Solve 1/frac{1{25}+1/35}

$$\frac{ 1 }{ \frac{ 1 }{ 25 } + \frac{ 1 }{ 35 } }$$

Evaluate

$$\frac{175}{12}\approx 14.583333333$$

Solution Steps

Least common multiple of 25 and 35 is 175. Convert \frac{1}{25} and \frac{1}{35} to fractions with denominator 175.

$$\frac{1}{\frac{7}{175}+\frac{5}{175}}$$

Since \frac{7}{175} and \frac{5}{175} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{7+5}{175}}$$

Add 7 and 5 to get 12.

$$\frac{1}{\frac{12}{175}}$$

Divide 1 by \frac{12}{175} by multiplying 1 by the reciprocal of \frac{12}{175}.

$$1\times \frac{175}{12}$$

Multiply 1 and \frac{175}{12} to get \frac{175}{12}.

$$\frac{175}{12}$$

Factor

$$\frac{5 ^ {2} \cdot 7}{2 ^ {2} \cdot 3} = 14\frac{7}{12} = 14.583333333333334$$