Solve 1div((1div100)+1div100)+(1div1000)+(1div1000)+(1div2200))

$$1 \div ((1 \div 100)+1 \div 100)+(1 \div 1000)+(1 \div 1000)+(1 \div 2200))$$

Evaluate

$$\frac{550027}{11000}\approx 50.002454545$$

Solution Steps

Since \frac{1}{100} and \frac{1}{100} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{1+1}{100}}+\frac{1}{1000}+\frac{1}{1000}+\frac{1}{2200}$$

Add 1 and 1 to get 2.

$$\frac{1}{\frac{2}{100}}+\frac{1}{1000}+\frac{1}{1000}+\frac{1}{2200}$$

Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{1}{50}}+\frac{1}{1000}+\frac{1}{1000}+\frac{1}{2200}$$

Divide 1 by \frac{1}{50} by multiplying 1 by the reciprocal of \frac{1}{50}.

$$1\times 50+\frac{1}{1000}+\frac{1}{1000}+\frac{1}{2200}$$

Multiply 1 and 50 to get 50.

$$50+\frac{1}{1000}+\frac{1}{1000}+\frac{1}{2200}$$

Convert 50 to fraction \frac{50000}{1000}.

$$\frac{50000}{1000}+\frac{1}{1000}+\frac{1}{1000}+\frac{1}{2200}$$

Since \frac{50000}{1000} and \frac{1}{1000} have the same denominator, add them by adding their numerators.

$$\frac{50000+1}{1000}+\frac{1}{1000}+\frac{1}{2200}$$

Add 50000 and 1 to get 50001.

$$\frac{50001}{1000}+\frac{1}{1000}+\frac{1}{2200}$$

Since \frac{50001}{1000} and \frac{1}{1000} have the same denominator, add them by adding their numerators.

$$\frac{50001+1}{1000}+\frac{1}{2200}$$

Add 50001 and 1 to get 50002.

$$\frac{50002}{1000}+\frac{1}{2200}$$

Reduce the fraction \frac{50002}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{25001}{500}+\frac{1}{2200}$$

Least common multiple of 500 and 2200 is 11000. Convert \frac{25001}{500} and \frac{1}{2200} to fractions with denominator 11000.

$$\frac{550022}{11000}+\frac{5}{11000}$$

Since \frac{550022}{11000} and \frac{5}{11000} have the same denominator, add them by adding their numerators.

$$\frac{550022+5}{11000}$$

Add 550022 and 5 to get 550027.

$$\frac{550027}{11000}$$

Factor

$$\frac{550027}{2 ^ {3} \cdot 5 ^ {3} \cdot 11} = 50\frac{27}{11000} = 50.00245454545455$$