Solve {r}{4,64/5,1:2/3+4,32/8,5*11/4}{-7frac{1}{4},quad9frac{2}{9}}

$$\left. \begin{array} { r } { \frac { 4,64 } { 5,1 } : \frac { 2 } { 3 } + \frac { 4,32 } { 8,5 } \cdot 1 \frac { 1 } { 4 } } \\ { - 7 \frac { 1 } { 4 } , \quad 9 \frac { 2 } { 9 } } \end{array} \right.$$

Sort

$$-5.25,\frac{83}{9}$$

Solution Steps

Divide \frac{4.64}{5.1} by \frac{2}{3} by multiplying \frac{4.64}{5.1} by the reciprocal of \frac{2}{3}.

$$sort(\frac{4.64\times 3}{5.1\times 2}+\frac{4.32}{8.5}\times \frac{1\times 4+1}{4}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Multiply 4.64 and 3 to get 13.92.

$$sort(\frac{13.92}{5.1\times 2}+\frac{4.32}{8.5}\times \frac{1\times 4+1}{4}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Multiply 5.1 and 2 to get 10.2.

$$sort(\frac{13.92}{10.2}+\frac{4.32}{8.5}\times \frac{1\times 4+1}{4}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Expand \frac{13.92}{10.2} by multiplying both numerator and the denominator by 100.

$$sort(\frac{1392}{1020}+\frac{4.32}{8.5}\times \frac{1\times 4+1}{4}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Reduce the fraction \frac{1392}{1020} to lowest terms by extracting and canceling out 12.

$$sort(\frac{116}{85}+\frac{4.32}{8.5}\times \frac{1\times 4+1}{4}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Expand \frac{4.32}{8.5} by multiplying both numerator and the denominator by 100.

$$sort(\frac{116}{85}+\frac{432}{850}\times \frac{1\times 4+1}{4}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Reduce the fraction \frac{432}{850} to lowest terms by extracting and canceling out 2.

$$sort(\frac{116}{85}+\frac{216}{425}\times \frac{1\times 4+1}{4}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Multiply 1 and 4 to get 4.

$$sort(\frac{116}{85}+\frac{216}{425}\times \frac{4+1}{4}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Add 4 and 1 to get 5.

$$sort(\frac{116}{85}+\frac{216}{425}\times \frac{5}{4}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Multiply \frac{216}{425} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{116}{85}+\frac{216\times 5}{425\times 4}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Do the multiplications in the fraction \frac{216\times 5}{425\times 4}.

$$sort(\frac{116}{85}+\frac{1080}{1700}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Reduce the fraction \frac{1080}{1700} to lowest terms by extracting and canceling out 20.

$$sort(\frac{116}{85}+\frac{54}{85}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Since \frac{116}{85} and \frac{54}{85} have the same denominator, add them by adding their numerators.

$$sort(\frac{116+54}{85}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Add 116 and 54 to get 170.

$$sort(\frac{170}{85}-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Divide 170 by 85 to get 2.

$$sort(2-\frac{7\times 4+1}{4},\frac{9\times 9+2}{9})$$

Multiply 7 and 4 to get 28.

$$sort(2-\frac{28+1}{4},\frac{9\times 9+2}{9})$$

Add 28 and 1 to get 29.

$$sort(2-\frac{29}{4},\frac{9\times 9+2}{9})$$

Convert 2 to fraction \frac{8}{4}.

$$sort(\frac{8}{4}-\frac{29}{4},\frac{9\times 9+2}{9})$$

Since \frac{8}{4} and \frac{29}{4} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{8-29}{4},\frac{9\times 9+2}{9})$$

Subtract 29 from 8 to get -21.

$$sort(-\frac{21}{4},\frac{9\times 9+2}{9})$$

Multiply 9 and 9 to get 81.

$$sort(-\frac{21}{4},\frac{81+2}{9})$$

Add 81 and 2 to get 83.

$$sort(-\frac{21}{4},\frac{83}{9})$$

Least common denominator of the numbers in the list -\frac{21}{4},\frac{83}{9} is 36. Convert numbers in the list to fractions with denominator 36.

$$-\frac{189}{36},\frac{332}{36}$$

Evaluate

$$-5.25,\frac{83}{9}$$