Solve 5/78+10/117+5/39

$$\frac{ 5 }{ 78 } + \frac{ 10 }{ 117 } + \frac{ 5 }{ 39 }$$

Evaluate

$$\frac{5}{18}\approx 0.277777778$$

Solution Steps

Least common multiple of 78 and 117 is 234. Convert \frac{5}{78} and \frac{10}{117} to fractions with denominator 234.

$$\frac{15}{234}+\frac{20}{234}+\frac{5}{39}$$

Since \frac{15}{234} and \frac{20}{234} have the same denominator, add them by adding their numerators.

$$\frac{15+20}{234}+\frac{5}{39}$$

Add 15 and 20 to get 35.

$$\frac{35}{234}+\frac{5}{39}$$

Least common multiple of 234 and 39 is 234. Convert \frac{35}{234} and \frac{5}{39} to fractions with denominator 234.

$$\frac{35}{234}+\frac{30}{234}$$

Since \frac{35}{234} and \frac{30}{234} have the same denominator, add them by adding their numerators.

$$\frac{35+30}{234}$$

Add 35 and 30 to get 65.

$$\frac{65}{234}$$

Reduce the fraction \frac{65}{234} to lowest terms by extracting and canceling out 13.

$$\frac{5}{18}$$

Factor

$$\frac{5}{2 \cdot 3 ^ {2}} = 0.2777777777777778$$