Solve -1/2-[2-(1/3-1/4)]-(11/3-2frac{1}{2})=

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

Evaluate

$$-\frac{5}{4}=-1.25$$

Solution Steps

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

$$-\frac{1}{2}-\left(2-\left(\frac{4}{12}-\frac{3}{12}\right)\right)-\left(\frac{1\times 3+1}{3}-\frac{2\times 2+1}{2}\right)$$

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

$$-\frac{1}{2}-\left(2-\frac{4-3}{12}\right)-\left(\frac{1\times 3+1}{3}-\frac{2\times 2+1}{2}\right)$$

Subtract 3 from 4 to get 1.

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

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

$$-\frac{1}{2}-\left(\frac{24}{12}-\frac{1}{12}\right)-\left(\frac{1\times 3+1}{3}-\frac{2\times 2+1}{2}\right)$$

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

$$-\frac{1}{2}-\frac{24-1}{12}-\left(\frac{1\times 3+1}{3}-\frac{2\times 2+1}{2}\right)$$

Subtract 1 from 24 to get 23.

$$-\frac{1}{2}-\frac{23}{12}-\left(\frac{1\times 3+1}{3}-\frac{2\times 2+1}{2}\right)$$

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

$$-\frac{6}{12}-\frac{23}{12}-\left(\frac{1\times 3+1}{3}-\frac{2\times 2+1}{2}\right)$$

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

$$\frac{-6-23}{12}-\left(\frac{1\times 3+1}{3}-\frac{2\times 2+1}{2}\right)$$

Subtract 23 from -6 to get -29.

$$-\frac{29}{12}-\left(\frac{1\times 3+1}{3}-\frac{2\times 2+1}{2}\right)$$

Multiply 1 and 3 to get 3.

$$-\frac{29}{12}-\left(\frac{3+1}{3}-\frac{2\times 2+1}{2}\right)$$

Add 3 and 1 to get 4.

$$-\frac{29}{12}-\left(\frac{4}{3}-\frac{2\times 2+1}{2}\right)$$

Multiply 2 and 2 to get 4.

$$-\frac{29}{12}-\left(\frac{4}{3}-\frac{4+1}{2}\right)$$

Add 4 and 1 to get 5.

$$-\frac{29}{12}-\left(\frac{4}{3}-\frac{5}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{5}{2} to fractions with denominator 6.

$$-\frac{29}{12}-\left(\frac{8}{6}-\frac{15}{6}\right)$$

Since \frac{8}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{29}{12}-\frac{8-15}{6}$$

Subtract 15 from 8 to get -7.

$$-\frac{29}{12}-\left(-\frac{7}{6}\right)$$

The opposite of -\frac{7}{6} is \frac{7}{6}.

$$-\frac{29}{12}+\frac{7}{6}$$

Least common multiple of 12 and 6 is 12. Convert -\frac{29}{12} and \frac{7}{6} to fractions with denominator 12.

$$-\frac{29}{12}+\frac{14}{12}$$

Since -\frac{29}{12} and \frac{14}{12} have the same denominator, add them by adding their numerators.

$$\frac{-29+14}{12}$$

Add -29 and 14 to get -15.

$$\frac{-15}{12}$$

Reduce the fraction \frac{-15}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{5}{4}$$

Factor

$$-\frac{5}{4} = -1\frac{1}{4} = -1.25$$