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

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

Evaluate

$$-\frac{7}{6}\approx -1.166666667$$

Solution Steps

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

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

Since -\frac{5}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 6 from -5 to get -11.

$$\frac{2}{3}\left(-\frac{11}{4}+\frac{5}{2}-\frac{6}{4}\right)$$

Least common multiple of 4 and 2 is 4. Convert -\frac{11}{4} and \frac{5}{2} to fractions with denominator 4.

$$\frac{2}{3}\left(-\frac{11}{4}+\frac{10}{4}-\frac{6}{4}\right)$$

Since -\frac{11}{4} and \frac{10}{4} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}\left(\frac{-11+10}{4}-\frac{6}{4}\right)$$

Add -11 and 10 to get -1.

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

Since -\frac{1}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}\times \frac{-1-6}{4}$$

Subtract 6 from -1 to get -7.

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

Multiply \frac{2}{3} times -\frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-7\right)}{3\times 4}$$

Do the multiplications in the fraction \frac{2\left(-7\right)}{3\times 4}.

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

Reduce the fraction \frac{-14}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{7}{6}$$

Factor

$$-\frac{7}{6} = -1\frac{1}{6} = -1.1666666666666667$$