Solve 1/frac{1{1200}+1/600+1/2000}

$$\frac{ 1 }{ \frac{ 1 }{ 1200 } + \frac{ 1 }{ 600 } + \frac{ 1 }{ 2000 } }$$

Evaluate

$$\frac{1000}{3}\approx 333.333333333$$

Solution Steps

Least common multiple of 1200 and 600 is 1200. Convert \frac{1}{1200} and \frac{1}{600} to fractions with denominator 1200.

$$\frac{1}{\frac{1}{1200}+\frac{2}{1200}+\frac{1}{2000}}$$

Since \frac{1}{1200} and \frac{2}{1200} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{1+2}{1200}+\frac{1}{2000}}$$

Add 1 and 2 to get 3.

$$\frac{1}{\frac{3}{1200}+\frac{1}{2000}}$$

Reduce the fraction \frac{3}{1200} to lowest terms by extracting and canceling out 3.

$$\frac{1}{\frac{1}{400}+\frac{1}{2000}}$$

Least common multiple of 400 and 2000 is 2000. Convert \frac{1}{400} and \frac{1}{2000} to fractions with denominator 2000.

$$\frac{1}{\frac{5}{2000}+\frac{1}{2000}}$$

Since \frac{5}{2000} and \frac{1}{2000} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{5+1}{2000}}$$

Add 5 and 1 to get 6.

$$\frac{1}{\frac{6}{2000}}$$

Reduce the fraction \frac{6}{2000} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{3}{1000}}$$

Divide 1 by \frac{3}{1000} by multiplying 1 by the reciprocal of \frac{3}{1000}.

$$1\times \frac{1000}{3}$$

Multiply 1 and \frac{1000}{3} to get \frac{1000}{3}.

$$\frac{1000}{3}$$

Factor

$$\frac{2 ^ {3} \cdot 5 ^ {3}}{3} = 333\frac{1}{3} = 333.3333333333333$$