Solve 1/frac{1{6}+1/8}

$$\frac{ 1 }{ \frac{ 1 }{ 6 } + \frac{ 1 }{ 8 } }$$

Evaluate

$$\frac{24}{7}\approx 3.428571429$$

Solution Steps

Least common multiple of 6 and 8 is 24. Convert \frac{1}{6} and \frac{1}{8} to fractions with denominator 24.

$$\frac{1}{\frac{4}{24}+\frac{3}{24}}$$

Since \frac{4}{24} and \frac{3}{24} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{4+3}{24}}$$

Add 4 and 3 to get 7.

$$\frac{1}{\frac{7}{24}}$$

Divide 1 by \frac{7}{24} by multiplying 1 by the reciprocal of \frac{7}{24}.

$$1\times \frac{24}{7}$$

Multiply 1 and \frac{24}{7} to get \frac{24}{7}.

$$\frac{24}{7}$$

Factor

$$\frac{2 ^ {3} \cdot 3}{7} = 3\frac{3}{7} = 3.4285714285714284$$