Solve 3/5+4/6+3/2+8/3

$$\frac{ 3 }{ 5 } + \frac{ 4 }{ 6 } + \frac{ 3 }{ 2 } + \frac{ 8 }{ 3 }$$

Evaluate

$$\frac{163}{30}\approx 5.433333333$$

Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{3}{5}+\frac{2}{3}+\frac{3}{2}+\frac{8}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{9}{15}+\frac{10}{15}+\frac{3}{2}+\frac{8}{3}$$

Since \frac{9}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{9+10}{15}+\frac{3}{2}+\frac{8}{3}$$

Add 9 and 10 to get 19.

$$\frac{19}{15}+\frac{3}{2}+\frac{8}{3}$$

Least common multiple of 15 and 2 is 30. Convert \frac{19}{15} and \frac{3}{2} to fractions with denominator 30.

$$\frac{38}{30}+\frac{45}{30}+\frac{8}{3}$$

Since \frac{38}{30} and \frac{45}{30} have the same denominator, add them by adding their numerators.

$$\frac{38+45}{30}+\frac{8}{3}$$

Add 38 and 45 to get 83.

$$\frac{83}{30}+\frac{8}{3}$$

Least common multiple of 30 and 3 is 30. Convert \frac{83}{30} and \frac{8}{3} to fractions with denominator 30.

$$\frac{83}{30}+\frac{80}{30}$$

Since \frac{83}{30} and \frac{80}{30} have the same denominator, add them by adding their numerators.

$$\frac{83+80}{30}$$

Add 83 and 80 to get 163.

$$\frac{163}{30}$$

Factor

$$\frac{163}{2 \cdot 3 \cdot 5} = 5\frac{13}{30} = 5.433333333333334$$