Solve {c}{34*(-4/9)+3/4*(-5/9)}{[(-2,2)+66]:11}

$$\left. \begin{array} { c } { 34 \cdot ( - \frac { 4 } { 9 } ) + \frac { 3 } { 4 } \cdot ( - \frac { 5 } { 9 } ) } \\ { [ ( - 2,2 ) + 66 ] : 11 } \end{array} \right.$$

Sort

$$-\frac{559}{36},\ 5,8$$

Solution Steps

Express 34\left(-\frac{4}{9}\right) as a single fraction.

$$sort(\frac{34\left(-4\right)}{9}+\frac{3}{4}\left(-\frac{5}{9}\right);\frac{-2,2+66}{11})$$

Multiply 34 and -4 to get -136.

$$sort(\frac{-136}{9}+\frac{3}{4}\left(-\frac{5}{9}\right);\frac{-2,2+66}{11})$$

Fraction \frac{-136}{9} can be rewritten as -\frac{136}{9} by extracting the negative sign.

$$sort(-\frac{136}{9}+\frac{3}{4}\left(-\frac{5}{9}\right);\frac{-2,2+66}{11})$$

Multiply \frac{3}{4} times -\frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$sort(-\frac{136}{9}+\frac{3\left(-5\right)}{4\times 9};\frac{-2,2+66}{11})$$

Do the multiplications in the fraction \frac{3\left(-5\right)}{4\times 9}.

$$sort(-\frac{136}{9}+\frac{-15}{36};\frac{-2,2+66}{11})$$

Reduce the fraction \frac{-15}{36} to lowest terms by extracting and canceling out 3.

$$sort(-\frac{136}{9}-\frac{5}{12};\frac{-2,2+66}{11})$$

Least common multiple of 9 and 12 is 36. Convert -\frac{136}{9} and \frac{5}{12} to fractions with denominator 36.

$$sort(-\frac{544}{36}-\frac{15}{36};\frac{-2,2+66}{11})$$

Since -\frac{544}{36} and \frac{15}{36} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{-544-15}{36};\frac{-2,2+66}{11})$$

Subtract 15 from -544 to get -559.

$$sort(-\frac{559}{36};\frac{-2,2+66}{11})$$

Add -2,2 and 66 to get 63,8.

$$sort(-\frac{559}{36};\frac{63,8}{11})$$

Expand \frac{63,8}{11} by multiplying both numerator and the denominator by 10.

$$sort(-\frac{559}{36};\frac{638}{110})$$

Reduce the fraction \frac{638}{110} to lowest terms by extracting and canceling out 22.

$$sort(-\frac{559}{36};\frac{29}{5})$$

Least common denominator of the numbers in the list -\frac{559}{36};\frac{29}{5} is 180. Convert numbers in the list to fractions with denominator 180.

$$-\frac{2795}{180};\frac{1044}{180}$$

Evaluate

$$-\frac{559}{36},\ 5,8$$