Solve 1/1+(-2/7)+(-5/6)+(+5/7)

$$\frac { 1 } { 1 } + ( - \frac { 2 } { 7 } ) + ( - \frac { 5 } { 6 } ) + ( + \frac { 5 } { 7 } )$$

Evaluate

$$\frac{25}{42}\approx 0.595238095$$

Solution Steps

Divide 1 by 1 to get 1.

$$1-\frac{2}{7}-\frac{5}{6}+\frac{5}{7}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{7}{7}-\frac{2}{7}-\frac{5}{6}+\frac{5}{7}$$

Since \frac{7}{7} and \frac{2}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-2}{7}-\frac{5}{6}+\frac{5}{7}$$

Subtract 2 from 7 to get 5.

$$\frac{5}{7}-\frac{5}{6}+\frac{5}{7}$$

Least common multiple of 7 and 6 is 42. Convert \frac{5}{7} and \frac{5}{6} to fractions with denominator 42.

$$\frac{30}{42}-\frac{35}{42}+\frac{5}{7}$$

Since \frac{30}{42} and \frac{35}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-35}{42}+\frac{5}{7}$$

Subtract 35 from 30 to get -5.

$$-\frac{5}{42}+\frac{5}{7}$$

Least common multiple of 42 and 7 is 42. Convert -\frac{5}{42} and \frac{5}{7} to fractions with denominator 42.

$$-\frac{5}{42}+\frac{30}{42}$$

Since -\frac{5}{42} and \frac{30}{42} have the same denominator, add them by adding their numerators.

$$\frac{-5+30}{42}$$

Add -5 and 30 to get 25.

$$\frac{25}{42}$$

Factor

$$\frac{5 ^ {2}}{2 \cdot 3 \cdot 7} = 0.5952380952380952$$