Solve 1/frac{1{600}+1/1000+1/2000}

$$\frac{ 1 }{ \frac{ 1 }{ 600 } + \frac{ 1 }{ 1000 } + \frac{ 1 }{ 2000 } }$$

Evaluate

$$\frac{6000}{19}\approx 315.789473684$$

Solution Steps

Least common multiple of 600 and 1000 is 3000. Convert \frac{1}{600} and \frac{1}{1000} to fractions with denominator 3000.

$$\frac{1}{\frac{5}{3000}+\frac{3}{3000}+\frac{1}{2000}}$$

Since \frac{5}{3000} and \frac{3}{3000} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{5+3}{3000}+\frac{1}{2000}}$$

Add 5 and 3 to get 8.

$$\frac{1}{\frac{8}{3000}+\frac{1}{2000}}$$

Reduce the fraction \frac{8}{3000} to lowest terms by extracting and canceling out 8.

$$\frac{1}{\frac{1}{375}+\frac{1}{2000}}$$

Least common multiple of 375 and 2000 is 6000. Convert \frac{1}{375} and \frac{1}{2000} to fractions with denominator 6000.

$$\frac{1}{\frac{16}{6000}+\frac{3}{6000}}$$

Since \frac{16}{6000} and \frac{3}{6000} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{16+3}{6000}}$$

Add 16 and 3 to get 19.

$$\frac{1}{\frac{19}{6000}}$$

Divide 1 by \frac{19}{6000} by multiplying 1 by the reciprocal of \frac{19}{6000}.

$$1\times \frac{6000}{19}$$

Multiply 1 and \frac{6000}{19} to get \frac{6000}{19}.

$$\frac{6000}{19}$$

Factor

$$\frac{2 ^ {4} \cdot 3 \cdot 5 ^ {3}}{19} = 315\frac{15}{19} = 315.7894736842105$$