Solve 1-1/2-1/3+1/4+1/5+frac{1}{6}-frac{1}{7}-frac{1}{8}-frac{1}{9}-frac{1}{10}

$$1 - \frac { 1 } { 2 } - \frac { 1 } { 3 } + \frac { 1 } { 4 } + \frac { 1 } { 5 } + \frac { 1 } { 6 } - \frac { 1 } { 7 } - \frac { 1 } { 8 } - \frac { 1 } { 9 } - \frac { 1 } { 10 }$$

Evaluate

$$\frac{767}{2520}\approx 0.304365079$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$\frac{2}{2}-\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-1}{2}-\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

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

$$\frac{3}{6}-\frac{2}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-2}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Subtract 2 from 3 to get 1.

$$\frac{1}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

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

$$\frac{2}{12}+\frac{3}{12}+\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Since \frac{2}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{12}+\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Add 2 and 3 to get 5.

$$\frac{5}{12}+\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

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

$$\frac{25}{60}+\frac{12}{60}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Since \frac{25}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.

$$\frac{25+12}{60}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Add 25 and 12 to get 37.

$$\frac{37}{60}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Least common multiple of 60 and 6 is 60. Convert \frac{37}{60} and \frac{1}{6} to fractions with denominator 60.

$$\frac{37}{60}+\frac{10}{60}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Since \frac{37}{60} and \frac{10}{60} have the same denominator, add them by adding their numerators.

$$\frac{37+10}{60}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Add 37 and 10 to get 47.

$$\frac{47}{60}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

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

$$\frac{329}{420}-\frac{60}{420}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

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

$$\frac{329-60}{420}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Subtract 60 from 329 to get 269.

$$\frac{269}{420}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}$$

Least common multiple of 420 and 8 is 840. Convert \frac{269}{420} and \frac{1}{8} to fractions with denominator 840.

$$\frac{538}{840}-\frac{105}{840}-\frac{1}{9}-\frac{1}{10}$$

Since \frac{538}{840} and \frac{105}{840} have the same denominator, subtract them by subtracting their numerators.

$$\frac{538-105}{840}-\frac{1}{9}-\frac{1}{10}$$

Subtract 105 from 538 to get 433.

$$\frac{433}{840}-\frac{1}{9}-\frac{1}{10}$$

Least common multiple of 840 and 9 is 2520. Convert \frac{433}{840} and \frac{1}{9} to fractions with denominator 2520.

$$\frac{1299}{2520}-\frac{280}{2520}-\frac{1}{10}$$

Since \frac{1299}{2520} and \frac{280}{2520} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1299-280}{2520}-\frac{1}{10}$$

Subtract 280 from 1299 to get 1019.

$$\frac{1019}{2520}-\frac{1}{10}$$

Least common multiple of 2520 and 10 is 2520. Convert \frac{1019}{2520} and \frac{1}{10} to fractions with denominator 2520.

$$\frac{1019}{2520}-\frac{252}{2520}$$

Since \frac{1019}{2520} and \frac{252}{2520} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1019-252}{2520}$$

Subtract 252 from 1019 to get 767.

$$\frac{767}{2520}$$

Factor

$$\frac{13 \cdot 59}{2 ^ {3} \cdot 3 ^ {2} \cdot 5 \cdot 7} = 0.30436507936507934$$