Solve 1/2+1/6+1/12+1/20+frac{1}{30}+frac{1}{42}+frac{1}{56}+frac{1}{72}+frac{1}{90}

$$\frac { 1 } { 2 } + \frac { 1 } { 6 } + \frac { 1 } { 12 } + \frac { 1 } { 20 } + \frac { 1 } { 30 } + \frac { 1 } { 42 } + \frac { 1 } { 56 } + \frac { 1 } { 72 } + \frac { 1 } { 90 }$$

Evaluate

$$\frac{9}{10}=0.9$$

Solution Steps

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

$$\frac{3}{6}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 3 and 1 to get 4.

$$\frac{4}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 3 and 12 is 12. Convert \frac{2}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{8}{12}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{8}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 8 and 1 to get 9.

$$\frac{9}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 4 and 20 is 20. Convert \frac{3}{4} and \frac{1}{20} to fractions with denominator 20.

$$\frac{15}{20}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{15}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$\frac{15+1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 15 and 1 to get 16.

$$\frac{16}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{16}{20} to lowest terms by extracting and canceling out 4.

$$\frac{4}{5}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 5 and 30 is 30. Convert \frac{4}{5} and \frac{1}{30} to fractions with denominator 30.

$$\frac{24}{30}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{24}{30} and \frac{1}{30} have the same denominator, add them by adding their numerators.

$$\frac{24+1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 24 and 1 to get 25.

$$\frac{25}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{25}{30} to lowest terms by extracting and canceling out 5.

$$\frac{5}{6}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 6 and 42 is 42. Convert \frac{5}{6} and \frac{1}{42} to fractions with denominator 42.

$$\frac{35}{42}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{35}{42} and \frac{1}{42} have the same denominator, add them by adding their numerators.

$$\frac{35+1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 35 and 1 to get 36.

$$\frac{36}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{36}{42} to lowest terms by extracting and canceling out 6.

$$\frac{6}{7}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 7 and 56 is 56. Convert \frac{6}{7} and \frac{1}{56} to fractions with denominator 56.

$$\frac{48}{56}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{48}{56} and \frac{1}{56} have the same denominator, add them by adding their numerators.

$$\frac{48+1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 48 and 1 to get 49.

$$\frac{49}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{49}{56} to lowest terms by extracting and canceling out 7.

$$\frac{7}{8}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 8 and 72 is 72. Convert \frac{7}{8} and \frac{1}{72} to fractions with denominator 72.

$$\frac{63}{72}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{63}{72} and \frac{1}{72} have the same denominator, add them by adding their numerators.

$$\frac{63+1}{72}+\frac{1}{90}$$

Add 63 and 1 to get 64.

$$\frac{64}{72}+\frac{1}{90}$$

Reduce the fraction \frac{64}{72} to lowest terms by extracting and canceling out 8.

$$\frac{8}{9}+\frac{1}{90}$$

Least common multiple of 9 and 90 is 90. Convert \frac{8}{9} and \frac{1}{90} to fractions with denominator 90.

$$\frac{80}{90}+\frac{1}{90}$$

Since \frac{80}{90} and \frac{1}{90} have the same denominator, add them by adding their numerators.

$$\frac{80+1}{90}$$

Add 80 and 1 to get 81.

$$\frac{81}{90}$$

Reduce the fraction \frac{81}{90} to lowest terms by extracting and canceling out 9.

$$\frac{9}{10}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 5} = 0.9$$