Solve (3/11+2/5-5/22-6/11)

$$( \frac { 3 } { 11 } + \frac { 2 } { 5 } - \frac { 5 } { 22 } - \frac { 6 } { 11 } )$$

Evaluate

$$-\frac{1}{10}=-0.1$$

Solution Steps

Least common multiple of 11 and 5 is 55. Convert \frac{3}{11} and \frac{2}{5} to fractions with denominator 55.

$$\frac{15}{55}+\frac{22}{55}-\frac{5}{22}-\frac{6}{11}$$

Since \frac{15}{55} and \frac{22}{55} have the same denominator, add them by adding their numerators.

$$\frac{15+22}{55}-\frac{5}{22}-\frac{6}{11}$$

Add 15 and 22 to get 37.

$$\frac{37}{55}-\frac{5}{22}-\frac{6}{11}$$

Least common multiple of 55 and 22 is 110. Convert \frac{37}{55} and \frac{5}{22} to fractions with denominator 110.

$$\frac{74}{110}-\frac{25}{110}-\frac{6}{11}$$

Since \frac{74}{110} and \frac{25}{110} have the same denominator, subtract them by subtracting their numerators.

$$\frac{74-25}{110}-\frac{6}{11}$$

Subtract 25 from 74 to get 49.

$$\frac{49}{110}-\frac{6}{11}$$

Least common multiple of 110 and 11 is 110. Convert \frac{49}{110} and \frac{6}{11} to fractions with denominator 110.

$$\frac{49}{110}-\frac{60}{110}$$

Since \frac{49}{110} and \frac{60}{110} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49-60}{110}$$

Subtract 60 from 49 to get -11.

$$\frac{-11}{110}$$

Reduce the fraction \frac{-11}{110} to lowest terms by extracting and canceling out 11.

$$-\frac{1}{10}$$

Factor

$$-\frac{1}{10} = -0.1$$