Solve (5/6-3/7+1/3-9/14)+(-frac{1}{42})

$$( \frac { 5 } { 6 } - \frac { 3 } { 7 } + \frac { 1 } { 3 } - \frac { 9 } { 14 } ) + ( - \frac { 1 } { 42 } )$$

Evaluate

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

Solution Steps

Least common multiple of 6 and 7 is 42. Convert \frac{5}{6} and \frac{3}{7} to fractions with denominator 42.

$$\frac{35}{42}-\frac{18}{42}+\frac{1}{3}-\frac{9}{14}-\frac{1}{42}$$

Since \frac{35}{42} and \frac{18}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-18}{42}+\frac{1}{3}-\frac{9}{14}-\frac{1}{42}$$

Subtract 18 from 35 to get 17.

$$\frac{17}{42}+\frac{1}{3}-\frac{9}{14}-\frac{1}{42}$$

Least common multiple of 42 and 3 is 42. Convert \frac{17}{42} and \frac{1}{3} to fractions with denominator 42.

$$\frac{17}{42}+\frac{14}{42}-\frac{9}{14}-\frac{1}{42}$$

Since \frac{17}{42} and \frac{14}{42} have the same denominator, add them by adding their numerators.

$$\frac{17+14}{42}-\frac{9}{14}-\frac{1}{42}$$

Add 17 and 14 to get 31.

$$\frac{31}{42}-\frac{9}{14}-\frac{1}{42}$$

Least common multiple of 42 and 14 is 42. Convert \frac{31}{42} and \frac{9}{14} to fractions with denominator 42.

$$\frac{31}{42}-\frac{27}{42}-\frac{1}{42}$$

Since \frac{31}{42} and \frac{27}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31-27}{42}-\frac{1}{42}$$

Subtract 27 from 31 to get 4.

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

Since \frac{4}{42} and \frac{1}{42} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 4 to get 3.

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

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

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

Factor

$$\frac{1}{2 \cdot 7} = 0.07142857142857142$$