Solve -(1/3-1/21+3/14-2/7)div(-frac{1}{42})

$$- ( \frac { 1 } { 3 } - \frac { 1 } { 21 } + \frac { 3 } { 14 } - \frac { 2 } { 7 } ) \div ( - \frac { 1 } { 42 } )$$

Evaluate

$$9$$

Solution Steps

Least common multiple of 3 and 21 is 21. Convert \frac{1}{3} and \frac{1}{21} to fractions with denominator 21.

$$\frac{-\left(\frac{7}{21}-\frac{1}{21}+\frac{3}{14}-\frac{2}{7}\right)}{-\frac{1}{42}}$$

Since \frac{7}{21} and \frac{1}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\left(\frac{7-1}{21}+\frac{3}{14}-\frac{2}{7}\right)}{-\frac{1}{42}}$$

Subtract 1 from 7 to get 6.

$$\frac{-\left(\frac{6}{21}+\frac{3}{14}-\frac{2}{7}\right)}{-\frac{1}{42}}$$

Reduce the fraction \frac{6}{21} to lowest terms by extracting and canceling out 3.

$$\frac{-\left(\frac{2}{7}+\frac{3}{14}-\frac{2}{7}\right)}{-\frac{1}{42}}$$

Least common multiple of 7 and 14 is 14. Convert \frac{2}{7} and \frac{3}{14} to fractions with denominator 14.

$$\frac{-\left(\frac{4}{14}+\frac{3}{14}-\frac{2}{7}\right)}{-\frac{1}{42}}$$

Since \frac{4}{14} and \frac{3}{14} have the same denominator, add them by adding their numerators.

$$\frac{-\left(\frac{4+3}{14}-\frac{2}{7}\right)}{-\frac{1}{42}}$$

Add 4 and 3 to get 7.

$$\frac{-\left(\frac{7}{14}-\frac{2}{7}\right)}{-\frac{1}{42}}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{-\left(\frac{1}{2}-\frac{2}{7}\right)}{-\frac{1}{42}}$$

Least common multiple of 2 and 7 is 14. Convert \frac{1}{2} and \frac{2}{7} to fractions with denominator 14.

$$\frac{-\left(\frac{7}{14}-\frac{4}{14}\right)}{-\frac{1}{42}}$$

Since \frac{7}{14} and \frac{4}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{7-4}{14}}{-\frac{1}{42}}$$

Subtract 4 from 7 to get 3.

$$\frac{-\frac{3}{14}}{-\frac{1}{42}}$$

Divide -\frac{3}{14} by -\frac{1}{42} by multiplying -\frac{3}{14} by the reciprocal of -\frac{1}{42}.

$$-\frac{3}{14}\left(-42\right)$$

Express -\frac{3}{14}\left(-42\right) as a single fraction.

$$\frac{-3\left(-42\right)}{14}$$

Multiply -3 and -42 to get 126.

$$\frac{126}{14}$$

Divide 126 by 14 to get 9.

$$9$$

Factor

$$3^{2}$$