Solve 1/12+1/20+1/30+1/42+frac{1}{20}+frac{1}{5}

$$\frac { 1 } { 12 } + \frac { 1 } { 20 } + \frac { 1 } { 30 } + \frac { 1 } { 42 } + \frac { 1 } { 20 } + \frac { 1 } { 5 }$$

Evaluate

$$\frac{37}{84}\approx 0.44047619$$

Solution Steps

Least common multiple of 12 and 20 is 60. Convert \frac{1}{12} and \frac{1}{20} to fractions with denominator 60.

$$\frac{5}{60}+\frac{3}{60}+\frac{1}{30}+\frac{1}{42}+\frac{1}{20}+\frac{1}{5}$$

Since \frac{5}{60} and \frac{3}{60} have the same denominator, add them by adding their numerators.

$$\frac{5+3}{60}+\frac{1}{30}+\frac{1}{42}+\frac{1}{20}+\frac{1}{5}$$

Add 5 and 3 to get 8.

$$\frac{8}{60}+\frac{1}{30}+\frac{1}{42}+\frac{1}{20}+\frac{1}{5}$$

Reduce the fraction \frac{8}{60} to lowest terms by extracting and canceling out 4.

$$\frac{2}{15}+\frac{1}{30}+\frac{1}{42}+\frac{1}{20}+\frac{1}{5}$$

Least common multiple of 15 and 30 is 30. Convert \frac{2}{15} and \frac{1}{30} to fractions with denominator 30.

$$\frac{4}{30}+\frac{1}{30}+\frac{1}{42}+\frac{1}{20}+\frac{1}{5}$$

Since \frac{4}{30} and \frac{1}{30} have the same denominator, add them by adding their numerators.

$$\frac{4+1}{30}+\frac{1}{42}+\frac{1}{20}+\frac{1}{5}$$

Add 4 and 1 to get 5.

$$\frac{5}{30}+\frac{1}{42}+\frac{1}{20}+\frac{1}{5}$$

Reduce the fraction \frac{5}{30} to lowest terms by extracting and canceling out 5.

$$\frac{1}{6}+\frac{1}{42}+\frac{1}{20}+\frac{1}{5}$$

Least common multiple of 6 and 42 is 42. Convert \frac{1}{6} and \frac{1}{42} to fractions with denominator 42.

$$\frac{7}{42}+\frac{1}{42}+\frac{1}{20}+\frac{1}{5}$$

Since \frac{7}{42} and \frac{1}{42} have the same denominator, add them by adding their numerators.

$$\frac{7+1}{42}+\frac{1}{20}+\frac{1}{5}$$

Add 7 and 1 to get 8.

$$\frac{8}{42}+\frac{1}{20}+\frac{1}{5}$$

Reduce the fraction \frac{8}{42} to lowest terms by extracting and canceling out 2.

$$\frac{4}{21}+\frac{1}{20}+\frac{1}{5}$$

Least common multiple of 21 and 20 is 420. Convert \frac{4}{21} and \frac{1}{20} to fractions with denominator 420.

$$\frac{80}{420}+\frac{21}{420}+\frac{1}{5}$$

Since \frac{80}{420} and \frac{21}{420} have the same denominator, add them by adding their numerators.

$$\frac{80+21}{420}+\frac{1}{5}$$

Add 80 and 21 to get 101.

$$\frac{101}{420}+\frac{1}{5}$$

Least common multiple of 420 and 5 is 420. Convert \frac{101}{420} and \frac{1}{5} to fractions with denominator 420.

$$\frac{101}{420}+\frac{84}{420}$$

Since \frac{101}{420} and \frac{84}{420} have the same denominator, add them by adding their numerators.

$$\frac{101+84}{420}$$

Add 101 and 84 to get 185.

$$\frac{185}{420}$$

Reduce the fraction \frac{185}{420} to lowest terms by extracting and canceling out 5.

$$\frac{37}{84}$$

Factor

$$\frac{37}{2 ^ {2} \cdot 3 \cdot 7} = 0.44047619047619047$$