Solve 52/9*34/47:(-32/5)+(-251/2+25,5)*3frac{2}{3}

$$5 \frac { 2 } { 9 } \cdot \frac { 34 } { 47 } : ( - 3 \frac { 2 } { 5 } ) + ( - 25 \frac { 1 } { 2 } + 25,5 ) \cdot 3 \frac { 2 } { 3 }$$

Evaluate

$$-\frac{10}{9}\approx -1,111111111$$

Solution Steps

Multiply 5 and 9 to get 45.

$$\frac{\frac{45+2}{9}\times \frac{34}{47}}{-\frac{3\times 5+2}{5}}+\left(-\frac{25\times 2+1}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Add 45 and 2 to get 47.

$$\frac{\frac{47}{9}\times \frac{34}{47}}{-\frac{3\times 5+2}{5}}+\left(-\frac{25\times 2+1}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Multiply \frac{47}{9} times \frac{34}{47} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{47\times 34}{9\times 47}}{-\frac{3\times 5+2}{5}}+\left(-\frac{25\times 2+1}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Cancel out 47 in both numerator and denominator.

$$\frac{\frac{34}{9}}{-\frac{3\times 5+2}{5}}+\left(-\frac{25\times 2+1}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Multiply 3 and 5 to get 15.

$$\frac{\frac{34}{9}}{-\frac{15+2}{5}}+\left(-\frac{25\times 2+1}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Add 15 and 2 to get 17.

$$\frac{\frac{34}{9}}{-\frac{17}{5}}+\left(-\frac{25\times 2+1}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Divide \frac{34}{9} by -\frac{17}{5} by multiplying \frac{34}{9} by the reciprocal of -\frac{17}{5}.

$$\frac{34}{9}\left(-\frac{5}{17}\right)+\left(-\frac{25\times 2+1}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Multiply \frac{34}{9} times -\frac{5}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{34\left(-5\right)}{9\times 17}+\left(-\frac{25\times 2+1}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Do the multiplications in the fraction \frac{34\left(-5\right)}{9\times 17}.

$$\frac{-170}{153}+\left(-\frac{25\times 2+1}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Reduce the fraction \frac{-170}{153} to lowest terms by extracting and canceling out 17.

$$-\frac{10}{9}+\left(-\frac{25\times 2+1}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Multiply 25 and 2 to get 50.

$$-\frac{10}{9}+\left(-\frac{50+1}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Add 50 and 1 to get 51.

$$-\frac{10}{9}+\left(-\frac{51}{2}+25,5\right)\times \frac{3\times 3+2}{3}$$

Add -\frac{51}{2} and 25,5 to get 0.

$$-\frac{10}{9}+0\times \frac{3\times 3+2}{3}$$

Multiply 3 and 3 to get 9.

$$-\frac{10}{9}+0\times \frac{9+2}{3}$$

Add 9 and 2 to get 11.

$$-\frac{10}{9}+0\times \frac{11}{3}$$

Multiply 0 and \frac{11}{3} to get 0.

$$-\frac{10}{9}+0$$

Add -\frac{10}{9} and 0 to get -\frac{10}{9}.

$$-\frac{10}{9}$$

Factor

$$-\frac{10}{9} = -1\frac{1}{9} = -1.1111111111111112$$