Solve -22/5+-11/6+-13/5+31/3

$$- 2 \frac { 2 } { 5 } + - 1 \frac { 1 } { 6 } + - 1 \frac { 3 } { 5 } + 3 \frac { 1 } { 3 }$$

Evaluate

$$-\frac{11}{6}\approx -1.833333333$$

Solution Steps

Multiply 2 and 5 to get 10.

$$-\frac{10+2}{5}-\frac{1\times 6+1}{6}-\frac{1\times 5+3}{5}+\frac{3\times 3+1}{3}$$

Add 10 and 2 to get 12.

$$-\frac{12}{5}-\frac{1\times 6+1}{6}-\frac{1\times 5+3}{5}+\frac{3\times 3+1}{3}$$

Multiply 1 and 6 to get 6.

$$-\frac{12}{5}-\frac{6+1}{6}-\frac{1\times 5+3}{5}+\frac{3\times 3+1}{3}$$

Add 6 and 1 to get 7.

$$-\frac{12}{5}-\frac{7}{6}-\frac{1\times 5+3}{5}+\frac{3\times 3+1}{3}$$

Least common multiple of 5 and 6 is 30. Convert -\frac{12}{5} and \frac{7}{6} to fractions with denominator 30.

$$-\frac{72}{30}-\frac{35}{30}-\frac{1\times 5+3}{5}+\frac{3\times 3+1}{3}$$

Since -\frac{72}{30} and \frac{35}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-72-35}{30}-\frac{1\times 5+3}{5}+\frac{3\times 3+1}{3}$$

Subtract 35 from -72 to get -107.

$$-\frac{107}{30}-\frac{1\times 5+3}{5}+\frac{3\times 3+1}{3}$$

Multiply 1 and 5 to get 5.

$$-\frac{107}{30}-\frac{5+3}{5}+\frac{3\times 3+1}{3}$$

Add 5 and 3 to get 8.

$$-\frac{107}{30}-\frac{8}{5}+\frac{3\times 3+1}{3}$$

Least common multiple of 30 and 5 is 30. Convert -\frac{107}{30} and \frac{8}{5} to fractions with denominator 30.

$$-\frac{107}{30}-\frac{48}{30}+\frac{3\times 3+1}{3}$$

Since -\frac{107}{30} and \frac{48}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-107-48}{30}+\frac{3\times 3+1}{3}$$

Subtract 48 from -107 to get -155.

$$\frac{-155}{30}+\frac{3\times 3+1}{3}$$

Reduce the fraction \frac{-155}{30} to lowest terms by extracting and canceling out 5.

$$-\frac{31}{6}+\frac{3\times 3+1}{3}$$

Multiply 3 and 3 to get 9.

$$-\frac{31}{6}+\frac{9+1}{3}$$

Add 9 and 1 to get 10.

$$-\frac{31}{6}+\frac{10}{3}$$

Least common multiple of 6 and 3 is 6. Convert -\frac{31}{6} and \frac{10}{3} to fractions with denominator 6.

$$-\frac{31}{6}+\frac{20}{6}$$

Since -\frac{31}{6} and \frac{20}{6} have the same denominator, add them by adding their numerators.

$$\frac{-31+20}{6}$$

Add -31 and 20 to get -11.

$$-\frac{11}{6}$$

Factor

$$-\frac{11}{6} = -1\frac{5}{6} = -1.8333333333333333$$