracting and canceling out 3.

$$sort(\frac{111}{16},\frac{2\times 6+4}{6}\times \frac{2\times 8+4}{8})$$

Multiply 2 and 6 to get 12.

$$sort(\frac{111}{16},\frac{12+4}{6}\times \frac{2\times 8+4}{8})$$

Add 12 and 4 to get 16.

$$sort(\frac{111}{16},\frac{16}{6}\times \frac{2\times 8+4}{8})$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$sort(\frac{111}{16},\frac{8}{3}\times \frac{2\times 8+4}{8})$$

Multiply 2 and 8 to get 16.

$$sort(\frac{111}{16},\frac{8}{3}\times \frac{16+4}{8})$$

Add 16 and 4 to get 20.

$$sort(\frac{111}{16},\frac{8}{3}\times \frac{20}{8})$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$sort(\frac{111}{16},\frac{8}{3}\times \frac{5}{2})$$

Multiply \frac{8}{3} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{111}{16},\frac{8\times 5}{3\times 2})$$

Do the multiplications in the fraction \frac{8\times 5}{3\times 2}.

$$sort(\frac{111}{16},\frac{40}{6})$$

Reduce the fraction \frac{40}{6} to lowest terms by extracting and canceling out 2.

$$sort(\frac{111}{16},\frac{20}{3})$$

Least common denominator of the numbers in the list \frac{111}{16},\frac{20}{3} is 48. Convert numbers in the list to fractions with denominator 48.

$$\frac{333}{48},\frac{320}{48}$$

To sort the list, start from a single element \frac{333}{48}.

$$\frac{333}{48}$$

Insert \frac{320}{48} to the appropriate location in the new list.

$$\frac{320}{48},\frac{333}{48}$$

Replace the obtained fractions with the initial values.

$$\frac{20}{3},\frac{111}{16}$$

Evaluate

$$\frac{111}{16},\ \frac{20}{3}$$