Solve 1/3+1/5+1/7+1/9

$$\frac { 1 } { 3 } + \frac { 1 } { 5 } + \frac { 1 } { 7 } + \frac { 1 } { 9 }$$

Evaluate

$$\frac{248}{315}\approx 0.787301587$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{5}{15}+\frac{3}{15}+\frac{1}{7}+\frac{1}{9}$$

Since \frac{5}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{5+3}{15}+\frac{1}{7}+\frac{1}{9}$$

Add 5 and 3 to get 8.

$$\frac{8}{15}+\frac{1}{7}+\frac{1}{9}$$

Least common multiple of 15 and 7 is 105. Convert \frac{8}{15} and \frac{1}{7} to fractions with denominator 105.

$$\frac{56}{105}+\frac{15}{105}+\frac{1}{9}$$

Since \frac{56}{105} and \frac{15}{105} have the same denominator, add them by adding their numerators.

$$\frac{56+15}{105}+\frac{1}{9}$$

Add 56 and 15 to get 71.

$$\frac{71}{105}+\frac{1}{9}$$

Least common multiple of 105 and 9 is 315. Convert \frac{71}{105} and \frac{1}{9} to fractions with denominator 315.

$$\frac{213}{315}+\frac{35}{315}$$

Since \frac{213}{315} and \frac{35}{315} have the same denominator, add them by adding their numerators.

$$\frac{213+35}{315}$$

Add 213 and 35 to get 248.

$$\frac{248}{315}$$

Factor

$$\frac{2 ^ {3} \cdot 31}{3 ^ {2} \cdot 5 \cdot 7} = 0.7873015873015873$$