Solve 1/frac{1{1200}+1/600+1/2000+1/7.36}

$$\frac{ 1 }{ \frac{ 1 }{ 1200 } + \frac{ 1 }{ 600 } + \frac{ 1 }{ 2000 } + \frac{ 1 }{ 7.36 } }$$

Evaluate

$$\frac{11500}{1597}\approx 7.201001879$$

Solution Steps

Least common multiple of 1200 and 600 is 1200. Convert \frac{1}{1200} and \frac{1}{600} to fractions with denominator 1200.

$$\frac{1}{\frac{1}{1200}+\frac{2}{1200}+\frac{1}{2000}+\frac{1}{7.36}}$$

Since \frac{1}{1200} and \frac{2}{1200} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{1+2}{1200}+\frac{1}{2000}+\frac{1}{7.36}}$$

Add 1 and 2 to get 3.

$$\frac{1}{\frac{3}{1200}+\frac{1}{2000}+\frac{1}{7.36}}$$

Reduce the fraction \frac{3}{1200} to lowest terms by extracting and canceling out 3.

$$\frac{1}{\frac{1}{400}+\frac{1}{2000}+\frac{1}{7.36}}$$

Least common multiple of 400 and 2000 is 2000. Convert \frac{1}{400} and \frac{1}{2000} to fractions with denominator 2000.

$$\frac{1}{\frac{5}{2000}+\frac{1}{2000}+\frac{1}{7.36}}$$

Since \frac{5}{2000} and \frac{1}{2000} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{5+1}{2000}+\frac{1}{7.36}}$$

Add 5 and 1 to get 6.

$$\frac{1}{\frac{6}{2000}+\frac{1}{7.36}}$$

Reduce the fraction \frac{6}{2000} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{3}{1000}+\frac{1}{7.36}}$$

Expand \frac{1}{7.36} by multiplying both numerator and the denominator by 100.

$$\frac{1}{\frac{3}{1000}+\frac{100}{736}}$$

Reduce the fraction \frac{100}{736} to lowest terms by extracting and canceling out 4.

$$\frac{1}{\frac{3}{1000}+\frac{25}{184}}$$

Least common multiple of 1000 and 184 is 23000. Convert \frac{3}{1000} and \frac{25}{184} to fractions with denominator 23000.

$$\frac{1}{\frac{69}{23000}+\frac{3125}{23000}}$$

Since \frac{69}{23000} and \frac{3125}{23000} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{69+3125}{23000}}$$

Add 69 and 3125 to get 3194.

$$\frac{1}{\frac{3194}{23000}}$$

Reduce the fraction \frac{3194}{23000} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{1597}{11500}}$$

Divide 1 by \frac{1597}{11500} by multiplying 1 by the reciprocal of \frac{1597}{11500}.

$$1\times \frac{11500}{1597}$$

Multiply 1 and \frac{11500}{1597} to get \frac{11500}{1597}.

$$\frac{11500}{1597}$$

Factor

$$\frac{23 \cdot 2 ^ {2} \cdot 5 ^ {3}}{1597} = 7\frac{321}{1597} = 7.201001878522229$$