Solve 1/5+1/6+1/7

$$\frac { 1 } { 5 } + \frac { 1 } { 6 } + \frac { 1 } { 7 }$$

Evaluate

$$\frac{107}{210}\approx 0.50952381$$

Solution Steps

Least common multiple of 5 and 6 is 30. Convert \frac{1}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{6}{30}+\frac{5}{30}+\frac{1}{7}$$

Since \frac{6}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{6+5}{30}+\frac{1}{7}$$

Add 6 and 5 to get 11.

$$\frac{11}{30}+\frac{1}{7}$$

Least common multiple of 30 and 7 is 210. Convert \frac{11}{30} and \frac{1}{7} to fractions with denominator 210.

$$\frac{77}{210}+\frac{30}{210}$$

Since \frac{77}{210} and \frac{30}{210} have the same denominator, add them by adding their numerators.

$$\frac{77+30}{210}$$

Add 77 and 30 to get 107.

$$\frac{107}{210}$$

Factor

$$\frac{107}{2 \cdot 3 \cdot 5 \cdot 7} = 0.5095238095238095$$