Solve {l}{-13,4*0,6+(-2,3)*3,8}{8/9*(-39/16)-45/6*(-7/58)}

$$\left. \begin{array} { l } { - 13,4 \cdot 0,6 + ( - 2,3 ) \cdot 3,8 } \\ { \frac { 8 } { 9 } \cdot ( - 3 \frac { 9 } { 16 } ) - 4 \frac { 5 } { 6 } \cdot ( - \frac { 7 } { 58 } ) } \end{array} \right.$$

Sort

$$-16,78,\ -\frac{31}{12}$$

Solution Steps

Multiply -13,4 and 0,6 to get -8,04.

$$sort(-8,04-2,3\times 3,8;\frac{8}{9}\left(-\frac{3\times 16+9}{16}\right)-\frac{4\times 6+5}{6}\left(-\frac{7}{58}\right))$$

Multiply -2,3 and 3,8 to get -8,74.

$$sort(-8,04-8,74;\frac{8}{9}\left(-\frac{3\times 16+9}{16}\right)-\frac{4\times 6+5}{6}\left(-\frac{7}{58}\right))$$

Subtract 8,74 from -8,04 to get -16,78.

$$sort(-16,78;\frac{8}{9}\left(-\frac{3\times 16+9}{16}\right)-\frac{4\times 6+5}{6}\left(-\frac{7}{58}\right))$$

Multiply 3 and 16 to get 48.

$$sort(-16,78;\frac{8}{9}\left(-\frac{48+9}{16}\right)-\frac{4\times 6+5}{6}\left(-\frac{7}{58}\right))$$

Add 48 and 9 to get 57.

$$sort(-16,78;\frac{8}{9}\left(-\frac{57}{16}\right)-\frac{4\times 6+5}{6}\left(-\frac{7}{58}\right))$$

Multiply \frac{8}{9} times -\frac{57}{16} by multiplying numerator times numerator and denominator times denominator.

$$sort(-16,78;\frac{8\left(-57\right)}{9\times 16}-\frac{4\times 6+5}{6}\left(-\frac{7}{58}\right))$$

Do the multiplications in the fraction \frac{8\left(-57\right)}{9\times 16}.

$$sort(-16,78;\frac{-456}{144}-\frac{4\times 6+5}{6}\left(-\frac{7}{58}\right))$$

Reduce the fraction \frac{-456}{144} to lowest terms by extracting and canceling out 24.

$$sort(-16,78;-\frac{19}{6}-\frac{4\times 6+5}{6}\left(-\frac{7}{58}\right))$$

Multiply 4 and 6 to get 24.

$$sort(-16,78;-\frac{19}{6}-\frac{24+5}{6}\left(-\frac{7}{58}\right))$$

Add 24 and 5 to get 29.

$$sort(-16,78;-\frac{19}{6}-\frac{29}{6}\left(-\frac{7}{58}\right))$$

Multiply \frac{29}{6} times -\frac{7}{58} by multiplying numerator times numerator and denominator times denominator.

$$sort(-16,78;-\frac{19}{6}-\frac{29\left(-7\right)}{6\times 58})$$

Do the multiplications in the fraction \frac{29\left(-7\right)}{6\times 58}.

$$sort(-16,78;-\frac{19}{6}-\frac{-203}{348})$$

Reduce the fraction \frac{-203}{348} to lowest terms by extracting and canceling out 29.

$$sort(-16,78;-\frac{19}{6}-\left(-\frac{7}{12}\right))$$

The opposite of -\frac{7}{12} is \frac{7}{12}.

$$sort(-16,78;-\frac{19}{6}+\frac{7}{12})$$

Least common multiple of 6 and 12 is 12. Convert -\frac{19}{6} and \frac{7}{12} to fractions with denominator 12.

$$sort(-16,78;-\frac{38}{12}+\frac{7}{12})$$

Since -\frac{38}{12} and \frac{7}{12} have the same denominator, add them by adding their numerators.

$$sort(-16,78;\frac{-38+7}{12})$$

Add -38 and 7 to get -31.

$$sort(-16,78;-\frac{31}{12})$$

Convert decimal numbers in the list -16,78;-\frac{31}{12} to fractions.

$$-\frac{839}{50};-\frac{31}{12}$$

Least common denominator of the numbers in the list -\frac{839}{50};-\frac{31}{12} is 300. Convert numbers in the list to fractions with denominator 300.

$$-\frac{5034}{300};-\frac{775}{300}$$

Evaluate

$$-16,78,\ -\frac{31}{12}$$