Solve -6/3-6/5/frac{-frac{3{2}+4/3}{(7-8)*5}}{(-45+30)*1/2}

$$\frac { - \frac { 6 } { 3 } - \frac { 6 } { 5 } } { \frac { - \frac { 3 } { 2 } + \frac { 4 } { 3 } } { ( 7 - 8 ) \cdot 5 } } { ( - 45 + 30 ) \cdot 1 / 2 }$$

Evaluate

$$720$$

Solution Steps

Divide 6 by 3 to get 2.

$$\frac{-2-\frac{6}{5}}{\frac{-\frac{3}{2}+\frac{4}{3}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

Convert -2 to fraction -\frac{10}{5}.

$$\frac{-\frac{10}{5}-\frac{6}{5}}{\frac{-\frac{3}{2}+\frac{4}{3}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

Since -\frac{10}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-10-6}{5}}{\frac{-\frac{3}{2}+\frac{4}{3}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

Subtract 6 from -10 to get -16.

$$\frac{-\frac{16}{5}}{\frac{-\frac{3}{2}+\frac{4}{3}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{3}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{-\frac{16}{5}}{\frac{-\frac{9}{6}+\frac{8}{6}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

Since -\frac{9}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{16}{5}}{\frac{\frac{-9+8}{6}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

Add -9 and 8 to get -1.

$$\frac{-\frac{16}{5}}{\frac{-\frac{1}{6}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

Subtract 8 from 7 to get -1.

$$\frac{-\frac{16}{5}}{\frac{-\frac{1}{6}}{-5}}\left(-45+30\right)\times \frac{1}{2}$$

Express \frac{-\frac{1}{6}}{-5} as a single fraction.

$$\frac{-\frac{16}{5}}{\frac{-1}{6\left(-5\right)}}\left(-45+30\right)\times \frac{1}{2}$$

Multiply 6 and -5 to get -30.

$$\frac{-\frac{16}{5}}{\frac{-1}{-30}}\left(-45+30\right)\times \frac{1}{2}$$

Fraction \frac{-1}{-30} can be simplified to \frac{1}{30} by removing the negative sign from both the numerator and the denominator.

$$\frac{-\frac{16}{5}}{\frac{1}{30}}\left(-45+30\right)\times \frac{1}{2}$$

Divide -\frac{16}{5} by \frac{1}{30} by multiplying -\frac{16}{5} by the reciprocal of \frac{1}{30}.

$$-\frac{16}{5}\times 30\left(-45+30\right)\times \frac{1}{2}$$

Express -\frac{16}{5}\times 30 as a single fraction.

$$\frac{-16\times 30}{5}\left(-45+30\right)\times \frac{1}{2}$$

Multiply -16 and 30 to get -480.

$$\frac{-480}{5}\left(-45+30\right)\times \frac{1}{2}$$

Divide -480 by 5 to get -96.

$$-96\left(-45+30\right)\times \frac{1}{2}$$

Add -45 and 30 to get -15.

$$-96\left(-15\right)\times \frac{1}{2}$$

Multiply -96 and -15 to get 1440.

$$1440\times \frac{1}{2}$$

Multiply 1440 and \frac{1}{2} to get \frac{1440}{2}.

$$\frac{1440}{2}$$

Divide 1440 by 2 to get 720.

$$720$$

Factor

$$2^{4}\times 3^{2}\times 5$$