Solve 1/frac{1{100}+1/220}

$$\frac{ 1 }{ \frac{ 1 }{ 100 } + \frac{ 1 }{ 220 } }$$

Evaluate

$$\frac{275}{4}=68.75$$

Solution Steps

Least common multiple of 100 and 220 is 1100. Convert \frac{1}{100} and \frac{1}{220} to fractions with denominator 1100.

$$\frac{1}{\frac{11}{1100}+\frac{5}{1100}}$$

Since \frac{11}{1100} and \frac{5}{1100} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{11+5}{1100}}$$

Add 11 and 5 to get 16.

$$\frac{1}{\frac{16}{1100}}$$

Reduce the fraction \frac{16}{1100} to lowest terms by extracting and canceling out 4.

$$\frac{1}{\frac{4}{275}}$$

Divide 1 by \frac{4}{275} by multiplying 1 by the reciprocal of \frac{4}{275}.

$$1\times \frac{275}{4}$$

Multiply 1 and \frac{275}{4} to get \frac{275}{4}.

$$\frac{275}{4}$$

Factor

$$\frac{5 ^ {2} \cdot 11}{2 ^ {2}} = 68\frac{3}{4} = 68.75$$