Solve -41/3+31/6-31/3-22/3

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

Evaluate

$$-\frac{43}{6}\approx -7.166666667$$

Solution Steps

Multiply 4 and 3 to get 12.

$$-\frac{12+1}{3}+\frac{3\times 6+1}{6}-\frac{3\times 3+1}{3}-\frac{2\times 3+2}{3}$$

Add 12 and 1 to get 13.

$$-\frac{13}{3}+\frac{3\times 6+1}{6}-\frac{3\times 3+1}{3}-\frac{2\times 3+2}{3}$$

Multiply 3 and 6 to get 18.

$$-\frac{13}{3}+\frac{18+1}{6}-\frac{3\times 3+1}{3}-\frac{2\times 3+2}{3}$$

Add 18 and 1 to get 19.

$$-\frac{13}{3}+\frac{19}{6}-\frac{3\times 3+1}{3}-\frac{2\times 3+2}{3}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{13}{3} and \frac{19}{6} to fractions with denominator 6.

$$-\frac{26}{6}+\frac{19}{6}-\frac{3\times 3+1}{3}-\frac{2\times 3+2}{3}$$

Since -\frac{26}{6} and \frac{19}{6} have the same denominator, add them by adding their numerators.

$$\frac{-26+19}{6}-\frac{3\times 3+1}{3}-\frac{2\times 3+2}{3}$$

Add -26 and 19 to get -7.

$$-\frac{7}{6}-\frac{3\times 3+1}{3}-\frac{2\times 3+2}{3}$$

Multiply 3 and 3 to get 9.

$$-\frac{7}{6}-\frac{9+1}{3}-\frac{2\times 3+2}{3}$$

Add 9 and 1 to get 10.

$$-\frac{7}{6}-\frac{10}{3}-\frac{2\times 3+2}{3}$$

Least common multiple of 6 and 3 is 6. Convert -\frac{7}{6} and \frac{10}{3} to fractions with denominator 6.

$$-\frac{7}{6}-\frac{20}{6}-\frac{2\times 3+2}{3}$$

Since -\frac{7}{6} and \frac{20}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-20}{6}-\frac{2\times 3+2}{3}$$

Subtract 20 from -7 to get -27.

$$\frac{-27}{6}-\frac{2\times 3+2}{3}$$

Reduce the fraction \frac{-27}{6} to lowest terms by extracting and canceling out 3.

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

Multiply 2 and 3 to get 6.

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

Add 6 and 2 to get 8.

$$-\frac{9}{2}-\frac{8}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{9}{2} and \frac{8}{3} to fractions with denominator 6.

$$-\frac{27}{6}-\frac{16}{6}$$

Since -\frac{27}{6} and \frac{16}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-27-16}{6}$$

Subtract 16 from -27 to get -43.

$$-\frac{43}{6}$$

Factor

$$-\frac{43}{6} = -7\frac{1}{6} = -7.166666666666667$$