Solve (4/5-5/6)-(3/10+1/6)=

$$( \frac { 4 } { 5 } - \frac { 5 } { 6 } ) - ( \frac { 3 } { 10 } + \frac { 1 } { 6 } ) =$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

Least common multiple of 5 and 6 is 30. Convert \frac{4}{5} and \frac{5}{6} to fractions with denominator 30.

$$\frac{24}{30}-\frac{25}{30}-\left(\frac{3}{10}+\frac{1}{6}\right)$$

Since \frac{24}{30} and \frac{25}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-25}{30}-\left(\frac{3}{10}+\frac{1}{6}\right)$$

Subtract 25 from 24 to get -1.

$$-\frac{1}{30}-\left(\frac{3}{10}+\frac{1}{6}\right)$$

Least common multiple of 10 and 6 is 30. Convert \frac{3}{10} and \frac{1}{6} to fractions with denominator 30.

$$-\frac{1}{30}-\left(\frac{9}{30}+\frac{5}{30}\right)$$

Since \frac{9}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$-\frac{1}{30}-\frac{9+5}{30}$$

Add 9 and 5 to get 14.

$$-\frac{1}{30}-\frac{14}{30}$$

Since -\frac{1}{30} and \frac{14}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-14}{30}$$

Subtract 14 from -1 to get -15.

$$\frac{-15}{30}$$

Reduce the fraction \frac{-15}{30} to lowest terms by extracting and canceling out 15.

$$-\frac{1}{2}$$

Factor

$$-\frac{1}{2} = -0.5$$