Solve 2/12+2/9+1/24+1/3

$$\frac{ 2 }{ 12 } + \frac{ 2 }{ 9 } + \frac{ 1 }{ 24 } + \frac{ 1 }{ 3 }$$

Evaluate

$$\frac{55}{72}\approx 0.763888889$$

Solution Steps

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}+\frac{2}{9}+\frac{1}{24}+\frac{1}{3}$$

Least common multiple of 6 and 9 is 18. Convert \frac{1}{6} and \frac{2}{9} to fractions with denominator 18.

$$\frac{3}{18}+\frac{4}{18}+\frac{1}{24}+\frac{1}{3}$$

Since \frac{3}{18} and \frac{4}{18} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{18}+\frac{1}{24}+\frac{1}{3}$$

Add 3 and 4 to get 7.

$$\frac{7}{18}+\frac{1}{24}+\frac{1}{3}$$

Least common multiple of 18 and 24 is 72. Convert \frac{7}{18} and \frac{1}{24} to fractions with denominator 72.

$$\frac{28}{72}+\frac{3}{72}+\frac{1}{3}$$

Since \frac{28}{72} and \frac{3}{72} have the same denominator, add them by adding their numerators.

$$\frac{28+3}{72}+\frac{1}{3}$$

Add 28 and 3 to get 31.

$$\frac{31}{72}+\frac{1}{3}$$

Least common multiple of 72 and 3 is 72. Convert \frac{31}{72} and \frac{1}{3} to fractions with denominator 72.

$$\frac{31}{72}+\frac{24}{72}$$

Since \frac{31}{72} and \frac{24}{72} have the same denominator, add them by adding their numerators.

$$\frac{31+24}{72}$$

Add 31 and 24 to get 55.

$$\frac{55}{72}$$

Factor

$$\frac{5 \cdot 11}{2 ^ {3} \cdot 3 ^ {2}} = 0.7638888888888888$$