Solve 1/9-1/2+6/7-2/3+frac{1}{5}

$$\frac { 1 } { 9 } - \frac { 1 } { 2 } + \frac { 6 } { 7 } - \frac { 2 } { 3 } + \frac { 1 } { 5 }$$

Evaluate

$$\frac{1}{630}\approx 0.001587302$$

Solution Steps

Least common multiple of 9 and 2 is 18. Convert \frac{1}{9} and \frac{1}{2} to fractions with denominator 18.

$$\frac{2}{18}-\frac{9}{18}+\frac{6}{7}-\frac{2}{3}+\frac{1}{5}$$

Since \frac{2}{18} and \frac{9}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-9}{18}+\frac{6}{7}-\frac{2}{3}+\frac{1}{5}$$

Subtract 9 from 2 to get -7.

$$-\frac{7}{18}+\frac{6}{7}-\frac{2}{3}+\frac{1}{5}$$

Least common multiple of 18 and 7 is 126. Convert -\frac{7}{18} and \frac{6}{7} to fractions with denominator 126.

$$-\frac{49}{126}+\frac{108}{126}-\frac{2}{3}+\frac{1}{5}$$

Since -\frac{49}{126} and \frac{108}{126} have the same denominator, add them by adding their numerators.

$$\frac{-49+108}{126}-\frac{2}{3}+\frac{1}{5}$$

Add -49 and 108 to get 59.

$$\frac{59}{126}-\frac{2}{3}+\frac{1}{5}$$

Least common multiple of 126 and 3 is 126. Convert \frac{59}{126} and \frac{2}{3} to fractions with denominator 126.

$$\frac{59}{126}-\frac{84}{126}+\frac{1}{5}$$

Since \frac{59}{126} and \frac{84}{126} have the same denominator, subtract them by subtracting their numerators.

$$\frac{59-84}{126}+\frac{1}{5}$$

Subtract 84 from 59 to get -25.

$$-\frac{25}{126}+\frac{1}{5}$$

Least common multiple of 126 and 5 is 630. Convert -\frac{25}{126} and \frac{1}{5} to fractions with denominator 630.

$$-\frac{125}{630}+\frac{126}{630}$$

Since -\frac{125}{630} and \frac{126}{630} have the same denominator, add them by adding their numerators.

$$\frac{-125+126}{630}$$

Add -125 and 126 to get 1.

$$\frac{1}{630}$$

Factor

$$\frac{1}{2 \cdot 3 ^ {2} \cdot 5 \cdot 7} = 0.0015873015873015873$$