Solve 1/9+1/27+1/63

$$\frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 63 }$$

Evaluate

$$\frac{31}{189}\approx 0.164021164$$

Solution Steps

Least common multiple of 9 and 27 is 27. Convert \frac{1}{9} and \frac{1}{27} to fractions with denominator 27.

$$\frac{3}{27}+\frac{1}{27}+\frac{1}{63}$$

Since \frac{3}{27} and \frac{1}{27} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{27}+\frac{1}{63}$$

Add 3 and 1 to get 4.

$$\frac{4}{27}+\frac{1}{63}$$

Least common multiple of 27 and 63 is 189. Convert \frac{4}{27} and \frac{1}{63} to fractions with denominator 189.

$$\frac{28}{189}+\frac{3}{189}$$

Since \frac{28}{189} and \frac{3}{189} have the same denominator, add them by adding their numerators.

$$\frac{28+3}{189}$$

Add 28 and 3 to get 31.

$$\frac{31}{189}$$

Factor

$$\frac{31}{3 ^ {3} \cdot 7} = 0.164021164021164$$