Solve 1/3+1/9+1/18+1/14+frac{11}{36}=

$$\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 18 } + \frac { 1 } { 14 } + \frac { 11 } { 36 } =$$

Evaluate

$$\frac{221}{252}\approx 0.876984127$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{1}{9} to fractions with denominator 9.

$$\frac{3}{9}+\frac{1}{9}+\frac{1}{18}+\frac{1}{14}+\frac{11}{36}$$

Since \frac{3}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{9}+\frac{1}{18}+\frac{1}{14}+\frac{11}{36}$$

Add 3 and 1 to get 4.

$$\frac{4}{9}+\frac{1}{18}+\frac{1}{14}+\frac{11}{36}$$

Least common multiple of 9 and 18 is 18. Convert \frac{4}{9} and \frac{1}{18} to fractions with denominator 18.

$$\frac{8}{18}+\frac{1}{18}+\frac{1}{14}+\frac{11}{36}$$

Since \frac{8}{18} and \frac{1}{18} have the same denominator, add them by adding their numerators.

$$\frac{8+1}{18}+\frac{1}{14}+\frac{11}{36}$$

Add 8 and 1 to get 9.

$$\frac{9}{18}+\frac{1}{14}+\frac{11}{36}$$

Reduce the fraction \frac{9}{18} to lowest terms by extracting and canceling out 9.

$$\frac{1}{2}+\frac{1}{14}+\frac{11}{36}$$

Least common multiple of 2 and 14 is 14. Convert \frac{1}{2} and \frac{1}{14} to fractions with denominator 14.

$$\frac{7}{14}+\frac{1}{14}+\frac{11}{36}$$

Since \frac{7}{14} and \frac{1}{14} have the same denominator, add them by adding their numerators.

$$\frac{7+1}{14}+\frac{11}{36}$$

Add 7 and 1 to get 8.

$$\frac{8}{14}+\frac{11}{36}$$

Reduce the fraction \frac{8}{14} to lowest terms by extracting and canceling out 2.

$$\frac{4}{7}+\frac{11}{36}$$

Least common multiple of 7 and 36 is 252. Convert \frac{4}{7} and \frac{11}{36} to fractions with denominator 252.

$$\frac{144}{252}+\frac{77}{252}$$

Since \frac{144}{252} and \frac{77}{252} have the same denominator, add them by adding their numerators.

$$\frac{144+77}{252}$$

Add 144 and 77 to get 221.

$$\frac{221}{252}$$

Factor

$$\frac{13 \cdot 17}{2 ^ {2} \cdot 3 ^ {2} \cdot 7} = 0.876984126984127$$