Solve 1/frac{1{50}+1/60+1/90+1/120}

$$\frac{ 1 }{ \frac{ 1 }{ 50 } + \frac{ 1 }{ 60 } + \frac{ 1 }{ 90 } + \frac{ 1 }{ 120 } }$$

Evaluate

$$\frac{1800}{101}\approx 17.821782178$$

Solution Steps

Least common multiple of 50 and 60 is 300. Convert \frac{1}{50} and \frac{1}{60} to fractions with denominator 300.

$$\frac{1}{\frac{6}{300}+\frac{5}{300}+\frac{1}{90}+\frac{1}{120}}$$

Since \frac{6}{300} and \frac{5}{300} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{6+5}{300}+\frac{1}{90}+\frac{1}{120}}$$

Add 6 and 5 to get 11.

$$\frac{1}{\frac{11}{300}+\frac{1}{90}+\frac{1}{120}}$$

Least common multiple of 300 and 90 is 900. Convert \frac{11}{300} and \frac{1}{90} to fractions with denominator 900.

$$\frac{1}{\frac{33}{900}+\frac{10}{900}+\frac{1}{120}}$$

Since \frac{33}{900} and \frac{10}{900} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{33+10}{900}+\frac{1}{120}}$$

Add 33 and 10 to get 43.

$$\frac{1}{\frac{43}{900}+\frac{1}{120}}$$

Least common multiple of 900 and 120 is 1800. Convert \frac{43}{900} and \frac{1}{120} to fractions with denominator 1800.

$$\frac{1}{\frac{86}{1800}+\frac{15}{1800}}$$

Since \frac{86}{1800} and \frac{15}{1800} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{86+15}{1800}}$$

Add 86 and 15 to get 101.

$$\frac{1}{\frac{101}{1800}}$$

Divide 1 by \frac{101}{1800} by multiplying 1 by the reciprocal of \frac{101}{1800}.

$$1\times \frac{1800}{101}$$

Multiply 1 and \frac{1800}{101} to get \frac{1800}{101}.

$$\frac{1800}{101}$$

Factor

$$\frac{2 ^ {3} \cdot 3 ^ {2} \cdot 5 ^ {2}}{101} = 17\frac{83}{101} = 17.821782178217823$$