Solve (-47/9)*(-1)-(-31/6)-(+22/9)+|-61/6|

$$( - 4 \frac { 7 } { 9 } ) \times ( - 1 ) - ( - 3 \frac { 1 } { 6 } ) - ( + 2 \frac { 2 } { 9 } ) + | - 6 \frac { 1 } { 6 } |$$

Evaluate

$$\frac{107}{9}\approx 11.888888889$$

Solution Steps

Multiply 4 and 9 to get 36.

$$\left(-\frac{36+7}{9}\right)\left(-1\right)-\left(-\frac{3\times 6+1}{6}\right)-\frac{2\times 9+2}{9}+|-\frac{6\times 6+1}{6}|$$

Add 36 and 7 to get 43.

$$-\frac{43}{9}\left(-1\right)-\left(-\frac{3\times 6+1}{6}\right)-\frac{2\times 9+2}{9}+|-\frac{6\times 6+1}{6}|$$

Multiply -\frac{43}{9} and -1 to get \frac{43}{9}.

$$\frac{43}{9}-\left(-\frac{3\times 6+1}{6}\right)-\frac{2\times 9+2}{9}+|-\frac{6\times 6+1}{6}|$$

Multiply 3 and 6 to get 18.

$$\frac{43}{9}-\left(-\frac{18+1}{6}\right)-\frac{2\times 9+2}{9}+|-\frac{6\times 6+1}{6}|$$

Add 18 and 1 to get 19.

$$\frac{43}{9}-\left(-\frac{19}{6}\right)-\frac{2\times 9+2}{9}+|-\frac{6\times 6+1}{6}|$$

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

$$\frac{43}{9}+\frac{19}{6}-\frac{2\times 9+2}{9}+|-\frac{6\times 6+1}{6}|$$

Least common multiple of 9 and 6 is 18. Convert \frac{43}{9} and \frac{19}{6} to fractions with denominator 18.

$$\frac{86}{18}+\frac{57}{18}-\frac{2\times 9+2}{9}+|-\frac{6\times 6+1}{6}|$$

Since \frac{86}{18} and \frac{57}{18} have the same denominator, add them by adding their numerators.

$$\frac{86+57}{18}-\frac{2\times 9+2}{9}+|-\frac{6\times 6+1}{6}|$$

Add 86 and 57 to get 143.

$$\frac{143}{18}-\frac{2\times 9+2}{9}+|-\frac{6\times 6+1}{6}|$$

Multiply 2 and 9 to get 18.

$$\frac{143}{18}-\frac{18+2}{9}+|-\frac{6\times 6+1}{6}|$$

Add 18 and 2 to get 20.

$$\frac{143}{18}-\frac{20}{9}+|-\frac{6\times 6+1}{6}|$$

Least common multiple of 18 and 9 is 18. Convert \frac{143}{18} and \frac{20}{9} to fractions with denominator 18.

$$\frac{143}{18}-\frac{40}{18}+|-\frac{6\times 6+1}{6}|$$

Since \frac{143}{18} and \frac{40}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{143-40}{18}+|-\frac{6\times 6+1}{6}|$$

Subtract 40 from 143 to get 103.

$$\frac{103}{18}+|-\frac{6\times 6+1}{6}|$$

Multiply 6 and 6 to get 36.

$$\frac{103}{18}+|-\frac{36+1}{6}|$$

Add 36 and 1 to get 37.

$$\frac{103}{18}+|-\frac{37}{6}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{37}{6} is \frac{37}{6}.

$$\frac{103}{18}+\frac{37}{6}$$

Least common multiple of 18 and 6 is 18. Convert \frac{103}{18} and \frac{37}{6} to fractions with denominator 18.

$$\frac{103}{18}+\frac{111}{18}$$

Since \frac{103}{18} and \frac{111}{18} have the same denominator, add them by adding their numerators.

$$\frac{103+111}{18}$$

Add 103 and 111 to get 214.

$$\frac{214}{18}$$

Reduce the fraction \frac{214}{18} to lowest terms by extracting and canceling out 2.

$$\frac{107}{9}$$

Factor

$$\frac{107}{3 ^ {2}} = 11\frac{8}{9} = 11.88888888888889$$