Solve (-53/4)8+(-21/3)*(-18/14)-187/48(-2frac{2}{15})

$$( - 5 \frac { 3 } { 4 } ) 8 + ( - 2 \frac { 1 } { 3 } ) \cdot ( - 1 \frac { 8 } { 14 } ) - 1 \frac { 87 } { 48 } ( - 2 \frac { 2 } { 15 } )$$

Evaluate

$$-\frac{109}{3}\approx -36.333333333$$

Solution Steps

Multiply 5 and 4 to get 20.

$$\left(-\frac{20+3}{4}\right)\times 8+\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+8}{14}\right)-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add 20 and 3 to get 23.

$$-\frac{23}{4}\times 8+\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+8}{14}\right)-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

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

$$\frac{-23\times 8}{4}+\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+8}{14}\right)-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply -23 and 8 to get -184.

$$\frac{-184}{4}+\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+8}{14}\right)-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Divide -184 by 4 to get -46.

$$-46+\left(-\frac{2\times 3+1}{3}\right)\left(-\frac{1\times 14+8}{14}\right)-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply 2 and 3 to get 6.

$$-46+\left(-\frac{6+1}{3}\right)\left(-\frac{1\times 14+8}{14}\right)-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add 6 and 1 to get 7.

$$-46-\frac{7}{3}\left(-\frac{14+8}{14}\right)-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add 14 and 8 to get 22.

$$-46-\frac{7}{3}\left(-\frac{22}{14}\right)-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Reduce the fraction \frac{22}{14} to lowest terms by extracting and canceling out 2.

$$-46-\frac{7}{3}\left(-\frac{11}{7}\right)-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply -\frac{7}{3} times -\frac{11}{7} by multiplying numerator times numerator and denominator times denominator.

$$-46+\frac{-7\left(-11\right)}{3\times 7}-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Do the multiplications in the fraction \frac{-7\left(-11\right)}{3\times 7}.

$$-46+\frac{77}{21}-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Reduce the fraction \frac{77}{21} to lowest terms by extracting and canceling out 7.

$$-46+\frac{11}{3}-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Convert -46 to fraction -\frac{138}{3}.

$$-\frac{138}{3}+\frac{11}{3}-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Since -\frac{138}{3} and \frac{11}{3} have the same denominator, add them by adding their numerators.

$$\frac{-138+11}{3}-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add -138 and 11 to get -127.

$$-\frac{127}{3}-\frac{1\times 48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply 1 and 48 to get 48.

$$-\frac{127}{3}-\frac{48+87}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Add 48 and 87 to get 135.

$$-\frac{127}{3}-\frac{135}{48}\left(-\frac{2\times 15+2}{15}\right)$$

Reduce the fraction \frac{135}{48} to lowest terms by extracting and canceling out 3.

$$-\frac{127}{3}-\frac{45}{16}\left(-\frac{2\times 15+2}{15}\right)$$

Multiply 2 and 15 to get 30.

$$-\frac{127}{3}-\frac{45}{16}\left(-\frac{30+2}{15}\right)$$

Add 30 and 2 to get 32.

$$-\frac{127}{3}-\frac{45}{16}\left(-\frac{32}{15}\right)$$

Multiply \frac{45}{16} times -\frac{32}{15} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{127}{3}-\frac{45\left(-32\right)}{16\times 15}$$

Do the multiplications in the fraction \frac{45\left(-32\right)}{16\times 15}.

$$-\frac{127}{3}-\frac{-1440}{240}$$

Divide -1440 by 240 to get -6.

$$-\frac{127}{3}-\left(-6\right)$$

The opposite of -6 is 6.

$$-\frac{127}{3}+6$$

Convert 6 to fraction \frac{18}{3}.

$$-\frac{127}{3}+\frac{18}{3}$$

Since -\frac{127}{3} and \frac{18}{3} have the same denominator, add them by adding their numerators.

$$\frac{-127+18}{3}$$

Add -127 and 18 to get -109.

$$-\frac{109}{3}$$

Factor

$$-\frac{109}{3} = -36\frac{1}{3} = -36.333333333333336$$