Solve (2/3+3/4+3/5)

$$( \frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 3 } { 5 } )$$

Evaluate

$$\frac{121}{60}\approx 2.016666667$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

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

Since \frac{8}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

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

Add 8 and 9 to get 17.

$$\frac{17}{12}+\frac{3}{5}$$

Least common multiple of 12 and 5 is 60. Convert \frac{17}{12} and \frac{3}{5} to fractions with denominator 60.

$$\frac{85}{60}+\frac{36}{60}$$

Since \frac{85}{60} and \frac{36}{60} have the same denominator, add them by adding their numerators.

$$\frac{85+36}{60}$$

Add 85 and 36 to get 121.

$$\frac{121}{60}$$

Factor

$$\frac{11 ^ {2}}{2 ^ {2} \cdot 3 \cdot 5} = 2\frac{1}{60} = 2.0166666666666666$$