Solve (1/2+1/3-3/4)-(1/5+frac{4}{5}-frac{5}{6})

$$( \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 3 } { 4 } ) - ( \frac { 1 } { 5 } + \frac { 4 } { 5 } - \frac { 5 } { 6 } )$$

Evaluate

$$-\frac{1}{12}\approx -0.083333333$$

Solution Steps

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

$$\frac{3}{6}+\frac{2}{6}-\frac{3}{4}-\left(\frac{1}{5}+\frac{4}{5}-\frac{5}{6}\right)$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{6}-\frac{3}{4}-\left(\frac{1}{5}+\frac{4}{5}-\frac{5}{6}\right)$$

Add 3 and 2 to get 5.

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

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{10}{12}-\frac{9}{12}-\left(\frac{1}{5}+\frac{4}{5}-\frac{5}{6}\right)$$

Since \frac{10}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-9}{12}-\left(\frac{1}{5}+\frac{4}{5}-\frac{5}{6}\right)$$

Subtract 9 from 10 to get 1.

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

Since \frac{1}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

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

Add 1 and 4 to get 5.

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

Divide 5 by 5 to get 1.

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

Convert 1 to fraction \frac{6}{6}.

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

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

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

Subtract 5 from 6 to get 1.

$$\frac{1}{12}-\frac{1}{6}$$

Least common multiple of 12 and 6 is 12. Convert \frac{1}{12} and \frac{1}{6} to fractions with denominator 12.

$$\frac{1}{12}-\frac{2}{12}$$

Since \frac{1}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-2}{12}$$

Subtract 2 from 1 to get -1.

$$-\frac{1}{12}$$

Factor

$$-\frac{1}{12} = -0.08333333333333333$$