Solve (7/9-5/6+3/4-7/18)*36

$$( \frac { 7 } { 9 } - \frac { 5 } { 6 } + \frac { 3 } { 4 } - \frac { 7 } { 18 } ) \times 36$$

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.

$$\left(\frac{14}{18}-\frac{15}{18}+\frac{3}{4}-\frac{7}{18}\right)\times 36$$

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

$$\left(\frac{14-15}{18}+\frac{3}{4}-\frac{7}{18}\right)\times 36$$

Subtract 15 from 14 to get -1.

$$\left(-\frac{1}{18}+\frac{3}{4}-\frac{7}{18}\right)\times 36$$

Least common multiple of 18 and 4 is 36. Convert -\frac{1}{18} and \frac{3}{4} to fractions with denominator 36.

$$\left(-\frac{2}{36}+\frac{27}{36}-\frac{7}{18}\right)\times 36$$

Since -\frac{2}{36} and \frac{27}{36} have the same denominator, add them by adding their numerators.

$$\left(\frac{-2+27}{36}-\frac{7}{18}\right)\times 36$$

Add -2 and 27 to get 25.

$$\left(\frac{25}{36}-\frac{7}{18}\right)\times 36$$

Least common multiple of 36 and 18 is 36. Convert \frac{25}{36} and \frac{7}{18} to fractions with denominator 36.

$$\left(\frac{25}{36}-\frac{14}{36}\right)\times 36$$

Since \frac{25}{36} and \frac{14}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-14}{36}\times 36$$

Subtract 14 from 25 to get 11.

$$\frac{11}{36}\times 36$$

Cancel out 36 and 36.

$$11$$

Factor

$$11$$