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

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

Evaluate

$$-\frac{3}{2}=-1.5$$

Solution Steps

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

$$\frac{4}{12}-\frac{9}{12}-\left(\frac{1}{3}+\frac{3}{4}\right)$$

Since \frac{4}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-9}{12}-\left(\frac{1}{3}+\frac{3}{4}\right)$$

Subtract 9 from 4 to get -5.

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

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

$$-\frac{5}{12}-\left(\frac{4}{12}+\frac{9}{12}\right)$$

Since \frac{4}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$-\frac{5}{12}-\frac{4+9}{12}$$

Add 4 and 9 to get 13.

$$-\frac{5}{12}-\frac{13}{12}$$

Since -\frac{5}{12} and \frac{13}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-13}{12}$$

Subtract 13 from -5 to get -18.

$$\frac{-18}{12}$$

Reduce the fraction \frac{-18}{12} to lowest terms by extracting and canceling out 6.

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

Factor

$$-\frac{3}{2} = -1\frac{1}{2} = -1.5$$