Solve -1/2+1/3-{1/4-2+[1/5+(3-frac{1}{4})-frac{1}{2}]+frac{2}{3}}=

$$- \frac { 1 } { 2 } + \frac { 1 } { 3 } - \{ \frac { 1 } { 4 } - 2 + [ \frac { 1 } { 5 } + ( 3 - \frac { 1 } { 4 } ) - \frac { 1 } { 2 } ] + \frac { 2 } { 3 } \} =$$

Evaluate

$$-\frac{23}{15}\approx -1.533333333$$

Solution Steps

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

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

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

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

Add -3 and 2 to get -1.

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

Convert 2 to fraction \frac{8}{4}.

$$-\frac{1}{6}-\left(\frac{1}{4}-\frac{8}{4}+\frac{1}{5}+3-\frac{1}{4}-\frac{1}{2}+\frac{2}{3}\right)$$

Since \frac{1}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{6}-\left(\frac{1-8}{4}+\frac{1}{5}+3-\frac{1}{4}-\frac{1}{2}+\frac{2}{3}\right)$$

Subtract 8 from 1 to get -7.

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

Least common multiple of 4 and 5 is 20. Convert -\frac{7}{4} and \frac{1}{5} to fractions with denominator 20.

$$-\frac{1}{6}-\left(-\frac{35}{20}+\frac{4}{20}+3-\frac{1}{4}-\frac{1}{2}+\frac{2}{3}\right)$$

Since -\frac{35}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$-\frac{1}{6}-\left(\frac{-35+4}{20}+3-\frac{1}{4}-\frac{1}{2}+\frac{2}{3}\right)$$

Add -35 and 4 to get -31.

$$-\frac{1}{6}-\left(-\frac{31}{20}+3-\frac{1}{4}-\frac{1}{2}+\frac{2}{3}\right)$$

Convert 3 to fraction \frac{60}{20}.

$$-\frac{1}{6}-\left(-\frac{31}{20}+\frac{60}{20}-\frac{1}{4}-\frac{1}{2}+\frac{2}{3}\right)$$

Since -\frac{31}{20} and \frac{60}{20} have the same denominator, add them by adding their numerators.

$$-\frac{1}{6}-\left(\frac{-31+60}{20}-\frac{1}{4}-\frac{1}{2}+\frac{2}{3}\right)$$

Add -31 and 60 to get 29.

$$-\frac{1}{6}-\left(\frac{29}{20}-\frac{1}{4}-\frac{1}{2}+\frac{2}{3}\right)$$

Least common multiple of 20 and 4 is 20. Convert \frac{29}{20} and \frac{1}{4} to fractions with denominator 20.

$$-\frac{1}{6}-\left(\frac{29}{20}-\frac{5}{20}-\frac{1}{2}+\frac{2}{3}\right)$$

Since \frac{29}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{6}-\left(\frac{29-5}{20}-\frac{1}{2}+\frac{2}{3}\right)$$

Subtract 5 from 29 to get 24.

$$-\frac{1}{6}-\left(\frac{24}{20}-\frac{1}{2}+\frac{2}{3}\right)$$

Reduce the fraction \frac{24}{20} to lowest terms by extracting and canceling out 4.

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

Least common multiple of 5 and 2 is 10. Convert \frac{6}{5} and \frac{1}{2} to fractions with denominator 10.

$$-\frac{1}{6}-\left(\frac{12}{10}-\frac{5}{10}+\frac{2}{3}\right)$$

Since \frac{12}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{6}-\left(\frac{12-5}{10}+\frac{2}{3}\right)$$

Subtract 5 from 12 to get 7.

$$-\frac{1}{6}-\left(\frac{7}{10}+\frac{2}{3}\right)$$

Least common multiple of 10 and 3 is 30. Convert \frac{7}{10} and \frac{2}{3} to fractions with denominator 30.

$$-\frac{1}{6}-\left(\frac{21}{30}+\frac{20}{30}\right)$$

Since \frac{21}{30} and \frac{20}{30} have the same denominator, add them by adding their numerators.

$$-\frac{1}{6}-\frac{21+20}{30}$$

Add 21 and 20 to get 41.

$$-\frac{1}{6}-\frac{41}{30}$$

Least common multiple of 6 and 30 is 30. Convert -\frac{1}{6} and \frac{41}{30} to fractions with denominator 30.

$$-\frac{5}{30}-\frac{41}{30}$$

Since -\frac{5}{30} and \frac{41}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-41}{30}$$

Subtract 41 from -5 to get -46.

$$\frac{-46}{30}$$

Reduce the fraction \frac{-46}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{23}{15}$$

Factor

$$-\frac{23}{15} = -1\frac{8}{15} = -1.5333333333333334$$