Solve -(1/3+1/4)-(1/5+1/6)

$$-( \frac{ 1 }{ 3 } + \frac{ 1 }{ 4 } )-( \frac{ 1 }{ 5 } + \frac{ 1 }{ 6 } )$$

Evaluate

$$-\frac{19}{20}=-0.95$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$-\left(\frac{4}{12}+\frac{3}{12}\right)-\left(\frac{1}{5}+\frac{1}{6}\right)$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$-\frac{4+3}{12}-\left(\frac{1}{5}+\frac{1}{6}\right)$$

Add 4 and 3 to get 7.

$$-\frac{7}{12}-\left(\frac{1}{5}+\frac{1}{6}\right)$$

Least common multiple of 5 and 6 is 30. Convert \frac{1}{5} and \frac{1}{6} to fractions with denominator 30.

$$-\frac{7}{12}-\left(\frac{6}{30}+\frac{5}{30}\right)$$

Since \frac{6}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$-\frac{7}{12}-\frac{6+5}{30}$$

Add 6 and 5 to get 11.

$$-\frac{7}{12}-\frac{11}{30}$$

Least common multiple of 12 and 30 is 60. Convert -\frac{7}{12} and \frac{11}{30} to fractions with denominator 60.

$$-\frac{35}{60}-\frac{22}{60}$$

Since -\frac{35}{60} and \frac{22}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-35-22}{60}$$

Subtract 22 from -35 to get -57.

$$\frac{-57}{60}$$

Reduce the fraction \frac{-57}{60} to lowest terms by extracting and canceling out 3.

$$-\frac{19}{20}$$

Factor

$$-\frac{19}{20} = -0.95$$