Solve 1/5+1/2+1/21

$$\frac { 1 } { 5 } + \frac { 1 } { 2 } + \frac { 1 } { 21 }$$

Evaluate

$$\frac{157}{210}\approx 0.747619048$$

Solution Steps

Least common multiple of 5 and 2 is 10. Convert \frac{1}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{2}{10}+\frac{5}{10}+\frac{1}{21}$$

Since \frac{2}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{2+5}{10}+\frac{1}{21}$$

Add 2 and 5 to get 7.

$$\frac{7}{10}+\frac{1}{21}$$

Least common multiple of 10 and 21 is 210. Convert \frac{7}{10} and \frac{1}{21} to fractions with denominator 210.

$$\frac{147}{210}+\frac{10}{210}$$

Since \frac{147}{210} and \frac{10}{210} have the same denominator, add them by adding their numerators.

$$\frac{147+10}{210}$$

Add 147 and 10 to get 157.

$$\frac{157}{210}$$

Factor

$$\frac{157}{2 \cdot 3 \cdot 5 \cdot 7} = 0.7476190476190476$$