Solve 1/frac{1{3}+1/16}

$$\frac{ 1 }{ \frac{ 1 }{ 3 } + \frac{ 1 }{ 16 } }$$

Evaluate

$$\frac{48}{19}\approx 2.526315789$$

Solution Steps

Least common multiple of 3 and 16 is 48. Convert \frac{1}{3} and \frac{1}{16} to fractions with denominator 48.

$$\frac{1}{\frac{16}{48}+\frac{3}{48}}$$

Since \frac{16}{48} and \frac{3}{48} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{16+3}{48}}$$

Add 16 and 3 to get 19.

$$\frac{1}{\frac{19}{48}}$$

Divide 1 by \frac{19}{48} by multiplying 1 by the reciprocal of \frac{19}{48}.

$$1\times \frac{48}{19}$$

Multiply 1 and \frac{48}{19} to get \frac{48}{19}.

$$\frac{48}{19}$$

Factor

$$\frac{2 ^ {4} \cdot 3}{19} = 2\frac{10}{19} = 2.526315789473684$$