Solve (+1/7)+(-2/3)+(+4/7)+(-6/7)

$$( + \frac { 1 } { 7 } ) + ( - \frac { 2 } { 3 } ) + ( + \frac { 4 } { 7 } ) + ( - \frac { 6 } { 7 } )$$

Evaluate

$$-\frac{17}{21}\approx -0.80952381$$

Solution Steps

Least common multiple of 7 and 3 is 21. Convert \frac{1}{7} and \frac{2}{3} to fractions with denominator 21.

$$\frac{3}{21}-\frac{14}{21}+\frac{4}{7}-\frac{6}{7}$$

Since \frac{3}{21} and \frac{14}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-14}{21}+\frac{4}{7}-\frac{6}{7}$$

Subtract 14 from 3 to get -11.

$$-\frac{11}{21}+\frac{4}{7}-\frac{6}{7}$$

Least common multiple of 21 and 7 is 21. Convert -\frac{11}{21} and \frac{4}{7} to fractions with denominator 21.

$$-\frac{11}{21}+\frac{12}{21}-\frac{6}{7}$$

Since -\frac{11}{21} and \frac{12}{21} have the same denominator, add them by adding their numerators.

$$\frac{-11+12}{21}-\frac{6}{7}$$

Add -11 and 12 to get 1.

$$\frac{1}{21}-\frac{6}{7}$$

Least common multiple of 21 and 7 is 21. Convert \frac{1}{21} and \frac{6}{7} to fractions with denominator 21.

$$\frac{1}{21}-\frac{18}{21}$$

Since \frac{1}{21} and \frac{18}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-18}{21}$$

Subtract 18 from 1 to get -17.

$$-\frac{17}{21}$$

Factor

$$-\frac{17}{21} = -0.8095238095238095$$