Solve 4/3-1/9-1/3+-3/2-1+frac{17}{18}

$$\frac{ 4 }{ 3 } - \frac{ 1 }{ 9 } - \frac{ 1 }{ 3 } +- \frac{ 3 }{ 2 } -1+ \frac{ 17 }{ 18 }$$

Evaluate

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

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{4}{3} and \frac{1}{9} to fractions with denominator 9.

$$\frac{12}{9}-\frac{1}{9}-\frac{1}{3}-\frac{3}{2}-1+\frac{17}{18}$$

Since \frac{12}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-1}{9}-\frac{1}{3}-\frac{3}{2}-1+\frac{17}{18}$$

Subtract 1 from 12 to get 11.

$$\frac{11}{9}-\frac{1}{3}-\frac{3}{2}-1+\frac{17}{18}$$

Least common multiple of 9 and 3 is 9. Convert \frac{11}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{11}{9}-\frac{3}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Since \frac{11}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-3}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Subtract 3 from 11 to get 8.

$$\frac{8}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Least common multiple of 9 and 2 is 18. Convert \frac{8}{9} and \frac{3}{2} to fractions with denominator 18.

$$\frac{16}{18}-\frac{27}{18}-1+\frac{17}{18}$$

Since \frac{16}{18} and \frac{27}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-27}{18}-1+\frac{17}{18}$$

Subtract 27 from 16 to get -11.

$$-\frac{11}{18}-1+\frac{17}{18}$$

Convert 1 to fraction \frac{18}{18}.

$$-\frac{11}{18}-\frac{18}{18}+\frac{17}{18}$$

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

$$\frac{-11-18}{18}+\frac{17}{18}$$

Subtract 18 from -11 to get -29.

$$-\frac{29}{18}+\frac{17}{18}$$

Since -\frac{29}{18} and \frac{17}{18} have the same denominator, add them by adding their numerators.

$$\frac{-29+17}{18}$$

Add -29 and 17 to get -12.

$$\frac{-12}{18}$$

Reduce the fraction \frac{-12}{18} to lowest terms by extracting and canceling out 6.

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

Factor

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