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

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

Evaluate

$$-\frac{11}{12}\approx -0.916666667$$

Solution Steps

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

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

Since -\frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

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

Add -2 and 3 to get 1.

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

Convert -2 to fraction -\frac{12}{6}.

$$-1-\left(\frac{1}{4}+-\frac{12}{6}+\frac{5}{6}-\left(\frac{1}{3}-1\right)-\frac{1}{6}\right)-\frac{1}{3}$$

Since -\frac{12}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$-1-\left(\frac{1}{4}+\frac{-12+5}{6}-\left(\frac{1}{3}-1\right)-\frac{1}{6}\right)-\frac{1}{3}$$

Add -12 and 5 to get -7.

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

Convert 1 to fraction \frac{3}{3}.

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

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

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

Subtract 3 from 1 to get -2.

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

The opposite of -\frac{2}{3} is \frac{2}{3}.

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

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

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

Since -\frac{7}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

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

Add -7 and 4 to get -3.

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

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

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

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

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

Since \frac{1}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 1 to get -1.

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

Least common multiple of 4 and 6 is 12. Convert -\frac{1}{4} and \frac{1}{6} to fractions with denominator 12.

$$-1-\left(-\frac{3}{12}-\frac{2}{12}\right)-\frac{1}{3}$$

Since -\frac{3}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$-1-\frac{-3-2}{12}-\frac{1}{3}$$

Subtract 2 from -3 to get -5.

$$-1-\left(-\frac{5}{12}\right)-\frac{1}{3}$$

The opposite of -\frac{5}{12} is \frac{5}{12}.

$$-1+\frac{5}{12}-\frac{1}{3}$$

Convert -1 to fraction -\frac{12}{12}.

$$-\frac{12}{12}+\frac{5}{12}-\frac{1}{3}$$

Since -\frac{12}{12} and \frac{5}{12} have the same denominator, add them by adding their numerators.

$$\frac{-12+5}{12}-\frac{1}{3}$$

Add -12 and 5 to get -7.

$$-\frac{7}{12}-\frac{1}{3}$$

Least common multiple of 12 and 3 is 12. Convert -\frac{7}{12} and \frac{1}{3} to fractions with denominator 12.

$$-\frac{7}{12}-\frac{4}{12}$$

Since -\frac{7}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-4}{12}$$

Subtract 4 from -7 to get -11.

$$-\frac{11}{12}$$

Factor

$$-\frac{11}{12} = -0.9166666666666666$$