Solve 1/10+1/9+1/8

$$\frac { 1 } { 10 } + \frac { 1 } { 9 } + \frac { 1 } { 8 }$$

Evaluate

$$\frac{121}{360}\approx 0.336111111$$

Solution Steps

Least common multiple of 10 and 9 is 90. Convert \frac{1}{10} and \frac{1}{9} to fractions with denominator 90.

$$\frac{9}{90}+\frac{10}{90}+\frac{1}{8}$$

Since \frac{9}{90} and \frac{10}{90} have the same denominator, add them by adding their numerators.

$$\frac{9+10}{90}+\frac{1}{8}$$

Add 9 and 10 to get 19.

$$\frac{19}{90}+\frac{1}{8}$$

Least common multiple of 90 and 8 is 360. Convert \frac{19}{90} and \frac{1}{8} to fractions with denominator 360.

$$\frac{76}{360}+\frac{45}{360}$$

Since \frac{76}{360} and \frac{45}{360} have the same denominator, add them by adding their numerators.

$$\frac{76+45}{360}$$

Add 76 and 45 to get 121.

$$\frac{121}{360}$$

Factor

$$\frac{11 ^ {2}}{2 ^ {3} \cdot 3 ^ {2} \cdot 5} = 0.33611111111111114$$