Solve [45-(7/9-11/12+5/6)*36]div5

$$[ 45 - ( \frac { 7 } { 9 } - \frac { 11 } { 12 } + \frac { 5 } { 6 } ) \times 36 ] \div 5$$

Evaluate

$$4$$

Solution Steps

Least common multiple of 9 and 12 is 36. Convert \frac{7}{9} and \frac{11}{12} to fractions with denominator 36.

$$\frac{45-\left(\frac{28}{36}-\frac{33}{36}+\frac{5}{6}\right)\times 36}{5}$$

Since \frac{28}{36} and \frac{33}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45-\left(\frac{28-33}{36}+\frac{5}{6}\right)\times 36}{5}$$

Subtract 33 from 28 to get -5.

$$\frac{45-\left(-\frac{5}{36}+\frac{5}{6}\right)\times 36}{5}$$

Least common multiple of 36 and 6 is 36. Convert -\frac{5}{36} and \frac{5}{6} to fractions with denominator 36.

$$\frac{45-\left(-\frac{5}{36}+\frac{30}{36}\right)\times 36}{5}$$

Since -\frac{5}{36} and \frac{30}{36} have the same denominator, add them by adding their numerators.

$$\frac{45-\frac{-5+30}{36}\times 36}{5}$$

Add -5 and 30 to get 25.

$$\frac{45-\frac{25}{36}\times 36}{5}$$

Cancel out 36 and 36.

$$\frac{45-25}{5}$$

Subtract 25 from 45 to get 20.

$$\frac{20}{5}$$

Divide 20 by 5 to get 4.

$$4$$

Factor

$$2^{2}$$