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

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

Evaluate

$$\frac{7}{60}\approx 0.116666667$$

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 -1.

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

The opposite of -\frac{1}{12} is \frac{1}{12}.

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

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

$$\frac{1}{12}-\left(-\frac{6}{30}+\frac{5}{30}\right)$$

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

$$\frac{1}{12}-\frac{-6+5}{30}$$

Add -6 and 5 to get -1.

$$\frac{1}{12}-\left(-\frac{1}{30}\right)$$

The opposite of -\frac{1}{30} is \frac{1}{30}.

$$\frac{1}{12}+\frac{1}{30}$$

Least common multiple of 12 and 30 is 60. Convert \frac{1}{12} and \frac{1}{30} to fractions with denominator 60.

$$\frac{5}{60}+\frac{2}{60}$$

Since \frac{5}{60} and \frac{2}{60} have the same denominator, add them by adding their numerators.

$$\frac{5+2}{60}$$

Add 5 and 2 to get 7.

$$\frac{7}{60}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3 \cdot 5} = 0.11666666666666667$$