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

$$-\frac{263}{1260}\approx -0.208730159$$

Solution Steps

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 5.

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

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

$$\frac{25}{30}+\frac{6}{30}-\frac{3}{4}+\frac{2}{9}-\frac{5}{7}$$

Since \frac{25}{30} and \frac{6}{30} have the same denominator, add them by adding their numerators.

$$\frac{25+6}{30}-\frac{3}{4}+\frac{2}{9}-\frac{5}{7}$$

Add 25 and 6 to get 31.

$$\frac{31}{30}-\frac{3}{4}+\frac{2}{9}-\frac{5}{7}$$

Least common multiple of 30 and 4 is 60. Convert \frac{31}{30} and \frac{3}{4} to fractions with denominator 60.

$$\frac{62}{60}-\frac{45}{60}+\frac{2}{9}-\frac{5}{7}$$

Since \frac{62}{60} and \frac{45}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{62-45}{60}+\frac{2}{9}-\frac{5}{7}$$

Subtract 45 from 62 to get 17.

$$\frac{17}{60}+\frac{2}{9}-\frac{5}{7}$$

Least common multiple of 60 and 9 is 180. Convert \frac{17}{60} and \frac{2}{9} to fractions with denominator 180.

$$\frac{51}{180}+\frac{40}{180}-\frac{5}{7}$$

Since \frac{51}{180} and \frac{40}{180} have the same denominator, add them by adding their numerators.

$$\frac{51+40}{180}-\frac{5}{7}$$

Add 51 and 40 to get 91.

$$\frac{91}{180}-\frac{5}{7}$$

Least common multiple of 180 and 7 is 1260. Convert \frac{91}{180} and \frac{5}{7} to fractions with denominator 1260.

$$\frac{637}{1260}-\frac{900}{1260}$$

Since \frac{637}{1260} and \frac{900}{1260} have the same denominator, subtract them by subtracting their numerators.

$$\frac{637-900}{1260}$$

Subtract 900 from 637 to get -263.

$$-\frac{263}{1260}$$

Factor

$$-\frac{263}{1260} = -0.20873015873015874$$