Solve 1/6+1/12+1/20+1/31+frac{1}{42}+frac{1}{56}

$$\frac{ 1 }{ 6 } + \frac{ 1 }{ 12 } + \frac{ 1 }{ 20 } + \frac{ 1 }{ 31 } + \frac{ 1 }{ 42 } + \frac{ 1 }{ 56 }$$

Evaluate

$$\frac{1391}{3720}\approx 0.373924731$$

Solution Steps

Least common multiple of 6 and 12 is 12. Convert \frac{1}{6} and \frac{1}{12} to fractions with denominator 12.

$$\frac{2}{12}+\frac{1}{12}+\frac{1}{20}+\frac{1}{31}+\frac{1}{42}+\frac{1}{56}$$

Since \frac{2}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{12}+\frac{1}{20}+\frac{1}{31}+\frac{1}{42}+\frac{1}{56}$$

Add 2 and 1 to get 3.

$$\frac{3}{12}+\frac{1}{20}+\frac{1}{31}+\frac{1}{42}+\frac{1}{56}$$

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

$$\frac{1}{4}+\frac{1}{20}+\frac{1}{31}+\frac{1}{42}+\frac{1}{56}$$

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

$$\frac{5}{20}+\frac{1}{20}+\frac{1}{31}+\frac{1}{42}+\frac{1}{56}$$

Since \frac{5}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$\frac{5+1}{20}+\frac{1}{31}+\frac{1}{42}+\frac{1}{56}$$

Add 5 and 1 to get 6.

$$\frac{6}{20}+\frac{1}{31}+\frac{1}{42}+\frac{1}{56}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{3}{10}+\frac{1}{31}+\frac{1}{42}+\frac{1}{56}$$

Least common multiple of 10 and 31 is 310. Convert \frac{3}{10} and \frac{1}{31} to fractions with denominator 310.

$$\frac{93}{310}+\frac{10}{310}+\frac{1}{42}+\frac{1}{56}$$

Since \frac{93}{310} and \frac{10}{310} have the same denominator, add them by adding their numerators.

$$\frac{93+10}{310}+\frac{1}{42}+\frac{1}{56}$$

Add 93 and 10 to get 103.

$$\frac{103}{310}+\frac{1}{42}+\frac{1}{56}$$

Least common multiple of 310 and 42 is 6510. Convert \frac{103}{310} and \frac{1}{42} to fractions with denominator 6510.

$$\frac{2163}{6510}+\frac{155}{6510}+\frac{1}{56}$$

Since \frac{2163}{6510} and \frac{155}{6510} have the same denominator, add them by adding their numerators.

$$\frac{2163+155}{6510}+\frac{1}{56}$$

Add 2163 and 155 to get 2318.

$$\frac{2318}{6510}+\frac{1}{56}$$

Reduce the fraction \frac{2318}{6510} to lowest terms by extracting and canceling out 2.

$$\frac{1159}{3255}+\frac{1}{56}$$

Least common multiple of 3255 and 56 is 26040. Convert \frac{1159}{3255} and \frac{1}{56} to fractions with denominator 26040.

$$\frac{9272}{26040}+\frac{465}{26040}$$

Since \frac{9272}{26040} and \frac{465}{26040} have the same denominator, add them by adding their numerators.

$$\frac{9272+465}{26040}$$

Add 9272 and 465 to get 9737.

$$\frac{9737}{26040}$$

Reduce the fraction \frac{9737}{26040} to lowest terms by extracting and canceling out 7.

$$\frac{1391}{3720}$$

Factor

$$\frac{13 \cdot 107}{2 ^ {3} \cdot 3 \cdot 5 \cdot 31} = 0.3739247311827957$$