Solve 1/frac{1{18}+1/24+1/30}

$$\frac { 1 } { \frac { 1 } { 18 } + \frac { 1 } { 24 } + \frac { 1 } { 30 } }$$

Evaluate

$$\frac{360}{47}\approx 7.659574468$$

Solution Steps

Least common multiple of 18 and 24 is 72. Convert \frac{1}{18} and \frac{1}{24} to fractions with denominator 72.

$$\frac{1}{\frac{4}{72}+\frac{3}{72}+\frac{1}{30}}$$

Since \frac{4}{72} and \frac{3}{72} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{4+3}{72}+\frac{1}{30}}$$

Add 4 and 3 to get 7.

$$\frac{1}{\frac{7}{72}+\frac{1}{30}}$$

Least common multiple of 72 and 30 is 360. Convert \frac{7}{72} and \frac{1}{30} to fractions with denominator 360.

$$\frac{1}{\frac{35}{360}+\frac{12}{360}}$$

Since \frac{35}{360} and \frac{12}{360} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{35+12}{360}}$$

Add 35 and 12 to get 47.

$$\frac{1}{\frac{47}{360}}$$

Divide 1 by \frac{47}{360} by multiplying 1 by the reciprocal of \frac{47}{360}.

$$1\times \frac{360}{47}$$

Multiply 1 and \frac{360}{47} to get \frac{360}{47}.

$$\frac{360}{47}$$

Factor

$$\frac{2 ^ {3} \cdot 3 ^ {2} \cdot 5}{47} = 7\frac{31}{47} = 7.659574468085107$$