Solve (-32/3)+(-11/2)+(-22/3)+2

$$( - 3 \frac { 2 } { 3 } ) + ( - 1 \frac { 1 } { 2 } ) + ( - 2 \frac { 2 } { 3 } ) + 2$$

Evaluate

$$-\frac{35}{6}\approx -5.833333333$$

Solution Steps

Multiply 3 and 3 to get 9.

$$-\frac{9+2}{3}-\frac{1\times 2+1}{2}-\frac{2\times 3+2}{3}+2$$

Add 9 and 2 to get 11.

$$-\frac{11}{3}-\frac{1\times 2+1}{2}-\frac{2\times 3+2}{3}+2$$

Multiply 1 and 2 to get 2.

$$-\frac{11}{3}-\frac{2+1}{2}-\frac{2\times 3+2}{3}+2$$

Add 2 and 1 to get 3.

$$-\frac{11}{3}-\frac{3}{2}-\frac{2\times 3+2}{3}+2$$

Least common multiple of 3 and 2 is 6. Convert -\frac{11}{3} and \frac{3}{2} to fractions with denominator 6.

$$-\frac{22}{6}-\frac{9}{6}-\frac{2\times 3+2}{3}+2$$

Since -\frac{22}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-22-9}{6}-\frac{2\times 3+2}{3}+2$$

Subtract 9 from -22 to get -31.

$$-\frac{31}{6}-\frac{2\times 3+2}{3}+2$$

Multiply 2 and 3 to get 6.

$$-\frac{31}{6}-\frac{6+2}{3}+2$$

Add 6 and 2 to get 8.

$$-\frac{31}{6}-\frac{8}{3}+2$$

Least common multiple of 6 and 3 is 6. Convert -\frac{31}{6} and \frac{8}{3} to fractions with denominator 6.

$$-\frac{31}{6}-\frac{16}{6}+2$$

Since -\frac{31}{6} and \frac{16}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-31-16}{6}+2$$

Subtract 16 from -31 to get -47.

$$-\frac{47}{6}+2$$

Convert 2 to fraction \frac{12}{6}.

$$-\frac{47}{6}+\frac{12}{6}$$

Since -\frac{47}{6} and \frac{12}{6} have the same denominator, add them by adding their numerators.

$$\frac{-47+12}{6}$$

Add -47 and 12 to get -35.

$$-\frac{35}{6}$$

Factor

$$-\frac{35}{6} = -5\frac{5}{6} = -5.833333333333333$$