Solve 1/-2+1/3+1/5-3/4+frac{2}{9}-frac{5}{7}=

$$\frac { 1 } { - 2 } + \frac { 1 } { 3 } + \frac { 1 } { 5 } - \frac { 3 } { 4 } + \frac { 2 } { 9 } - \frac { 5 } { 7 } =$$

Evaluate

$$-\frac{1523}{1260}\approx -1.208730159$$

Solution Steps

Fraction \frac{1}{-2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$-\frac{1}{2}+\frac{1}{3}+\frac{1}{5}-\frac{3}{4}+\frac{2}{9}-\frac{5}{7}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$-\frac{3}{6}+\frac{2}{6}+\frac{1}{5}-\frac{3}{4}+\frac{2}{9}-\frac{5}{7}$$

Since -\frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{-3+2}{6}+\frac{1}{5}-\frac{3}{4}+\frac{2}{9}-\frac{5}{7}$$

Add -3 and 2 to get -1.

$$-\frac{1}{6}+\frac{1}{5}-\frac{3}{4}+\frac{2}{9}-\frac{5}{7}$$

Least common multiple of 6 and 5 is 30. Convert -\frac{1}{6} and \frac{1}{5} to fractions with denominator 30.

$$-\frac{5}{30}+\frac{6}{30}-\frac{3}{4}+\frac{2}{9}-\frac{5}{7}$$

Since -\frac{5}{30} and \frac{6}{30} have the same denominator, add them by adding their numerators.

$$\frac{-5+6}{30}-\frac{3}{4}+\frac{2}{9}-\frac{5}{7}$$

Add -5 and 6 to get 1.

$$\frac{1}{30}-\frac{3}{4}+\frac{2}{9}-\frac{5}{7}$$

Least common multiple of 30 and 4 is 60. Convert \frac{1}{30} and \frac{3}{4} to fractions with denominator 60.

$$\frac{2}{60}-\frac{45}{60}+\frac{2}{9}-\frac{5}{7}$$

Since \frac{2}{60} and \frac{45}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-45}{60}+\frac{2}{9}-\frac{5}{7}$$

Subtract 45 from 2 to get -43.

$$-\frac{43}{60}+\frac{2}{9}-\frac{5}{7}$$

Least common multiple of 60 and 9 is 180. Convert -\frac{43}{60} and \frac{2}{9} to fractions with denominator 180.

$$-\frac{129}{180}+\frac{40}{180}-\frac{5}{7}$$

Since -\frac{129}{180} and \frac{40}{180} have the same denominator, add them by adding their numerators.

$$\frac{-129+40}{180}-\frac{5}{7}$$

Add -129 and 40 to get -89.

$$-\frac{89}{180}-\frac{5}{7}$$

Least common multiple of 180 and 7 is 1260. Convert -\frac{89}{180} and \frac{5}{7} to fractions with denominator 1260.

$$-\frac{623}{1260}-\frac{900}{1260}$$

Since -\frac{623}{1260} and \frac{900}{1260} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-623-900}{1260}$$

Subtract 900 from -623 to get -1523.

$$-\frac{1523}{1260}$$

Factor

$$-\frac{1523}{1260} = -1\frac{263}{1260} = -1.2087301587301587$$