Solve 2/3+8/9-5/12+3/8

$$\frac { 2 } { 3 } + \frac { 8 } { 9 } - \frac { 5 } { 12 } + \frac { 3 } { 8 }$$

Evaluate

$$\frac{109}{72}\approx 1.513888889$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{8}{9} to fractions with denominator 9.

$$\frac{6}{9}+\frac{8}{9}-\frac{5}{12}+\frac{3}{8}$$

Since \frac{6}{9} and \frac{8}{9} have the same denominator, add them by adding their numerators.

$$\frac{6+8}{9}-\frac{5}{12}+\frac{3}{8}$$

Add 6 and 8 to get 14.

$$\frac{14}{9}-\frac{5}{12}+\frac{3}{8}$$

Least common multiple of 9 and 12 is 36. Convert \frac{14}{9} and \frac{5}{12} to fractions with denominator 36.

$$\frac{56}{36}-\frac{15}{36}+\frac{3}{8}$$

Since \frac{56}{36} and \frac{15}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{56-15}{36}+\frac{3}{8}$$

Subtract 15 from 56 to get 41.

$$\frac{41}{36}+\frac{3}{8}$$

Least common multiple of 36 and 8 is 72. Convert \frac{41}{36} and \frac{3}{8} to fractions with denominator 72.

$$\frac{82}{72}+\frac{27}{72}$$

Since \frac{82}{72} and \frac{27}{72} have the same denominator, add them by adding their numerators.

$$\frac{82+27}{72}$$

Add 82 and 27 to get 109.

$$\frac{109}{72}$$

Factor

$$\frac{109}{2 ^ {3} \cdot 3 ^ {2}} = 1\frac{37}{72} = 1.5138888888888888$$