Solve 1/2+1/6+1/12+1/20+frac{1}{420}

$$\frac{ 1 }{ 2 } + \frac{ 1 }{ 6 } + \frac{ 1 }{ 12 } + \frac{ 1 }{ 20 } + \frac{ 1 }{ 420 }$$

Evaluate

$$\frac{337}{420}\approx 0.802380952$$

Solution Steps

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{1}{6} to fractions with denominator 6.

$$\frac{3}{6}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{420}$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{420}$$

Add 3 and 1 to get 4.

$$\frac{4}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{420}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}+\frac{1}{12}+\frac{1}{20}+\frac{1}{420}$$

Least common multiple of 3 and 12 is 12. Convert \frac{2}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{8}{12}+\frac{1}{12}+\frac{1}{20}+\frac{1}{420}$$

Since \frac{8}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+1}{12}+\frac{1}{20}+\frac{1}{420}$$

Add 8 and 1 to get 9.

$$\frac{9}{12}+\frac{1}{20}+\frac{1}{420}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}+\frac{1}{20}+\frac{1}{420}$$

Least common multiple of 4 and 20 is 20. Convert \frac{3}{4} and \frac{1}{20} to fractions with denominator 20.

$$\frac{15}{20}+\frac{1}{20}+\frac{1}{420}$$

Since \frac{15}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$\frac{15+1}{20}+\frac{1}{420}$$

Add 15 and 1 to get 16.

$$\frac{16}{20}+\frac{1}{420}$$

Reduce the fraction \frac{16}{20} to lowest terms by extracting and canceling out 4.

$$\frac{4}{5}+\frac{1}{420}$$

Least common multiple of 5 and 420 is 420. Convert \frac{4}{5} and \frac{1}{420} to fractions with denominator 420.

$$\frac{336}{420}+\frac{1}{420}$$

Since \frac{336}{420} and \frac{1}{420} have the same denominator, add them by adding their numerators.

$$\frac{336+1}{420}$$

Add 336 and 1 to get 337.

$$\frac{337}{420}$$

Factor

$$\frac{337}{2 ^ {2} \cdot 3 \cdot 5 \cdot 7} = 0.8023809523809524$$