Solve 1/frac{1{5}+1/8+1/10}

$$\frac { 1 } { \frac { 1 } { 5 } + \frac { 1 } { 8 } + \frac { 1 } { 10 } }$$

Evaluate

$$\frac{40}{17}\approx 2.352941176$$

Solution Steps

Least common multiple of 5 and 8 is 40. Convert \frac{1}{5} and \frac{1}{8} to fractions with denominator 40.

$$\frac{1}{\frac{8}{40}+\frac{5}{40}+\frac{1}{10}}$$

Since \frac{8}{40} and \frac{5}{40} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{8+5}{40}+\frac{1}{10}}$$

Add 8 and 5 to get 13.

$$\frac{1}{\frac{13}{40}+\frac{1}{10}}$$

Least common multiple of 40 and 10 is 40. Convert \frac{13}{40} and \frac{1}{10} to fractions with denominator 40.

$$\frac{1}{\frac{13}{40}+\frac{4}{40}}$$

Since \frac{13}{40} and \frac{4}{40} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{13+4}{40}}$$

Add 13 and 4 to get 17.

$$\frac{1}{\frac{17}{40}}$$

Divide 1 by \frac{17}{40} by multiplying 1 by the reciprocal of \frac{17}{40}.

$$1\times \frac{40}{17}$$

Multiply 1 and \frac{40}{17} to get \frac{40}{17}.

$$\frac{40}{17}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{17} = 2\frac{6}{17} = 2.3529411764705883$$