Solve 1/frac{1{10000}+1/4700+1/4700}

$$\frac{ 1 }{ \frac{ 1 }{ 10000 } + \frac{ 1 }{ 4700 } + \frac{ 1 }{ 4700 } }$$

Evaluate

$$\frac{470000}{247}\approx 1902.834008097$$

Solution Steps

Least common multiple of 10000 and 4700 is 470000. Convert \frac{1}{10000} and \frac{1}{4700} to fractions with denominator 470000.

$$\frac{1}{\frac{47}{470000}+\frac{100}{470000}+\frac{1}{4700}}$$

Since \frac{47}{470000} and \frac{100}{470000} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{47+100}{470000}+\frac{1}{4700}}$$

Add 47 and 100 to get 147.

$$\frac{1}{\frac{147}{470000}+\frac{1}{4700}}$$

Least common multiple of 470000 and 4700 is 470000. Convert \frac{147}{470000} and \frac{1}{4700} to fractions with denominator 470000.

$$\frac{1}{\frac{147}{470000}+\frac{100}{470000}}$$

Since \frac{147}{470000} and \frac{100}{470000} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{147+100}{470000}}$$

Add 147 and 100 to get 247.

$$\frac{1}{\frac{247}{470000}}$$

Divide 1 by \frac{247}{470000} by multiplying 1 by the reciprocal of \frac{247}{470000}.

$$1\times \frac{470000}{247}$$

Multiply 1 and \frac{470000}{247} to get \frac{470000}{247}.

$$\frac{470000}{247}$$

Factor

$$\frac{2 ^ {4} \cdot 5 ^ {4} \cdot 47}{13 \cdot 19} = 1902\frac{206}{247} = 1902.834008097166$$