Solve 1/frac{1{1500}+1/1968.3}

$$\frac{ 1 }{ \frac{ 1 }{ 1500 } + \frac{ 1 }{ 1968.3 } }$$

Evaluate

$$\frac{9841500}{11561}\approx 851.267191419$$

Solution Steps

Expand \frac{1}{1968.3} by multiplying both numerator and the denominator by 10.

$$\frac{1}{\frac{1}{1500}+\frac{10}{19683}}$$

Least common multiple of 1500 and 19683 is 9841500. Convert \frac{1}{1500} and \frac{10}{19683} to fractions with denominator 9841500.

$$\frac{1}{\frac{6561}{9841500}+\frac{5000}{9841500}}$$

Since \frac{6561}{9841500} and \frac{5000}{9841500} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{6561+5000}{9841500}}$$

Add 6561 and 5000 to get 11561.

$$\frac{1}{\frac{11561}{9841500}}$$

Divide 1 by \frac{11561}{9841500} by multiplying 1 by the reciprocal of \frac{11561}{9841500}.

$$1\times \frac{9841500}{11561}$$

Multiply 1 and \frac{9841500}{11561} to get \frac{9841500}{11561}.

$$\frac{9841500}{11561}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {9} \cdot 5 ^ {3}}{11 \cdot 1051} = 851\frac{3089}{11561} = 851.2671914194274$$