Solve 0.593+1/frac{1{105.796}+1/176.38}

$$0.593+ \frac{ 1 }{ \frac{ 1 }{ 105.796 } + \frac{ 1 }{ 176.38 } }$$

Evaluate

$$\frac{1176726803}{17636000}\approx 66.722998582$$

Solution Steps

Expand \frac{1}{105.796} by multiplying both numerator and the denominator by 1000.

$$0.593+\frac{1}{\frac{1000}{105796}+\frac{1}{176.38}}$$

Reduce the fraction \frac{1000}{105796} to lowest terms by extracting and canceling out 4.

$$0.593+\frac{1}{\frac{250}{26449}+\frac{1}{176.38}}$$

Expand \frac{1}{176.38} by multiplying both numerator and the denominator by 100.

$$0.593+\frac{1}{\frac{250}{26449}+\frac{100}{17638}}$$

Reduce the fraction \frac{100}{17638} to lowest terms by extracting and canceling out 2.

$$0.593+\frac{1}{\frac{250}{26449}+\frac{50}{8819}}$$

Least common multiple of 26449 and 8819 is 233253731. Convert \frac{250}{26449} and \frac{50}{8819} to fractions with denominator 233253731.

$$0.593+\frac{1}{\frac{2204750}{233253731}+\frac{1322450}{233253731}}$$

Since \frac{2204750}{233253731} and \frac{1322450}{233253731} have the same denominator, add them by adding their numerators.

$$0.593+\frac{1}{\frac{2204750+1322450}{233253731}}$$

Add 2204750 and 1322450 to get 3527200.

$$0.593+\frac{1}{\frac{3527200}{233253731}}$$

Divide 1 by \frac{3527200}{233253731} by multiplying 1 by the reciprocal of \frac{3527200}{233253731}.

$$0.593+1\times \frac{233253731}{3527200}$$

Multiply 1 and \frac{233253731}{3527200} to get \frac{233253731}{3527200}.

$$0.593+\frac{233253731}{3527200}$$

Convert decimal number 0.593 to fraction \frac{593}{1000}.

$$\frac{593}{1000}+\frac{233253731}{3527200}$$

Least common multiple of 1000 and 3527200 is 17636000. Convert \frac{593}{1000} and \frac{233253731}{3527200} to fractions with denominator 17636000.

$$\frac{10458148}{17636000}+\frac{1166268655}{17636000}$$

Since \frac{10458148}{17636000} and \frac{1166268655}{17636000} have the same denominator, add them by adding their numerators.

$$\frac{10458148+1166268655}{17636000}$$

Add 10458148 and 1166268655 to get 1176726803.

$$\frac{1176726803}{17636000}$$

Factor

$$\frac{7 \cdot 168103829}{4409 \cdot 2 ^ {5} \cdot 5 ^ {3}} = 66\frac{12750803}{17636000} = 66.722998582445$$