Solve (-1/42)div(1/6-3/14+2/3-frac{2}{7})

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

Evaluate

$$-\frac{1}{14}\approx -0.071428571$$

Solution Steps

Least common multiple of 6 and 14 is 42. Convert \frac{1}{6} and \frac{3}{14} to fractions with denominator 42.

$$\frac{-\frac{1}{42}}{\frac{7}{42}-\frac{9}{42}+\frac{2}{3}-\frac{2}{7}}$$

Since \frac{7}{42} and \frac{9}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{42}}{\frac{7-9}{42}+\frac{2}{3}-\frac{2}{7}}$$

Subtract 9 from 7 to get -2.

$$\frac{-\frac{1}{42}}{\frac{-2}{42}+\frac{2}{3}-\frac{2}{7}}$$

Reduce the fraction \frac{-2}{42} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{1}{42}}{-\frac{1}{21}+\frac{2}{3}-\frac{2}{7}}$$

Least common multiple of 21 and 3 is 21. Convert -\frac{1}{21} and \frac{2}{3} to fractions with denominator 21.

$$\frac{-\frac{1}{42}}{-\frac{1}{21}+\frac{14}{21}-\frac{2}{7}}$$

Since -\frac{1}{21} and \frac{14}{21} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{42}}{\frac{-1+14}{21}-\frac{2}{7}}$$

Add -1 and 14 to get 13.

$$\frac{-\frac{1}{42}}{\frac{13}{21}-\frac{2}{7}}$$

Least common multiple of 21 and 7 is 21. Convert \frac{13}{21} and \frac{2}{7} to fractions with denominator 21.

$$\frac{-\frac{1}{42}}{\frac{13}{21}-\frac{6}{21}}$$

Since \frac{13}{21} and \frac{6}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{42}}{\frac{13-6}{21}}$$

Subtract 6 from 13 to get 7.

$$\frac{-\frac{1}{42}}{\frac{7}{21}}$$

Reduce the fraction \frac{7}{21} to lowest terms by extracting and canceling out 7.

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

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

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

Express -\frac{1}{42}\times 3 as a single fraction.

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

Reduce the fraction \frac{-3}{42} to lowest terms by extracting and canceling out 3.

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

Factor

$$-\frac{1}{14} = -0.07142857142857142$$