Solve (1/6+1/36-1/4+1/12)*(-48)

$$( \frac { 1 } { 6 } + \frac { 1 } { 36 } - \frac { 1 } { 4 } + \frac { 1 } { 12 } ) \times ( - 48 )$$

Evaluate

$$-\frac{4}{3}\approx -1.333333333$$

Solution Steps

Least common multiple of 6 and 36 is 36. Convert \frac{1}{6} and \frac{1}{36} to fractions with denominator 36.

$$\left(\frac{6}{36}+\frac{1}{36}-\frac{1}{4}+\frac{1}{12}\right)\left(-48\right)$$

Since \frac{6}{36} and \frac{1}{36} have the same denominator, add them by adding their numerators.

$$\left(\frac{6+1}{36}-\frac{1}{4}+\frac{1}{12}\right)\left(-48\right)$$

Add 6 and 1 to get 7.

$$\left(\frac{7}{36}-\frac{1}{4}+\frac{1}{12}\right)\left(-48\right)$$

Least common multiple of 36 and 4 is 36. Convert \frac{7}{36} and \frac{1}{4} to fractions with denominator 36.

$$\left(\frac{7}{36}-\frac{9}{36}+\frac{1}{12}\right)\left(-48\right)$$

Since \frac{7}{36} and \frac{9}{36} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{7-9}{36}+\frac{1}{12}\right)\left(-48\right)$$

Subtract 9 from 7 to get -2.

$$\left(\frac{-2}{36}+\frac{1}{12}\right)\left(-48\right)$$

Reduce the fraction \frac{-2}{36} to lowest terms by extracting and canceling out 2.

$$\left(-\frac{1}{18}+\frac{1}{12}\right)\left(-48\right)$$

Least common multiple of 18 and 12 is 36. Convert -\frac{1}{18} and \frac{1}{12} to fractions with denominator 36.

$$\left(-\frac{2}{36}+\frac{3}{36}\right)\left(-48\right)$$

Since -\frac{2}{36} and \frac{3}{36} have the same denominator, add them by adding their numerators.

$$\frac{-2+3}{36}\left(-48\right)$$

Add -2 and 3 to get 1.

$$\frac{1}{36}\left(-48\right)$$

Multiply \frac{1}{36} and -48 to get \frac{-48}{36}.

$$\frac{-48}{36}$$

Reduce the fraction \frac{-48}{36} to lowest terms by extracting and canceling out 12.

$$-\frac{4}{3}$$

Factor

$$-\frac{4}{3} = -1\frac{1}{3} = -1.3333333333333333$$