Solve -(-1/2+3)-[2-(1/3-1/4)]=

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

Evaluate

$$-\frac{53}{12}\approx -4.416666667$$

Solution Steps

Convert 3 to fraction \frac{6}{2}.

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

Since -\frac{1}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

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

Add -1 and 6 to get 5.

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

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$-\frac{5}{2}-\left(2-\left(\frac{4}{12}-\frac{3}{12}\right)\right)$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{2}-\left(2-\frac{4-3}{12}\right)$$

Subtract 3 from 4 to get 1.

$$-\frac{5}{2}-\left(2-\frac{1}{12}\right)$$

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

$$-\frac{5}{2}-\left(\frac{24}{12}-\frac{1}{12}\right)$$

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

$$-\frac{5}{2}-\frac{24-1}{12}$$

Subtract 1 from 24 to get 23.

$$-\frac{5}{2}-\frac{23}{12}$$

Least common multiple of 2 and 12 is 12. Convert -\frac{5}{2} and \frac{23}{12} to fractions with denominator 12.

$$-\frac{30}{12}-\frac{23}{12}$$

Since -\frac{30}{12} and \frac{23}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-30-23}{12}$$

Subtract 23 from -30 to get -53.

$$-\frac{53}{12}$$

Factor

$$-\frac{53}{12} = -4\frac{5}{12} = -4.416666666666667$$