Solve -2/3+(-4/7+1/14)

$$- \frac { 2 } { 3 } + ( - \frac { 4 } { 7 } + \frac { 1 } { 14 } )$$

Evaluate

$$-\frac{7}{6}\approx -1.166666667$$

Solution Steps

Least common multiple of 3 and 7 is 21. Convert -\frac{2}{3} and \frac{4}{7} to fractions with denominator 21.

$$-\frac{14}{21}-\frac{12}{21}+\frac{1}{14}$$

Since -\frac{14}{21} and \frac{12}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-14-12}{21}+\frac{1}{14}$$

Subtract 12 from -14 to get -26.

$$-\frac{26}{21}+\frac{1}{14}$$

Least common multiple of 21 and 14 is 42. Convert -\frac{26}{21} and \frac{1}{14} to fractions with denominator 42.

$$-\frac{52}{42}+\frac{3}{42}$$

Since -\frac{52}{42} and \frac{3}{42} have the same denominator, add them by adding their numerators.

$$\frac{-52+3}{42}$$

Add -52 and 3 to get -49.

$$\frac{-49}{42}$$

Reduce the fraction \frac{-49}{42} to lowest terms by extracting and canceling out 7.

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

Factor

$$-\frac{7}{6} = -1\frac{1}{6} = -1.1666666666666667$$