Solve 1/frac{1{1500}+1/15002.2}

$$\frac{ 1 }{ \frac{ 1 }{ 1500 } + \frac{ 1 }{ 15002.2 } }$$

Evaluate

$$\frac{112516500}{82511}\approx 1363.654543031$$

Solution Steps

Expand \frac{1}{15002.2} by multiplying both numerator and the denominator by 10.

$$\frac{1}{\frac{1}{1500}+\frac{10}{150022}}$$

Reduce the fraction \frac{10}{150022} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{1}{1500}+\frac{5}{75011}}$$

Least common multiple of 1500 and 75011 is 112516500. Convert \frac{1}{1500} and \frac{5}{75011} to fractions with denominator 112516500.

$$\frac{1}{\frac{75011}{112516500}+\frac{7500}{112516500}}$$

Since \frac{75011}{112516500} and \frac{7500}{112516500} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{75011+7500}{112516500}}$$

Add 75011 and 7500 to get 82511.

$$\frac{1}{\frac{82511}{112516500}}$$

Divide 1 by \frac{82511}{112516500} by multiplying 1 by the reciprocal of \frac{82511}{112516500}.

$$1\times \frac{112516500}{82511}$$

Multiply 1 and \frac{112516500}{82511} to get \frac{112516500}{82511}.

$$\frac{112516500}{82511}$$

Factor

$$\frac{3 \cdot 75011 \cdot 2 ^ {2} \cdot 5 ^ {3}}{11 \cdot 13 \cdot 577} = 1363\frac{54007}{82511} = 1363.6545430306262$$