Solve S=1/9+1/18+1/30+1/45+frac{1}{63}

$$S = \frac { 1 } { 9 } + \frac { 1 } { 18 } + \frac { 1 } { 30 } + \frac { 1 } { 45 } + \frac { 1 } { 63 }$$

Solve for S

$$S=\frac{5}{21}\approx 0.238095238$$

Steps for Solving Linear Equation

Least common multiple of 9 and 18 is 18. Convert \frac{1}{9} and \frac{1}{18} to fractions with denominator 18.

$$S=\frac{2}{18}+\frac{1}{18}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}$$

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

$$S=\frac{2+1}{18}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}$$

Add 2 and 1 to get 3.

$$S=\frac{3}{18}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$S=\frac{1}{6}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}$$

Least common multiple of 6 and 30 is 30. Convert \frac{1}{6} and \frac{1}{30} to fractions with denominator 30.

$$S=\frac{5}{30}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}$$

Since \frac{5}{30} and \frac{1}{30} have the same denominator, add them by adding their numerators.

$$S=\frac{5+1}{30}+\frac{1}{45}+\frac{1}{63}$$

Add 5 and 1 to get 6.

$$S=\frac{6}{30}+\frac{1}{45}+\frac{1}{63}$$

Reduce the fraction \frac{6}{30} to lowest terms by extracting and canceling out 6.

$$S=\frac{1}{5}+\frac{1}{45}+\frac{1}{63}$$

Least common multiple of 5 and 45 is 45. Convert \frac{1}{5} and \frac{1}{45} to fractions with denominator 45.

$$S=\frac{9}{45}+\frac{1}{45}+\frac{1}{63}$$

Since \frac{9}{45} and \frac{1}{45} have the same denominator, add them by adding their numerators.

$$S=\frac{9+1}{45}+\frac{1}{63}$$

Add 9 and 1 to get 10.

$$S=\frac{10}{45}+\frac{1}{63}$$

Reduce the fraction \frac{10}{45} to lowest terms by extracting and canceling out 5.

$$S=\frac{2}{9}+\frac{1}{63}$$

Least common multiple of 9 and 63 is 63. Convert \frac{2}{9} and \frac{1}{63} to fractions with denominator 63.

$$S=\frac{14}{63}+\frac{1}{63}$$

Since \frac{14}{63} and \frac{1}{63} have the same denominator, add them by adding their numerators.

$$S=\frac{14+1}{63}$$

Add 14 and 1 to get 15.

$$S=\frac{15}{63}$$

Reduce the fraction \frac{15}{63} to lowest terms by extracting and canceling out 3.

$$S=\frac{5}{21}$$

Assign S

$$S≔\frac{5}{21}$$