Solve 1/3+1/6+1/10+1/15+frac{1}{21}+frac{1}{28}+frac{1}{36}+frac{1}{45}+frac{1}{55}

$$\frac { 1 } { 3 } + \frac { 1 } { 6 } + \frac { 1 } { 10 } + \frac { 1 } { 15 } + \frac { 1 } { 21 } + \frac { 1 } { 28 } + \frac { 1 } { 36 } + \frac { 1 } { 45 } + \frac { 1 } { 55 }$$

Evaluate

$$\frac{9}{11}\approx 0.818181818$$

Solution Steps

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

$$\frac{2}{6}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Since \frac{2}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Add 2 and 1 to get 3.

$$\frac{3}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Least common multiple of 2 and 10 is 10. Convert \frac{1}{2} and \frac{1}{10} to fractions with denominator 10.

$$\frac{5}{10}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Since \frac{5}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{5+1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Add 5 and 1 to get 6.

$$\frac{6}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{3}{5}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Least common multiple of 5 and 15 is 15. Convert \frac{3}{5} and \frac{1}{15} to fractions with denominator 15.

$$\frac{9}{15}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Since \frac{9}{15} and \frac{1}{15} have the same denominator, add them by adding their numerators.

$$\frac{9+1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Add 9 and 1 to get 10.

$$\frac{10}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$\frac{2}{3}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Least common multiple of 3 and 21 is 21. Convert \frac{2}{3} and \frac{1}{21} to fractions with denominator 21.

$$\frac{14}{21}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Since \frac{14}{21} and \frac{1}{21} have the same denominator, add them by adding their numerators.

$$\frac{14+1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Add 14 and 1 to get 15.

$$\frac{15}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Reduce the fraction \frac{15}{21} to lowest terms by extracting and canceling out 3.

$$\frac{5}{7}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Least common multiple of 7 and 28 is 28. Convert \frac{5}{7} and \frac{1}{28} to fractions with denominator 28.

$$\frac{20}{28}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Since \frac{20}{28} and \frac{1}{28} have the same denominator, add them by adding their numerators.

$$\frac{20+1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Add 20 and 1 to get 21.

$$\frac{21}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Reduce the fraction \frac{21}{28} to lowest terms by extracting and canceling out 7.

$$\frac{3}{4}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Least common multiple of 4 and 36 is 36. Convert \frac{3}{4} and \frac{1}{36} to fractions with denominator 36.

$$\frac{27}{36}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}$$

Since \frac{27}{36} and \frac{1}{36} have the same denominator, add them by adding their numerators.

$$\frac{27+1}{36}+\frac{1}{45}+\frac{1}{55}$$

Add 27 and 1 to get 28.

$$\frac{28}{36}+\frac{1}{45}+\frac{1}{55}$$

Reduce the fraction \frac{28}{36} to lowest terms by extracting and canceling out 4.

$$\frac{7}{9}+\frac{1}{45}+\frac{1}{55}$$

Least common multiple of 9 and 45 is 45. Convert \frac{7}{9} and \frac{1}{45} to fractions with denominator 45.

$$\frac{35}{45}+\frac{1}{45}+\frac{1}{55}$$

Since \frac{35}{45} and \frac{1}{45} have the same denominator, add them by adding their numerators.

$$\frac{35+1}{45}+\frac{1}{55}$$

Add 35 and 1 to get 36.

$$\frac{36}{45}+\frac{1}{55}$$

Reduce the fraction \frac{36}{45} to lowest terms by extracting and canceling out 9.

$$\frac{4}{5}+\frac{1}{55}$$

Least common multiple of 5 and 55 is 55. Convert \frac{4}{5} and \frac{1}{55} to fractions with denominator 55.

$$\frac{44}{55}+\frac{1}{55}$$

Since \frac{44}{55} and \frac{1}{55} have the same denominator, add them by adding their numerators.

$$\frac{44+1}{55}$$

Add 44 and 1 to get 45.

$$\frac{45}{55}$$

Reduce the fraction \frac{45}{55} to lowest terms by extracting and canceling out 5.

$$\frac{9}{11}$$

Factor

$$\frac{3 ^ {2}}{11} = 0.8181818181818182$$