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

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

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

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

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

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

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

Subtract 1 from 12 to get 11.

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

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

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

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

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

Subtract 3 from 11 to get 8.

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

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

$$\frac{8}{9}-\frac{6}{9}-1+\frac{17}{18}$$

Since \frac{8}{9} and \frac{6}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-6}{9}-1+\frac{17}{18}$$

Subtract 6 from 8 to get 2.

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

Convert 1 to fraction \frac{9}{9}.

$$\frac{2}{9}-\frac{9}{9}+\frac{17}{18}$$

Since \frac{2}{9} and \frac{9}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-9}{9}+\frac{17}{18}$$

Subtract 9 from 2 to get -7.

$$-\frac{7}{9}+\frac{17}{18}$$

Least common multiple of 9 and 18 is 18. Convert -\frac{7}{9} and \frac{17}{18} to fractions with denominator 18.

$$-\frac{14}{18}+\frac{17}{18}$$

Since -\frac{14}{18} and \frac{17}{18} have the same denominator, add them by adding their numerators.

$$\frac{-14+17}{18}$$

Add -14 and 17 to get 3.

$$\frac{3}{18}$$

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

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$