Solve 1/frac{1{5}+1/15}

$$\frac{ 1 }{ \frac{ 1 }{ 5 } + \frac{ 1 }{ 15 } }$$

Evaluate

$$\frac{15}{4}=3.75$$

Solution Steps

Least common multiple of 5 and 15 is 15. Convert \frac{1}{5} and \frac{1}{15} to fractions with denominator 15.

$$\frac{1}{\frac{3}{15}+\frac{1}{15}}$$

Since \frac{3}{15} and \frac{1}{15} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{3+1}{15}}$$

Add 3 and 1 to get 4.

$$\frac{1}{\frac{4}{15}}$$

Divide 1 by \frac{4}{15} by multiplying 1 by the reciprocal of \frac{4}{15}.

$$1\times \frac{15}{4}$$

Multiply 1 and \frac{15}{4} to get \frac{15}{4}.

$$\frac{15}{4}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {2}} = 3\frac{3}{4} = 3.75$$