Solve 4/15+10/11+9/14

$$\frac { 4 } { 15 } + \frac { 10 } { 11 } + \frac { 9 } { 14 }$$

Evaluate

$$\frac{4201}{2310}\approx 1.818614719$$

Solution Steps

Least common multiple of 15 and 11 is 165. Convert \frac{4}{15} and \frac{10}{11} to fractions with denominator 165.

$$\frac{44}{165}+\frac{150}{165}+\frac{9}{14}$$

Since \frac{44}{165} and \frac{150}{165} have the same denominator, add them by adding their numerators.

$$\frac{44+150}{165}+\frac{9}{14}$$

Add 44 and 150 to get 194.

$$\frac{194}{165}+\frac{9}{14}$$

Least common multiple of 165 and 14 is 2310. Convert \frac{194}{165} and \frac{9}{14} to fractions with denominator 2310.

$$\frac{2716}{2310}+\frac{1485}{2310}$$

Since \frac{2716}{2310} and \frac{1485}{2310} have the same denominator, add them by adding their numerators.

$$\frac{2716+1485}{2310}$$

Add 2716 and 1485 to get 4201.

$$\frac{4201}{2310}$$

Factor

$$\frac{4201}{2 \cdot 3 \cdot 5 \cdot 7 \cdot 11} = 1\frac{1891}{2310} = 1.8186147186147186$$