Solve 30-left(7/9+5/6-11/12right)*(-36)/-5

$$\frac{ 30- \left( \frac{ 7 }{ 9 } + \frac{ 5 }{ 6 } - \frac{ 11 }{ 12 } \right) \times (-36) }{ -5 }$$

Evaluate

$$-11$$

Solution Steps

Least common multiple of 9 and 6 is 18. Convert \frac{7}{9} and \frac{5}{6} to fractions with denominator 18.

$$\frac{30-\left(\frac{14}{18}+\frac{15}{18}-\frac{11}{12}\right)\left(-36\right)}{-5}$$

Since \frac{14}{18} and \frac{15}{18} have the same denominator, add them by adding their numerators.

$$\frac{30-\left(\frac{14+15}{18}-\frac{11}{12}\right)\left(-36\right)}{-5}$$

Add 14 and 15 to get 29.

$$\frac{30-\left(\frac{29}{18}-\frac{11}{12}\right)\left(-36\right)}{-5}$$

Least common multiple of 18 and 12 is 36. Convert \frac{29}{18} and \frac{11}{12} to fractions with denominator 36.

$$\frac{30-\left(\frac{58}{36}-\frac{33}{36}\right)\left(-36\right)}{-5}$$

Since \frac{58}{36} and \frac{33}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-\frac{58-33}{36}\left(-36\right)}{-5}$$

Subtract 33 from 58 to get 25.

$$\frac{30-\frac{25}{36}\left(-36\right)}{-5}$$

Express \frac{25}{36}\left(-36\right) as a single fraction.

$$\frac{30-\frac{25\left(-36\right)}{36}}{-5}$$

Multiply 25 and -36 to get -900.

$$\frac{30-\frac{-900}{36}}{-5}$$

Divide -900 by 36 to get -25.

$$\frac{30-\left(-25\right)}{-5}$$

The opposite of -25 is 25.

$$\frac{30+25}{-5}$$

Add 30 and 25 to get 55.

$$\frac{55}{-5}$$

Divide 55 by -5 to get -11.

$$-11$$

Factor

$$-11$$