Solve 37/11-28/19+15/31=

$$3 \frac { 7 } { 11 } - \frac { 28 } { 19 } + \frac { 15 } { 31 } =$$

Evaluate

$$\frac{17147}{6479}\approx 2.646550394$$

Solution Steps

Multiply 3 and 11 to get 33.

$$\frac{33+7}{11}-\frac{28}{19}+\frac{15}{31}$$

Add 33 and 7 to get 40.

$$\frac{40}{11}-\frac{28}{19}+\frac{15}{31}$$

Least common multiple of 11 and 19 is 209. Convert \frac{40}{11} and \frac{28}{19} to fractions with denominator 209.

$$\frac{760}{209}-\frac{308}{209}+\frac{15}{31}$$

Since \frac{760}{209} and \frac{308}{209} have the same denominator, subtract them by subtracting their numerators.

$$\frac{760-308}{209}+\frac{15}{31}$$

Subtract 308 from 760 to get 452.

$$\frac{452}{209}+\frac{15}{31}$$

Least common multiple of 209 and 31 is 6479. Convert \frac{452}{209} and \frac{15}{31} to fractions with denominator 6479.

$$\frac{14012}{6479}+\frac{3135}{6479}$$

Since \frac{14012}{6479} and \frac{3135}{6479} have the same denominator, add them by adding their numerators.

$$\frac{14012+3135}{6479}$$

Add 14012 and 3135 to get 17147.

$$\frac{17147}{6479}$$

Factor

$$\frac{13 \cdot 1319}{11 \cdot 19 \cdot 31} = 2\frac{4189}{6479} = 2.6465503935792563$$