Solve 9+1/2+1/6+1/12+1/20+frac{1}{30}+frac{1}{42}+frac{1}{56}+frac{1}{72}+frac{1}{90}

$$9+ \frac{ 1 }{ 2 } + \frac{ 1 }{ 6 } + \frac{ 1 }{ 12 } + \frac{ 1 }{ 20 } + \frac{ 1 }{ 30 } + \frac{ 1 }{ 42 } + \frac{ 1 }{ 56 } + \frac{ 1 }{ 72 } + \frac{ 1 }{ 90 }$$

Evaluate

$$\frac{99}{10}=9.9$$

Solution Steps

Convert 9 to fraction \frac{18}{2}.

$$\frac{18}{2}+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{18}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{18+1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 18 and 1 to get 19.

$$\frac{19}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 2 and 6 is 6. Convert \frac{19}{2} and \frac{1}{6} to fractions with denominator 6.

$$\frac{57}{6}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{57}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{57+1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 57 and 1 to get 58.

$$\frac{58}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{58}{6} to lowest terms by extracting and canceling out 2.

$$\frac{29}{3}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 3 and 12 is 12. Convert \frac{29}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{116}{12}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{116}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{116+1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 116 and 1 to get 117.

$$\frac{117}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{117}{12} to lowest terms by extracting and canceling out 3.

$$\frac{39}{4}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 4 and 20 is 20. Convert \frac{39}{4} and \frac{1}{20} to fractions with denominator 20.

$$\frac{195}{20}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{195}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$\frac{195+1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 195 and 1 to get 196.

$$\frac{196}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{196}{20} to lowest terms by extracting and canceling out 4.

$$\frac{49}{5}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 5 and 30 is 30. Convert \frac{49}{5} and \frac{1}{30} to fractions with denominator 30.

$$\frac{294}{30}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{294}{30} and \frac{1}{30} have the same denominator, add them by adding their numerators.

$$\frac{294+1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 294 and 1 to get 295.

$$\frac{295}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{295}{30} to lowest terms by extracting and canceling out 5.

$$\frac{59}{6}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 6 and 42 is 42. Convert \frac{59}{6} and \frac{1}{42} to fractions with denominator 42.

$$\frac{413}{42}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{413}{42} and \frac{1}{42} have the same denominator, add them by adding their numerators.

$$\frac{413+1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 413 and 1 to get 414.

$$\frac{414}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{414}{42} to lowest terms by extracting and canceling out 6.

$$\frac{69}{7}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 7 and 56 is 56. Convert \frac{69}{7} and \frac{1}{56} to fractions with denominator 56.

$$\frac{552}{56}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{552}{56} and \frac{1}{56} have the same denominator, add them by adding their numerators.

$$\frac{552+1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 552 and 1 to get 553.

$$\frac{553}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{553}{56} to lowest terms by extracting and canceling out 7.

$$\frac{79}{8}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 8 and 72 is 72. Convert \frac{79}{8} and \frac{1}{72} to fractions with denominator 72.

$$\frac{711}{72}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{711}{72} and \frac{1}{72} have the same denominator, add them by adding their numerators.

$$\frac{711+1}{72}+\frac{1}{90}$$

Add 711 and 1 to get 712.

$$\frac{712}{72}+\frac{1}{90}$$

Reduce the fraction \frac{712}{72} to lowest terms by extracting and canceling out 8.

$$\frac{89}{9}+\frac{1}{90}$$

Least common multiple of 9 and 90 is 90. Convert \frac{89}{9} and \frac{1}{90} to fractions with denominator 90.

$$\frac{890}{90}+\frac{1}{90}$$

Since \frac{890}{90} and \frac{1}{90} have the same denominator, add them by adding their numerators.

$$\frac{890+1}{90}$$

Add 890 and 1 to get 891.

$$\frac{891}{90}$$

Reduce the fraction \frac{891}{90} to lowest terms by extracting and canceling out 9.

$$\frac{99}{10}$$

Factor

$$\frac{3 ^ {2} \cdot 11}{2 \cdot 5} = 9\frac{9}{10} = 9.9$$