Solve (1/2-1/6+1/9)div(-1/36)

$$( \frac { 1 } { 2 } - \frac { 1 } { 6 } + \frac { 1 } { 9 } ) \div ( - \frac { 1 } { 36 } )$$

Evaluate

$$-16$$

Solution Steps

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{1}{6} to fractions with denominator 6.

$$\frac{\frac{3}{6}-\frac{1}{6}+\frac{1}{9}}{-\frac{1}{36}}$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-1}{6}+\frac{1}{9}}{-\frac{1}{36}}$$

Subtract 1 from 3 to get 2.

$$\frac{\frac{2}{6}+\frac{1}{9}}{-\frac{1}{36}}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{3}+\frac{1}{9}}{-\frac{1}{36}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{1}{9} to fractions with denominator 9.

$$\frac{\frac{3}{9}+\frac{1}{9}}{-\frac{1}{36}}$$

Since \frac{3}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+1}{9}}{-\frac{1}{36}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{4}{9}}{-\frac{1}{36}}$$

Divide \frac{4}{9} by -\frac{1}{36} by multiplying \frac{4}{9} by the reciprocal of -\frac{1}{36}.

$$\frac{4}{9}\left(-36\right)$$

Express \frac{4}{9}\left(-36\right) as a single fraction.

$$\frac{4\left(-36\right)}{9}$$

Multiply 4 and -36 to get -144.

$$\frac{-144}{9}$$

Divide -144 by 9 to get -16.

$$-16$$

Factor

$$-16$$