Solve (+6/5-4/3)-(-5/2+7/3-frac{1}{6})+(-frac{4}{5}+frac{3}{4})-(-frac{7}{20})=

$$( + \frac { 6 } { 5 } - \frac { 4 } { 3 } ) - ( - \frac { 5 } { 2 } + \frac { 7 } { 3 } - \frac { 1 } { 6 } ) + ( - \frac { 4 } { 5 } + \frac { 3 } { 4 } ) - ( - \frac { 7 } { 20 } ) =$$

Evaluate

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

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{6}{5} and \frac{4}{3} to fractions with denominator 15.

$$\frac{18}{15}-\frac{20}{15}-\left(-\frac{5}{2}+\frac{7}{3}-\frac{1}{6}\right)-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Since \frac{18}{15} and \frac{20}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-20}{15}-\left(-\frac{5}{2}+\frac{7}{3}-\frac{1}{6}\right)-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Subtract 20 from 18 to get -2.

$$-\frac{2}{15}-\left(-\frac{5}{2}+\frac{7}{3}-\frac{1}{6}\right)-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Least common multiple of 2 and 3 is 6. Convert -\frac{5}{2} and \frac{7}{3} to fractions with denominator 6.

$$-\frac{2}{15}-\left(-\frac{15}{6}+\frac{14}{6}-\frac{1}{6}\right)-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Since -\frac{15}{6} and \frac{14}{6} have the same denominator, add them by adding their numerators.

$$-\frac{2}{15}-\left(\frac{-15+14}{6}-\frac{1}{6}\right)-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Add -15 and 14 to get -1.

$$-\frac{2}{15}-\left(-\frac{1}{6}-\frac{1}{6}\right)-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

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

$$-\frac{2}{15}-\frac{-1-1}{6}-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Subtract 1 from -1 to get -2.

$$-\frac{2}{15}-\frac{-2}{6}-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{15}-\left(-\frac{1}{3}\right)-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

The opposite of -\frac{1}{3} is \frac{1}{3}.

$$-\frac{2}{15}+\frac{1}{3}-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Least common multiple of 15 and 3 is 15. Convert -\frac{2}{15} and \frac{1}{3} to fractions with denominator 15.

$$-\frac{2}{15}+\frac{5}{15}-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Since -\frac{2}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\frac{-2+5}{15}-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Add -2 and 5 to get 3.

$$\frac{3}{15}-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Reduce the fraction \frac{3}{15} to lowest terms by extracting and canceling out 3.

$$\frac{1}{5}-\frac{4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

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

$$\frac{1-4}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Subtract 4 from 1 to get -3.

$$-\frac{3}{5}+\frac{3}{4}-\left(-\frac{7}{20}\right)$$

Least common multiple of 5 and 4 is 20. Convert -\frac{3}{5} and \frac{3}{4} to fractions with denominator 20.

$$-\frac{12}{20}+\frac{15}{20}-\left(-\frac{7}{20}\right)$$

Since -\frac{12}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{-12+15}{20}-\left(-\frac{7}{20}\right)$$

Add -12 and 15 to get 3.

$$\frac{3}{20}-\left(-\frac{7}{20}\right)$$

The opposite of -\frac{7}{20} is \frac{7}{20}.

$$\frac{3}{20}+\frac{7}{20}$$

Since \frac{3}{20} and \frac{7}{20} have the same denominator, add them by adding their numerators.

$$\frac{3+7}{20}$$

Add 3 and 7 to get 10.

$$\frac{10}{20}$$

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

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

Factor

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