Solve 6/7-5/6+7/12

$$\frac{ 6 }{ 7 } - \frac{ 5 }{ 6 } + \frac{ 7 }{ 12 }$$

Evaluate

$$\frac{17}{28}\approx 0.607142857$$

Solution Steps

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

$$\frac{36}{42}-\frac{35}{42}+\frac{7}{12}$$

Since \frac{36}{42} and \frac{35}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{36-35}{42}+\frac{7}{12}$$

Subtract 35 from 36 to get 1.

$$\frac{1}{42}+\frac{7}{12}$$

Least common multiple of 42 and 12 is 84. Convert \frac{1}{42} and \frac{7}{12} to fractions with denominator 84.

$$\frac{2}{84}+\frac{49}{84}$$

Since \frac{2}{84} and \frac{49}{84} have the same denominator, add them by adding their numerators.

$$\frac{2+49}{84}$$

Add 2 and 49 to get 51.

$$\frac{51}{84}$$

Reduce the fraction \frac{51}{84} to lowest terms by extracting and canceling out 3.

$$\frac{17}{28}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 7} = 0.6071428571428571$$