Solve 1+1/3-1/2-1/4+1/5+frac{1}{7}-frac{1}{8}-frac{1}{10}+frac{1}{11}+frac{1}{13}

$$1 + \frac { 1 } { 3 } - \frac { 1 } { 2 } - \frac { 1 } { 4 } + \frac { 1 } { 5 } + \frac { 1 } { 7 } - \frac { 1 } { 8 } - \frac { 1 } { 10 } + \frac { 1 } { 11 } + \frac { 1 } { 13 }$$

Evaluate

$$\frac{104387}{120120}\approx 0.869022644$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{3}+\frac{1}{3}-\frac{1}{2}-\frac{1}{4}+\frac{1}{5}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{3}-\frac{1}{2}-\frac{1}{4}+\frac{1}{5}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Add 3 and 1 to get 4.

$$\frac{4}{3}-\frac{1}{2}-\frac{1}{4}+\frac{1}{5}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{8}{6}-\frac{3}{6}-\frac{1}{4}+\frac{1}{5}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Since \frac{8}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-3}{6}-\frac{1}{4}+\frac{1}{5}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Subtract 3 from 8 to get 5.

$$\frac{5}{6}-\frac{1}{4}+\frac{1}{5}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{10}{12}-\frac{3}{12}+\frac{1}{5}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-3}{12}+\frac{1}{5}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Subtract 3 from 10 to get 7.

$$\frac{7}{12}+\frac{1}{5}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Least common multiple of 12 and 5 is 60. Convert \frac{7}{12} and \frac{1}{5} to fractions with denominator 60.

$$\frac{35}{60}+\frac{12}{60}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Since \frac{35}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.

$$\frac{35+12}{60}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Add 35 and 12 to get 47.

$$\frac{47}{60}+\frac{1}{7}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Least common multiple of 60 and 7 is 420. Convert \frac{47}{60} and \frac{1}{7} to fractions with denominator 420.

$$\frac{329}{420}+\frac{60}{420}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Since \frac{329}{420} and \frac{60}{420} have the same denominator, add them by adding their numerators.

$$\frac{329+60}{420}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Add 329 and 60 to get 389.

$$\frac{389}{420}-\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Least common multiple of 420 and 8 is 840. Convert \frac{389}{420} and \frac{1}{8} to fractions with denominator 840.

$$\frac{778}{840}-\frac{105}{840}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Since \frac{778}{840} and \frac{105}{840} have the same denominator, subtract them by subtracting their numerators.

$$\frac{778-105}{840}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Subtract 105 from 778 to get 673.

$$\frac{673}{840}-\frac{1}{10}+\frac{1}{11}+\frac{1}{13}$$

Least common multiple of 840 and 10 is 840. Convert \frac{673}{840} and \frac{1}{10} to fractions with denominator 840.

$$\frac{673}{840}-\frac{84}{840}+\frac{1}{11}+\frac{1}{13}$$

Since \frac{673}{840} and \frac{84}{840} have the same denominator, subtract them by subtracting their numerators.

$$\frac{673-84}{840}+\frac{1}{11}+\frac{1}{13}$$

Subtract 84 from 673 to get 589.

$$\frac{589}{840}+\frac{1}{11}+\frac{1}{13}$$

Least common multiple of 840 and 11 is 9240. Convert \frac{589}{840} and \frac{1}{11} to fractions with denominator 9240.

$$\frac{6479}{9240}+\frac{840}{9240}+\frac{1}{13}$$

Since \frac{6479}{9240} and \frac{840}{9240} have the same denominator, add them by adding their numerators.

$$\frac{6479+840}{9240}+\frac{1}{13}$$

Add 6479 and 840 to get 7319.

$$\frac{7319}{9240}+\frac{1}{13}$$

Least common multiple of 9240 and 13 is 120120. Convert \frac{7319}{9240} and \frac{1}{13} to fractions with denominator 120120.

$$\frac{95147}{120120}+\frac{9240}{120120}$$

Since \frac{95147}{120120} and \frac{9240}{120120} have the same denominator, add them by adding their numerators.

$$\frac{95147+9240}{120120}$$

Add 95147 and 9240 to get 104387.

$$\frac{104387}{120120}$$

Factor

$$\frac{47 \cdot 2221}{2 ^ {3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13} = 0.8690226440226441$$