Solve 1/frac{1{36}-1/45}

$$\frac{ 1 }{ \frac{ 1 }{ 36 } - \frac{ 1 }{ 45 } }$$

Evaluate

$$180$$

Solution Steps

Least common multiple of 36 and 45 is 180. Convert \frac{1}{36} and \frac{1}{45} to fractions with denominator 180.

$$\frac{1}{\frac{5}{180}-\frac{4}{180}}$$

Since \frac{5}{180} and \frac{4}{180} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{5-4}{180}}$$

Subtract 4 from 5 to get 1.

$$\frac{1}{\frac{1}{180}}$$

Divide 1 by \frac{1}{180} by multiplying 1 by the reciprocal of \frac{1}{180}.

$$1\times 180$$

Multiply 1 and 180 to get 180.

$$180$$

Factor

$$2^{2}\times 3^{2}\times 5$$