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

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

Evaluate

$$345$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert -\frac{1}{3} and \frac{6}{5} to fractions with denominator 15.

$$\frac{-\frac{5}{15}-\frac{18}{15}}{\frac{-\frac{3}{2}+\frac{4}{3}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

Since -\frac{5}{15} and \frac{18}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-5-18}{15}}{\frac{-\frac{3}{2}+\frac{4}{3}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

Subtract 18 from -5 to get -23.

$$\frac{-\frac{23}{15}}{\frac{-\frac{3}{2}+\frac{4}{3}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

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

$$\frac{-\frac{23}{15}}{\frac{-\frac{9}{6}+\frac{8}{6}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

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

$$\frac{-\frac{23}{15}}{\frac{\frac{-9+8}{6}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

Add -9 and 8 to get -1.

$$\frac{-\frac{23}{15}}{\frac{-\frac{1}{6}}{\left(7-8\right)\times 5}}\left(-45+30\right)\times \frac{1}{2}$$

Subtract 8 from 7 to get -1.

$$\frac{-\frac{23}{15}}{\frac{-\frac{1}{6}}{-5}}\left(-45+30\right)\times \frac{1}{2}$$

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

$$\frac{-\frac{23}{15}}{\frac{-1}{6\left(-5\right)}}\left(-45+30\right)\times \frac{1}{2}$$

Multiply 6 and -5 to get -30.

$$\frac{-\frac{23}{15}}{\frac{-1}{-30}}\left(-45+30\right)\times \frac{1}{2}$$

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

$$\frac{-\frac{23}{15}}{\frac{1}{30}}\left(-45+30\right)\times \frac{1}{2}$$

Divide -\frac{23}{15} by \frac{1}{30} by multiplying -\frac{23}{15} by the reciprocal of \frac{1}{30}.

$$-\frac{23}{15}\times 30\left(-45+30\right)\times \frac{1}{2}$$

Express -\frac{23}{15}\times 30 as a single fraction.

$$\frac{-23\times 30}{15}\left(-45+30\right)\times \frac{1}{2}$$

Multiply -23 and 30 to get -690.

$$\frac{-690}{15}\left(-45+30\right)\times \frac{1}{2}$$

Divide -690 by 15 to get -46.

$$-46\left(-45+30\right)\times \frac{1}{2}$$

Add -45 and 30 to get -15.

$$-46\left(-15\right)\times \frac{1}{2}$$

Multiply -46 and -15 to get 690.

$$690\times \frac{1}{2}$$

Multiply 690 and \frac{1}{2} to get \frac{690}{2}.

$$\frac{690}{2}$$

Divide 690 by 2 to get 345.

$$345$$

Factor

$$3\times 5\times 23$$