Solve 1/frac{1{12}+1/13}

$$\frac { 1 } { \frac { 1 } { 12 } + \frac { 1 } { 13 } }$$

Evaluate

$$\frac{156}{25}=6.24$$

Solution Steps

Least common multiple of 12 and 13 is 156. Convert \frac{1}{12} and \frac{1}{13} to fractions with denominator 156.

$$\frac{1}{\frac{13}{156}+\frac{12}{156}}$$

Since \frac{13}{156} and \frac{12}{156} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{13+12}{156}}$$

Add 13 and 12 to get 25.

$$\frac{1}{\frac{25}{156}}$$

Divide 1 by \frac{25}{156} by multiplying 1 by the reciprocal of \frac{25}{156}.

$$1\times \frac{156}{25}$$

Multiply 1 and \frac{156}{25} to get \frac{156}{25}.

$$\frac{156}{25}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 13}{5 ^ {2}} = 6\frac{6}{25} = 6.24$$