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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Add 3 and 4 to get 7.

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

Least common multiple of 18 and 3 is 18. Convert \frac{7}{18} and \frac{1}{3} to fractions with denominator 18.

$$\frac{7}{18}+\frac{6}{18}+\frac{1}{24}$$

Since \frac{7}{18} and \frac{6}{18} have the same denominator, add them by adding their numerators.

$$\frac{7+6}{18}+\frac{1}{24}$$

Add 7 and 6 to get 13.

$$\frac{13}{18}+\frac{1}{24}$$

Least common multiple of 18 and 24 is 72. Convert \frac{13}{18} and \frac{1}{24} to fractions with denominator 72.

$$\frac{52}{72}+\frac{3}{72}$$

Since \frac{52}{72} and \frac{3}{72} have the same denominator, add them by adding their numerators.

$$\frac{52+3}{72}$$

Add 52 and 3 to get 55.

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

Factor

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