Solve 10/3-4/9-1/6+11/18

$$\frac { 10 } { 3 } - \frac { 4 } { 9 } - \frac { 1 } { 6 } + \frac { 11 } { 18 }$$

Evaluate

$$\frac{10}{3}\approx 3.333333333$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{10}{3} and \frac{4}{9} to fractions with denominator 9.

$$\frac{30}{9}-\frac{4}{9}-\frac{1}{6}+\frac{11}{18}$$

Since \frac{30}{9} and \frac{4}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-4}{9}-\frac{1}{6}+\frac{11}{18}$$

Subtract 4 from 30 to get 26.

$$\frac{26}{9}-\frac{1}{6}+\frac{11}{18}$$

Least common multiple of 9 and 6 is 18. Convert \frac{26}{9} and \frac{1}{6} to fractions with denominator 18.

$$\frac{52}{18}-\frac{3}{18}+\frac{11}{18}$$

Since \frac{52}{18} and \frac{3}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{52-3}{18}+\frac{11}{18}$$

Subtract 3 from 52 to get 49.

$$\frac{49}{18}+\frac{11}{18}$$

Since \frac{49}{18} and \frac{11}{18} have the same denominator, add them by adding their numerators.

$$\frac{49+11}{18}$$

Add 49 and 11 to get 60.

$$\frac{60}{18}$$

Reduce the fraction \frac{60}{18} to lowest terms by extracting and canceling out 6.

$$\frac{10}{3}$$

Factor

$$\frac{2 \cdot 5}{3} = 3\frac{1}{3} = 3.3333333333333335$$