Solve {l}{-1+3/2+1/4-2/3+2-2+2/3-frac{2}{3}-frac{2}{3}}{-2+frac{2}{3}+frac{1}{2}-1+frac{1}{2}-frac{1}{2}+1-frac{1}{2}+1-frac{1}{2}+frac{1}{2}+frac{1}{2}}

$$\left. \begin{array} { l } { - 1 + \frac { 3 } { 2 } + \frac { 1 } { 4 } - \frac { 2 } { 3 } + 2 - 2 + \frac { 2 } { 3 } - \frac { 2 } { 3 } - \frac { 2 } { 3 } } \\ { - 2 + \frac { 2 } { 3 } + \frac { 1 } { 2 } - 1 + \frac { 1 } { 2 } - \frac { 1 } { 2 } + 1 - \frac { 1 } { 2 } + 1 - \frac { 1 } { 2 } + \frac { 1 } { 2 } + \frac { 1 } { 2 } } \end{array} \right.$$

Evaluate

$$-\frac{5}{12}\approx -0.416666667$$

Solution Steps

Convert -1 to fraction -\frac{2}{2}.

$$-\frac{2}{2}+\frac{3}{2}+\frac{1}{4}-\frac{2}{3}+2-2+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

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

$$\frac{-2+3}{2}+\frac{1}{4}-\frac{2}{3}+2-2+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Add -2 and 3 to get 1.

$$\frac{1}{2}+\frac{1}{4}-\frac{2}{3}+2-2+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

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

$$\frac{2}{4}+\frac{1}{4}-\frac{2}{3}+2-2+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

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

$$\frac{2+1}{4}-\frac{2}{3}+2-2+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Add 2 and 1 to get 3.

$$\frac{3}{4}-\frac{2}{3}+2-2+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{9}{12}-\frac{8}{12}+2-2+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since \frac{9}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-8}{12}+2-2+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Subtract 8 from 9 to get 1.

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

Convert 2 to fraction \frac{24}{12}.

$$\frac{1}{12}+\frac{24}{12}-2+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since \frac{1}{12} and \frac{24}{12} have the same denominator, add them by adding their numerators.

$$\frac{1+24}{12}-2+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Add 1 and 24 to get 25.

$$\frac{25}{12}-2+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Convert 2 to fraction \frac{24}{12}.

$$\frac{25}{12}-\frac{24}{12}+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since \frac{25}{12} and \frac{24}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-24}{12}+\frac{2}{3}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Subtract 24 from 25 to get 1.

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

Least common multiple of 12 and 3 is 12. Convert \frac{1}{12} and \frac{2}{3} to fractions with denominator 12.

$$\frac{1}{12}+\frac{8}{12}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since \frac{1}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{1+8}{12}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Add 1 and 8 to get 9.

$$\frac{9}{12}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}-\frac{2}{3}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{9}{12}-\frac{8}{12}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since \frac{9}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-8}{12}-\frac{2}{3}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Subtract 8 from 9 to get 1.

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

Least common multiple of 12 and 3 is 12. Convert \frac{1}{12} and \frac{2}{3} to fractions with denominator 12.

$$\frac{1}{12}-\frac{8}{12}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since \frac{1}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-8}{12}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Subtract 8 from 1 to get -7.

$$-\frac{7}{12}-2+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Convert 2 to fraction \frac{24}{12}.

$$-\frac{7}{12}-\frac{24}{12}+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since -\frac{7}{12} and \frac{24}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-24}{12}+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Subtract 24 from -7 to get -31.

$$-\frac{31}{12}+\frac{2}{3}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Least common multiple of 12 and 3 is 12. Convert -\frac{31}{12} and \frac{2}{3} to fractions with denominator 12.

$$-\frac{31}{12}+\frac{8}{12}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since -\frac{31}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{-31+8}{12}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Add -31 and 8 to get -23.

$$-\frac{23}{12}+\frac{1}{2}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Least common multiple of 12 and 2 is 12. Convert -\frac{23}{12} and \frac{1}{2} to fractions with denominator 12.

$$-\frac{23}{12}+\frac{6}{12}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since -\frac{23}{12} and \frac{6}{12} have the same denominator, add them by adding their numerators.

$$\frac{-23+6}{12}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Add -23 and 6 to get -17.

$$-\frac{17}{12}-1+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

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

$$-\frac{17}{12}-\frac{12}{12}+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since -\frac{17}{12} and \frac{12}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-17-12}{12}+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Subtract 12 from -17 to get -29.

$$-\frac{29}{12}+\frac{1}{2}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Least common multiple of 12 and 2 is 12. Convert -\frac{29}{12} and \frac{1}{2} to fractions with denominator 12.

$$-\frac{29}{12}+\frac{6}{12}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since -\frac{29}{12} and \frac{6}{12} have the same denominator, add them by adding their numerators.

$$\frac{-29+6}{12}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Add -29 and 6 to get -23.

$$-\frac{23}{12}-\frac{1}{2}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Least common multiple of 12 and 2 is 12. Convert -\frac{23}{12} and \frac{1}{2} to fractions with denominator 12.

$$-\frac{23}{12}-\frac{6}{12}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since -\frac{23}{12} and \frac{6}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-23-6}{12}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Subtract 6 from -23 to get -29.

$$-\frac{29}{12}+1-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

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

$$-\frac{29}{12}+\frac{12}{12}-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since -\frac{29}{12} and \frac{12}{12} have the same denominator, add them by adding their numerators.

$$\frac{-29+12}{12}-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Add -29 and 12 to get -17.

$$-\frac{17}{12}-\frac{1}{2}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Least common multiple of 12 and 2 is 12. Convert -\frac{17}{12} and \frac{1}{2} to fractions with denominator 12.

$$-\frac{17}{12}-\frac{6}{12}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since -\frac{17}{12} and \frac{6}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-17-6}{12}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Subtract 6 from -17 to get -23.

$$-\frac{23}{12}+1-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

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

$$-\frac{23}{12}+\frac{12}{12}-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Since -\frac{23}{12} and \frac{12}{12} have the same denominator, add them by adding their numerators.

$$\frac{-23+12}{12}-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Add -23 and 12 to get -11.

$$-\frac{11}{12}-\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$$

Least common multiple of 12 and 2 is 12. Convert -\frac{11}{12} and \frac{1}{2} to fractions with denominator 12.

$$-\frac{11}{12}-\frac{6}{12}+\frac{1}{2}+\frac{1}{2}$$

Since -\frac{11}{12} and \frac{6}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-6}{12}+\frac{1}{2}+\frac{1}{2}$$

Subtract 6 from -11 to get -17.

$$-\frac{17}{12}+\frac{1}{2}+\frac{1}{2}$$

Least common multiple of 12 and 2 is 12. Convert -\frac{17}{12} and \frac{1}{2} to fractions with denominator 12.

$$-\frac{17}{12}+\frac{6}{12}+\frac{1}{2}$$

Since -\frac{17}{12} and \frac{6}{12} have the same denominator, add them by adding their numerators.

$$\frac{-17+6}{12}+\frac{1}{2}$$

Add -17 and 6 to get -11.

$$-\frac{11}{12}+\frac{1}{2}$$

Least common multiple of 12 and 2 is 12. Convert -\frac{11}{12} and \frac{1}{2} to fractions with denominator 12.

$$-\frac{11}{12}+\frac{6}{12}$$

Since -\frac{11}{12} and \frac{6}{12} have the same denominator, add them by adding their numerators.

$$\frac{-11+6}{12}$$

Add -11 and 6 to get -5.

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

Factor

$$-\frac{5}{12} = -0.4166666666666667$$