Solve (1/3-3/7+5/6)div(-1/42)

$$( \frac { 1 } { 3 } - \frac { 3 } { 7 } + \frac { 5 } { 6 } ) \div ( - \frac { 1 } { 42 } )$$

Evaluate

$$-31$$

Solution Steps

Least common multiple of 3 and 7 is 21. Convert \frac{1}{3} and \frac{3}{7} to fractions with denominator 21.

$$\frac{\frac{7}{21}-\frac{9}{21}+\frac{5}{6}}{-\frac{1}{42}}$$

Since \frac{7}{21} and \frac{9}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-9}{21}+\frac{5}{6}}{-\frac{1}{42}}$$

Subtract 9 from 7 to get -2.

$$\frac{-\frac{2}{21}+\frac{5}{6}}{-\frac{1}{42}}$$

Least common multiple of 21 and 6 is 42. Convert -\frac{2}{21} and \frac{5}{6} to fractions with denominator 42.

$$\frac{-\frac{4}{42}+\frac{35}{42}}{-\frac{1}{42}}$$

Since -\frac{4}{42} and \frac{35}{42} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-4+35}{42}}{-\frac{1}{42}}$$

Add -4 and 35 to get 31.

$$\frac{\frac{31}{42}}{-\frac{1}{42}}$$

Divide \frac{31}{42} by -\frac{1}{42} by multiplying \frac{31}{42} by the reciprocal of -\frac{1}{42}.

$$\frac{31}{42}\left(-42\right)$$

Express \frac{31}{42}\left(-42\right) as a single fraction.

$$\frac{31\left(-42\right)}{42}$$

Multiply 31 and -42 to get -1302.

$$\frac{-1302}{42}$$

Divide -1302 by 42 to get -31.

$$-31$$

Factor

$$-31$$