Solve 2/3-16/3-9/2+3

$$\frac { 2 } { 3 } - \frac { 16 } { 3 } - \frac { 9 } { 2 } + 3$$

Evaluate

$$-\frac{37}{6}\approx -6.166666667$$

Solution Steps

Since \frac{2}{3} and \frac{16}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-16}{3}-\frac{9}{2}+3$$

Subtract 16 from 2 to get -14.

$$-\frac{14}{3}-\frac{9}{2}+3$$

Least common multiple of 3 and 2 is 6. Convert -\frac{14}{3} and \frac{9}{2} to fractions with denominator 6.

$$-\frac{28}{6}-\frac{27}{6}+3$$

Since -\frac{28}{6} and \frac{27}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-28-27}{6}+3$$

Subtract 27 from -28 to get -55.

$$-\frac{55}{6}+3$$

Convert 3 to fraction \frac{18}{6}.

$$-\frac{55}{6}+\frac{18}{6}$$

Since -\frac{55}{6} and \frac{18}{6} have the same denominator, add them by adding their numerators.

$$\frac{-55+18}{6}$$

Add -55 and 18 to get -37.

$$-\frac{37}{6}$$

Factor

$$-\frac{37}{6} = -6\frac{1}{6} = -6.166666666666667$$