Solve -5,6*42/3+647/48*5,6+25/16*(-5,6)

$$- 5,6 \cdot 4 \frac { 2 } { 3 } + 6 \frac { 47 } { 48 } \cdot 5,6 + 2 \frac { 5 } { 16 } \cdot ( - 5,6 )$$

Evaluate

$$0$$

Solution Steps

Multiply 4 and 3 to get 12.

$$-5,6\times \frac{12+2}{3}+\frac{6\times 48+47}{48}\times 5,6+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Add 12 and 2 to get 14.

$$-5,6\times \frac{14}{3}+\frac{6\times 48+47}{48}\times 5,6+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Convert decimal number -5,6 to fraction -\frac{56}{10}. Reduce the fraction -\frac{56}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{28}{5}\times \frac{14}{3}+\frac{6\times 48+47}{48}\times 5,6+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Multiply -\frac{28}{5} times \frac{14}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-28\times 14}{5\times 3}+\frac{6\times 48+47}{48}\times 5,6+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Do the multiplications in the fraction \frac{-28\times 14}{5\times 3}.

$$\frac{-392}{15}+\frac{6\times 48+47}{48}\times 5,6+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Fraction \frac{-392}{15} can be rewritten as -\frac{392}{15} by extracting the negative sign.

$$-\frac{392}{15}+\frac{6\times 48+47}{48}\times 5,6+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Multiply 6 and 48 to get 288.

$$-\frac{392}{15}+\frac{288+47}{48}\times 5,6+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Add 288 and 47 to get 335.

$$-\frac{392}{15}+\frac{335}{48}\times 5,6+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Convert decimal number 5,6 to fraction \frac{56}{10}. Reduce the fraction \frac{56}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{392}{15}+\frac{335}{48}\times \frac{28}{5}+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Multiply \frac{335}{48} times \frac{28}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{392}{15}+\frac{335\times 28}{48\times 5}+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Do the multiplications in the fraction \frac{335\times 28}{48\times 5}.

$$-\frac{392}{15}+\frac{9380}{240}+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Reduce the fraction \frac{9380}{240} to lowest terms by extracting and canceling out 20.

$$-\frac{392}{15}+\frac{469}{12}+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Least common multiple of 15 and 12 is 60. Convert -\frac{392}{15} and \frac{469}{12} to fractions with denominator 60.

$$-\frac{1568}{60}+\frac{2345}{60}+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Since -\frac{1568}{60} and \frac{2345}{60} have the same denominator, add them by adding their numerators.

$$\frac{-1568+2345}{60}+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Add -1568 and 2345 to get 777.

$$\frac{777}{60}+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Reduce the fraction \frac{777}{60} to lowest terms by extracting and canceling out 3.

$$\frac{259}{20}+\frac{2\times 16+5}{16}\left(-5,6\right)$$

Multiply 2 and 16 to get 32.

$$\frac{259}{20}+\frac{32+5}{16}\left(-5,6\right)$$

Add 32 and 5 to get 37.

$$\frac{259}{20}+\frac{37}{16}\left(-5,6\right)$$

Convert decimal number -5,6 to fraction -\frac{56}{10}. Reduce the fraction -\frac{56}{10} to lowest terms by extracting and canceling out 2.

$$\frac{259}{20}+\frac{37}{16}\left(-\frac{28}{5}\right)$$

Multiply \frac{37}{16} times -\frac{28}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{259}{20}+\frac{37\left(-28\right)}{16\times 5}$$

Do the multiplications in the fraction \frac{37\left(-28\right)}{16\times 5}.

$$\frac{259}{20}+\frac{-1036}{80}$$

Reduce the fraction \frac{-1036}{80} to lowest terms by extracting and canceling out 4.

$$\frac{259}{20}-\frac{259}{20}$$

Subtract \frac{259}{20} from \frac{259}{20} to get 0.

$$0$$

Factor

$$0$$