Solve 11/17-(1/2-2/17)+1/3

$$\frac { 11 } { 17 } - ( \frac { 1 } { 2 } - \frac { 2 } { 17 } ) + \frac { 1 } { 3 }$$

Evaluate

$$\frac{61}{102}\approx 0.598039216$$

Solution Steps

Least common multiple of 2 and 17 is 34. Convert \frac{1}{2} and \frac{2}{17} to fractions with denominator 34.

$$\frac{11}{17}-\left(\frac{17}{34}-\frac{4}{34}\right)+\frac{1}{3}$$

Since \frac{17}{34} and \frac{4}{34} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{17}-\frac{17-4}{34}+\frac{1}{3}$$

Subtract 4 from 17 to get 13.

$$\frac{11}{17}-\frac{13}{34}+\frac{1}{3}$$

Least common multiple of 17 and 34 is 34. Convert \frac{11}{17} and \frac{13}{34} to fractions with denominator 34.

$$\frac{22}{34}-\frac{13}{34}+\frac{1}{3}$$

Since \frac{22}{34} and \frac{13}{34} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-13}{34}+\frac{1}{3}$$

Subtract 13 from 22 to get 9.

$$\frac{9}{34}+\frac{1}{3}$$

Least common multiple of 34 and 3 is 102. Convert \frac{9}{34} and \frac{1}{3} to fractions with denominator 102.

$$\frac{27}{102}+\frac{34}{102}$$

Since \frac{27}{102} and \frac{34}{102} have the same denominator, add them by adding their numerators.

$$\frac{27+34}{102}$$

Add 27 and 34 to get 61.

$$\frac{61}{102}$$

Factor

$$\frac{61}{2 \cdot 3 \cdot 17} = 0.5980392156862745$$