Solve (-53/4)*8(-21/3)*(-13/14)-137/48*(-2frac{2}{15})

$$(-5 \frac{ 3 }{ 4 } ) \times 8(-2 \frac{ 1 }{ 3 } ) \times (-1 \frac{ 3 }{ 14 } )-1 \frac{ 37 }{ 48 } \times (-2 \frac{ 2 }{ 15 } )$$

Evaluate

$$-\frac{1139}{9}\approx -126.555555556$$

Solution Steps

Multiply 5 and 4 to get 20.

$$\left(-\frac{20+3}{4}\right)\times 8\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+3}{14}\right)-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add 20 and 3 to get 23.

$$-\frac{23}{4}\times 8\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{14+3}{14}\right)-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Express -\frac{23}{4}\times 8 as a single fraction.

$$\frac{-23\times 8}{4}\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+3}{14}\right)-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply -23 and 8 to get -184.

$$\frac{-184}{4}\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+3}{14}\right)-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Divide -184 by 4 to get -46.

$$-46\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{14+3}{14}\right)-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply 2 and 3 to get 6.

$$-46\left(-\frac{6+1}{3}\right)\left(-\frac{14+3}{14}\right)-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add 6 and 1 to get 7.

$$-46\left(-\frac{7}{3}\right)\left(-\frac{14+3}{14}\right)-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Express -46\left(-\frac{7}{3}\right) as a single fraction.

$$\frac{-46\left(-7\right)}{3}\left(-\frac{1\times 14+3}{14}\right)-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply -46 and -7 to get 322.

$$\frac{322}{3}\left(-\frac{1\times 14+3}{14}\right)-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply 1 and 14 to get 14.

$$\frac{322}{3}\left(-\frac{14+3}{14}\right)-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add 14 and 3 to get 17.

$$\frac{322}{3}\left(-\frac{17}{14}\right)-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply \frac{322}{3} times -\frac{17}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{322\left(-17\right)}{3\times 14}-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Do the multiplications in the fraction \frac{322\left(-17\right)}{3\times 14}.

$$\frac{-5474}{42}-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Reduce the fraction \frac{-5474}{42} to lowest terms by extracting and canceling out 14.

$$-\frac{391}{3}-\frac{1\times 48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply 1 and 48 to get 48.

$$-\frac{391}{3}-\frac{48+37}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add 48 and 37 to get 85.

$$-\frac{391}{3}-\frac{85}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply 2 and 15 to get 30.

$$-\frac{391}{3}-\frac{85}{48}\left(-\frac{30+2}{15}\right)$$

Add 30 and 2 to get 32.

$$-\frac{391}{3}-\frac{85}{48}\left(-\frac{32}{15}\right)$$

Multiply \frac{85}{48} times -\frac{32}{15} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{391}{3}-\frac{85\left(-32\right)}{48\times 15}$$

Do the multiplications in the fraction \frac{85\left(-32\right)}{48\times 15}.

$$-\frac{391}{3}-\frac{-2720}{720}$$

Reduce the fraction \frac{-2720}{720} to lowest terms by extracting and canceling out 80.

$$-\frac{391}{3}-\left(-\frac{34}{9}\right)$$

The opposite of -\frac{34}{9} is \frac{34}{9}.

$$-\frac{391}{3}+\frac{34}{9}$$

Least common multiple of 3 and 9 is 9. Convert -\frac{391}{3} and \frac{34}{9} to fractions with denominator 9.

$$-\frac{1173}{9}+\frac{34}{9}$$

Since -\frac{1173}{9} and \frac{34}{9} have the same denominator, add them by adding their numerators.

$$\frac{-1173+34}{9}$$

Add -1173 and 34 to get -1139.

$$-\frac{1139}{9}$$

Factor

$$-\frac{1139}{9} = -126\frac{5}{9} = -126.55555555555556$$