Solve {l}{(-64/12):(-4/3)}{(-8/7):(+2/4)}

$$\left. \begin{array} { l } { ( - \frac { 64 } { 12 } ) : ( - \frac { 4 } { 3 } ) } \\ { ( - \frac { 8 } { 7 } ) : ( + \frac { 2 } { 4 } ) } \end{array} \right.$$

Sort

$$-\frac{16}{7},4$$

Solution Steps

Reduce the fraction \frac{64}{12} to lowest terms by extracting and canceling out 4.

$$sort(\frac{-\frac{16}{3}}{-\frac{4}{3}},\frac{-\frac{8}{7}}{\frac{2}{4}})$$

Divide -\frac{16}{3} by -\frac{4}{3} by multiplying -\frac{16}{3} by the reciprocal of -\frac{4}{3}.

$$sort(-\frac{16}{3}\left(-\frac{3}{4}\right),\frac{-\frac{8}{7}}{\frac{2}{4}})$$

Multiply -\frac{16}{3} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{-16\left(-3\right)}{3\times 4},\frac{-\frac{8}{7}}{\frac{2}{4}})$$

Do the multiplications in the fraction \frac{-16\left(-3\right)}{3\times 4}.

$$sort(\frac{48}{12},\frac{-\frac{8}{7}}{\frac{2}{4}})$$

Divide 48 by 12 to get 4.

$$sort(4,\frac{-\frac{8}{7}}{\frac{2}{4}})$$

Divide -\frac{8}{7} by \frac{2}{4} by multiplying -\frac{8}{7} by the reciprocal of \frac{2}{4}.

$$sort(4,\frac{-8\times 4}{7\times 2})$$

Cancel out 2 in both numerator and denominator.

$$sort(4,\frac{-4\times 4}{7})$$

Multiply -4 and 4 to get -16.

$$sort(4,\frac{-16}{7})$$

Fraction \frac{-16}{7} can be rewritten as -\frac{16}{7} by extracting the negative sign.

$$sort(4,-\frac{16}{7})$$

Convert decimal numbers in the list 4,-\frac{16}{7} to fractions.

$$4,-\frac{16}{7}$$

To sort the list, start from a single element 4.

$$4$$

Insert -\frac{16}{7} to the appropriate location in the new list.

$$-\frac{16}{7},4$$

Evaluate

$$4,\ -\frac{16}{7}$$