Solve (-5/6)+(+2/9)+-8/9+1/6+(-frac{5}{9})

$$( - \frac { 5 } { 6 } ) + ( + \frac { 2 } { 9 } ) + \frac { - 8 } { 9 } + \frac { 1 } { 6 } + ( - \frac { 5 } { 9 } )$$

Evaluate

$$-\frac{17}{9}\approx -1.888888889$$

Solution Steps

Least common multiple of 6 and 9 is 18. Convert -\frac{5}{6} and \frac{2}{9} to fractions with denominator 18.

$$-\frac{15}{18}+\frac{4}{18}+\frac{-8}{9}+\frac{1}{6}-\frac{5}{9}$$

Since -\frac{15}{18} and \frac{4}{18} have the same denominator, add them by adding their numerators.

$$\frac{-15+4}{18}+\frac{-8}{9}+\frac{1}{6}-\frac{5}{9}$$

Add -15 and 4 to get -11.

$$-\frac{11}{18}+\frac{-8}{9}+\frac{1}{6}-\frac{5}{9}$$

Fraction \frac{-8}{9} can be rewritten as -\frac{8}{9} by extracting the negative sign.

$$-\frac{11}{18}-\frac{8}{9}+\frac{1}{6}-\frac{5}{9}$$

Least common multiple of 18 and 9 is 18. Convert -\frac{11}{18} and \frac{8}{9} to fractions with denominator 18.

$$-\frac{11}{18}-\frac{16}{18}+\frac{1}{6}-\frac{5}{9}$$

Since -\frac{11}{18} and \frac{16}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-16}{18}+\frac{1}{6}-\frac{5}{9}$$

Subtract 16 from -11 to get -27.

$$\frac{-27}{18}+\frac{1}{6}-\frac{5}{9}$$

Reduce the fraction \frac{-27}{18} to lowest terms by extracting and canceling out 9.

$$-\frac{3}{2}+\frac{1}{6}-\frac{5}{9}$$

Least common multiple of 2 and 6 is 6. Convert -\frac{3}{2} and \frac{1}{6} to fractions with denominator 6.

$$-\frac{9}{6}+\frac{1}{6}-\frac{5}{9}$$

Since -\frac{9}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{-9+1}{6}-\frac{5}{9}$$

Add -9 and 1 to get -8.

$$\frac{-8}{6}-\frac{5}{9}$$

Reduce the fraction \frac{-8}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{4}{3}-\frac{5}{9}$$

Least common multiple of 3 and 9 is 9. Convert -\frac{4}{3} and \frac{5}{9} to fractions with denominator 9.

$$-\frac{12}{9}-\frac{5}{9}$$

Since -\frac{12}{9} and \frac{5}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-12-5}{9}$$

Subtract 5 from -12 to get -17.

$$-\frac{17}{9}$$

Factor

$$-\frac{17}{9} = -1\frac{8}{9} = -1.8888888888888888$$