Solve 1/frac{1{390}+1/680}

$$\frac{ 1 }{ \frac{ 1 }{ 390 } + \frac{ 1 }{ 680 } }$$

Evaluate

$$\frac{26520}{107}\approx 247.85046729$$

Solution Steps

Least common multiple of 390 and 680 is 26520. Convert \frac{1}{390} and \frac{1}{680} to fractions with denominator 26520.

$$\frac{1}{\frac{68}{26520}+\frac{39}{26520}}$$

Since \frac{68}{26520} and \frac{39}{26520} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{68+39}{26520}}$$

Add 68 and 39 to get 107.

$$\frac{1}{\frac{107}{26520}}$$

Divide 1 by \frac{107}{26520} by multiplying 1 by the reciprocal of \frac{107}{26520}.

$$1\times \frac{26520}{107}$$

Multiply 1 and \frac{26520}{107} to get \frac{26520}{107}.

$$\frac{26520}{107}$$

Factor

$$\frac{2 ^ {3} \cdot 3 \cdot 5 \cdot 13 \cdot 17}{107} = 247\frac{91}{107} = 247.85046728971963$$