Solve 1/frac{1{36}-1/44}

$$\frac { 1 } { \frac { 1 } { 36 } - \frac { 1 } { 44 } }$$

Evaluate

$$198$$

Solution Steps

Least common multiple of 36 and 44 is 396. Convert \frac{1}{36} and \frac{1}{44} to fractions with denominator 396.

$$\frac{1}{\frac{11}{396}-\frac{9}{396}}$$

Since \frac{11}{396} and \frac{9}{396} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{11-9}{396}}$$

Subtract 9 from 11 to get 2.

$$\frac{1}{\frac{2}{396}}$$

Reduce the fraction \frac{2}{396} to lowest terms by extracting and canceling out 2.

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

Divide 1 by \frac{1}{198} by multiplying 1 by the reciprocal of \frac{1}{198}.

$$1\times 198$$

Multiply 1 and 198 to get 198.

$$198$$

Factor

$$2\times 3^{2}\times 11$$