Solve 1/frac{1{22}+1/18}

$$\frac { 1 } { \frac { 1 } { 22 } + \frac { 1 } { 18 } }$$

Evaluate

$$\frac{99}{10}=9.9$$

Solution Steps

Least common multiple of 22 and 18 is 198. Convert \frac{1}{22} and \frac{1}{18} to fractions with denominator 198.

$$\frac{1}{\frac{9}{198}+\frac{11}{198}}$$

Since \frac{9}{198} and \frac{11}{198} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{9+11}{198}}$$

Add 9 and 11 to get 20.

$$\frac{1}{\frac{20}{198}}$$

Reduce the fraction \frac{20}{198} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{10}{99}}$$

Divide 1 by \frac{10}{99} by multiplying 1 by the reciprocal of \frac{10}{99}.

$$1\times \frac{99}{10}$$

Multiply 1 and \frac{99}{10} to get \frac{99}{10}.

$$\frac{99}{10}$$

Factor

$$\frac{3 ^ {2} \cdot 11}{2 \cdot 5} = 9\frac{9}{10} = 9.9$$