Solve 17/11-(2/5-5/11)

$$\frac { 17 } { 11 } - ( \frac { 2 } { 5 } - \frac { 5 } { 11 } )$$

Evaluate

$$\frac{8}{5}=1.6$$

Solution Steps

Least common multiple of 5 and 11 is 55. Convert \frac{2}{5} and \frac{5}{11} to fractions with denominator 55.

$$\frac{17}{11}-\left(\frac{22}{55}-\frac{25}{55}\right)$$

Since \frac{22}{55} and \frac{25}{55} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{11}-\frac{22-25}{55}$$

Subtract 25 from 22 to get -3.

$$\frac{17}{11}-\left(-\frac{3}{55}\right)$$

The opposite of -\frac{3}{55} is \frac{3}{55}.

$$\frac{17}{11}+\frac{3}{55}$$

Least common multiple of 11 and 55 is 55. Convert \frac{17}{11} and \frac{3}{55} to fractions with denominator 55.

$$\frac{85}{55}+\frac{3}{55}$$

Since \frac{85}{55} and \frac{3}{55} have the same denominator, add them by adding their numerators.

$$\frac{85+3}{55}$$

Add 85 and 3 to get 88.

$$\frac{88}{55}$$

Reduce the fraction \frac{88}{55} to lowest terms by extracting and canceling out 11.

$$\frac{8}{5}$$

Factor

$$\frac{2 ^ {3}}{5} = 1\frac{3}{5} = 1.6$$