Solve 1/12+2/13+2/14

$$\frac { 1 } { 12 } + \frac { 2 } { 13 } + \frac { 2 } { 14 }$$

Evaluate

$$\frac{415}{1092}\approx 0.38003663$$

Solution Steps

Least common multiple of 12 and 13 is 156. Convert \frac{1}{12} and \frac{2}{13} to fractions with denominator 156.

$$\frac{13}{156}+\frac{24}{156}+\frac{2}{14}$$

Since \frac{13}{156} and \frac{24}{156} have the same denominator, add them by adding their numerators.

$$\frac{13+24}{156}+\frac{2}{14}$$

Add 13 and 24 to get 37.

$$\frac{37}{156}+\frac{2}{14}$$

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$\frac{37}{156}+\frac{1}{7}$$

Least common multiple of 156 and 7 is 1092. Convert \frac{37}{156} and \frac{1}{7} to fractions with denominator 1092.

$$\frac{259}{1092}+\frac{156}{1092}$$

Since \frac{259}{1092} and \frac{156}{1092} have the same denominator, add them by adding their numerators.

$$\frac{259+156}{1092}$$

Add 259 and 156 to get 415.

$$\frac{415}{1092}$$

Factor

$$\frac{5 \cdot 83}{2 ^ {2} \cdot 3 \cdot 7 \cdot 13} = 0.38003663003663$$