Solve 1/frac{1{1500}+1/470}

$$\frac{ 1 }{ \frac{ 1 }{ 1500 } + \frac{ 1 }{ 470 } }$$

Evaluate

$$\frac{70500}{197}\approx 357.868020305$$

Solution Steps

Least common multiple of 1500 and 470 is 70500. Convert \frac{1}{1500} and \frac{1}{470} to fractions with denominator 70500.

$$\frac{1}{\frac{47}{70500}+\frac{150}{70500}}$$

Since \frac{47}{70500} and \frac{150}{70500} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{47+150}{70500}}$$

Add 47 and 150 to get 197.

$$\frac{1}{\frac{197}{70500}}$$

Divide 1 by \frac{197}{70500} by multiplying 1 by the reciprocal of \frac{197}{70500}.

$$1\times \frac{70500}{197}$$

Multiply 1 and \frac{70500}{197} to get \frac{70500}{197}.

$$\frac{70500}{197}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 5 ^ {3} \cdot 47}{197} = 357\frac{171}{197} = 357.8680203045685$$