Solve (-5-3/4)*8+(-21/3)(-13/14)-133/48*(-2frac{2}{15})

$$( - 5 \frac { - 3 } { 4 } ) \cdot 8 + ( - 2 \frac { 1 } { 3 } ) ( - 1 \frac { 3 } { 14 } ) - 1 \frac { 33 } { 48 } \cdot ( - 2 \frac { 2 } { 15 } )$$

Evaluate

$$-\frac{827}{30}\approx -27.566666667$$

Solution Steps

Multiply 5 and 4 to get 20.

$$\left(-\frac{20-3}{4}\right)\times 8+\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+3}{14}\right)-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Subtract 3 from 20 to get 17.

$$-\frac{17}{4}\times 8+\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+3}{14}\right)-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Express -\frac{17}{4}\times 8 as a single fraction.

$$\frac{-17\times 8}{4}+\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+3}{14}\right)-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply -17 and 8 to get -136.

$$\frac{-136}{4}+\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+3}{14}\right)-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Divide -136 by 4 to get -34.

$$-34+\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+3}{14}\right)-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply 2 and 3 to get 6.

$$-34+\left(-\frac{6+1}{3}\right)\left(-\frac{1\times 14+3}{14}\right)-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add 6 and 1 to get 7.

$$-34-\frac{7}{3}\left(-\frac{14+3}{14}\right)-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add 14 and 3 to get 17.

$$-34-\frac{7}{3}\left(-\frac{17}{14}\right)-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply -\frac{7}{3} times -\frac{17}{14} by multiplying numerator times numerator and denominator times denominator.

$$-34+\frac{-7\left(-17\right)}{3\times 14}-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Do the multiplications in the fraction \frac{-7\left(-17\right)}{3\times 14}.

$$-34+\frac{119}{42}-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Reduce the fraction \frac{119}{42} to lowest terms by extracting and canceling out 7.

$$-34+\frac{17}{6}-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Convert -34 to fraction -\frac{204}{6}.

$$-\frac{204}{6}+\frac{17}{6}-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Since -\frac{204}{6} and \frac{17}{6} have the same denominator, add them by adding their numerators.

$$\frac{-204+17}{6}-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add -204 and 17 to get -187.

$$-\frac{187}{6}-\frac{1\times 48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply 1 and 48 to get 48.

$$-\frac{187}{6}-\frac{48+33}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add 48 and 33 to get 81.

$$-\frac{187}{6}-\frac{81}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Reduce the fraction \frac{81}{48} to lowest terms by extracting and canceling out 3.

$$-\frac{187}{6}-\frac{27}{16}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply 2 and 15 to get 30.

$$-\frac{187}{6}-\frac{27}{16}\left(-\frac{30+2}{15}\right)$$

Add 30 and 2 to get 32.

$$-\frac{187}{6}-\frac{27}{16}\left(-\frac{32}{15}\right)$$

Multiply \frac{27}{16} times -\frac{32}{15} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{187}{6}-\frac{27\left(-32\right)}{16\times 15}$$

Do the multiplications in the fraction \frac{27\left(-32\right)}{16\times 15}.

$$-\frac{187}{6}-\frac{-864}{240}$$

Reduce the fraction \frac{-864}{240} to lowest terms by extracting and canceling out 48.

$$-\frac{187}{6}-\left(-\frac{18}{5}\right)$$

The opposite of -\frac{18}{5} is \frac{18}{5}.

$$-\frac{187}{6}+\frac{18}{5}$$

Least common multiple of 6 and 5 is 30. Convert -\frac{187}{6} and \frac{18}{5} to fractions with denominator 30.

$$-\frac{935}{30}+\frac{108}{30}$$

Since -\frac{935}{30} and \frac{108}{30} have the same denominator, add them by adding their numerators.

$$\frac{-935+108}{30}$$

Add -935 and 108 to get -827.

$$-\frac{827}{30}$$

Factor

$$-\frac{827}{30} = -27\frac{17}{30} = -27.566666666666666$$