Solve (-45/9)-(-31/6)-24/9+31/6=

$$( - 4 \frac { 5 } { 9 } ) - ( - 3 \frac { 1 } { 6 } ) - 2 \frac { 4 } { 9 } + 3 \frac { 1 } { 6 } =$$

Evaluate

$$-\frac{2}{3}\approx -0.666666667$$

Solution Steps

Multiply 4 and 9 to get 36.

$$-\frac{36+5}{9}-\left(-\frac{3\times 6+1}{6}\right)-\frac{2\times 9+4}{9}+\frac{3\times 6+1}{6}$$

Add 36 and 5 to get 41.

$$-\frac{41}{9}-\left(-\frac{3\times 6+1}{6}\right)-\frac{2\times 9+4}{9}+\frac{3\times 6+1}{6}$$

Multiply 3 and 6 to get 18.

$$-\frac{41}{9}-\left(-\frac{18+1}{6}\right)-\frac{2\times 9+4}{9}+\frac{3\times 6+1}{6}$$

Add 18 and 1 to get 19.

$$-\frac{41}{9}-\left(-\frac{19}{6}\right)-\frac{2\times 9+4}{9}+\frac{3\times 6+1}{6}$$

The opposite of -\frac{19}{6} is \frac{19}{6}.

$$-\frac{41}{9}+\frac{19}{6}-\frac{2\times 9+4}{9}+\frac{3\times 6+1}{6}$$

Least common multiple of 9 and 6 is 18. Convert -\frac{41}{9} and \frac{19}{6} to fractions with denominator 18.

$$-\frac{82}{18}+\frac{57}{18}-\frac{2\times 9+4}{9}+\frac{3\times 6+1}{6}$$

Since -\frac{82}{18} and \frac{57}{18} have the same denominator, add them by adding their numerators.

$$\frac{-82+57}{18}-\frac{2\times 9+4}{9}+\frac{3\times 6+1}{6}$$

Add -82 and 57 to get -25.

$$-\frac{25}{18}-\frac{2\times 9+4}{9}+\frac{3\times 6+1}{6}$$

Multiply 2 and 9 to get 18.

$$-\frac{25}{18}-\frac{18+4}{9}+\frac{3\times 6+1}{6}$$

Add 18 and 4 to get 22.

$$-\frac{25}{18}-\frac{22}{9}+\frac{3\times 6+1}{6}$$

Least common multiple of 18 and 9 is 18. Convert -\frac{25}{18} and \frac{22}{9} to fractions with denominator 18.

$$-\frac{25}{18}-\frac{44}{18}+\frac{3\times 6+1}{6}$$

Since -\frac{25}{18} and \frac{44}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-25-44}{18}+\frac{3\times 6+1}{6}$$

Subtract 44 from -25 to get -69.

$$\frac{-69}{18}+\frac{3\times 6+1}{6}$$

Reduce the fraction \frac{-69}{18} to lowest terms by extracting and canceling out 3.

$$-\frac{23}{6}+\frac{3\times 6+1}{6}$$

Multiply 3 and 6 to get 18.

$$-\frac{23}{6}+\frac{18+1}{6}$$

Add 18 and 1 to get 19.

$$-\frac{23}{6}+\frac{19}{6}$$

Since -\frac{23}{6} and \frac{19}{6} have the same denominator, add them by adding their numerators.

$$\frac{-23+19}{6}$$

Add -23 and 19 to get -4.

$$\frac{-4}{6}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{2}{3} = -0.6666666666666666$$