Solve (1/2-4/3)-(1/2-1/6)

$$( \frac{ 1 }{ 2 } - \frac{ 4 }{ 3 } )-( \frac{ 1 }{ 2 } - \frac{ 1 }{ 6 } )$$

Evaluate

$$-\frac{7}{6}\approx -1.166666667$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{3}{6}-\frac{8}{6}-\left(\frac{1}{2}-\frac{1}{6}\right)$$

Since \frac{3}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-8}{6}-\left(\frac{1}{2}-\frac{1}{6}\right)$$

Subtract 8 from 3 to get -5.

$$-\frac{5}{6}-\left(\frac{1}{2}-\frac{1}{6}\right)$$

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{1}{6} to fractions with denominator 6.

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

Since \frac{3}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{6}-\frac{3-1}{6}$$

Subtract 1 from 3 to get 2.

$$-\frac{5}{6}-\frac{2}{6}$$

Since -\frac{5}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-2}{6}$$

Subtract 2 from -5 to get -7.

$$-\frac{7}{6}$$

Factor

$$-\frac{7}{6} = -1\frac{1}{6} = -1.1666666666666667$$