Solve 59/66-13/14-5/12

$$\frac{ 59 }{ 66 } - \frac{ 13 }{ 14 } - \frac{ 5 }{ 12 }$$

Evaluate

$$-\frac{139}{308}\approx -0.451298701$$

Solution Steps

Least common multiple of 66 and 14 is 462. Convert \frac{59}{66} and \frac{13}{14} to fractions with denominator 462.

$$\frac{413}{462}-\frac{429}{462}-\frac{5}{12}$$

Since \frac{413}{462} and \frac{429}{462} have the same denominator, subtract them by subtracting their numerators.

$$\frac{413-429}{462}-\frac{5}{12}$$

Subtract 429 from 413 to get -16.

$$\frac{-16}{462}-\frac{5}{12}$$

Reduce the fraction \frac{-16}{462} to lowest terms by extracting and canceling out 2.

$$-\frac{8}{231}-\frac{5}{12}$$

Least common multiple of 231 and 12 is 924. Convert -\frac{8}{231} and \frac{5}{12} to fractions with denominator 924.

$$-\frac{32}{924}-\frac{385}{924}$$

Since -\frac{32}{924} and \frac{385}{924} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-32-385}{924}$$

Subtract 385 from -32 to get -417.

$$\frac{-417}{924}$$

Reduce the fraction \frac{-417}{924} to lowest terms by extracting and canceling out 3.

$$-\frac{139}{308}$$

Factor

$$-\frac{139}{308} = -0.4512987012987013$$