Solve 1/frac{1{72}-1/99}

$$\frac { 1 } { \frac { 1 } { 72 } - \frac { 1 } { 99 } }$$

Evaluate

$$264$$

Solution Steps

Least common multiple of 72 and 99 is 792. Convert \frac{1}{72} and \frac{1}{99} to fractions with denominator 792.

$$\frac{1}{\frac{11}{792}-\frac{8}{792}}$$

Since \frac{11}{792} and \frac{8}{792} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{11-8}{792}}$$

Subtract 8 from 11 to get 3.

$$\frac{1}{\frac{3}{792}}$$

Reduce the fraction \frac{3}{792} to lowest terms by extracting and canceling out 3.

$$\frac{1}{\frac{1}{264}}$$

Divide 1 by \frac{1}{264} by multiplying 1 by the reciprocal of \frac{1}{264}.

$$1\times 264$$

Multiply 1 and 264 to get 264.

$$264$$

Factor

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