Solve 9/frac{1{232}+1/226+1/232+1/225+1+1+1+1+1}

$$\frac{ 9 }{ \frac{ 1 }{ 232 } + \frac{ 1 }{ 226 } + \frac{ 1 }{ 232 } + \frac{ 1 }{ 225 } +1+1+1+1+1 }$$

Evaluate

$$\frac{26543700}{14798083}\approx 1.793725579$$

Solution Steps

Least common multiple of 232 and 226 is 26216. Convert \frac{1}{232} and \frac{1}{226} to fractions with denominator 26216.

$$\frac{9}{\frac{113}{26216}+\frac{116}{26216}+\frac{1}{232}+\frac{1}{225}+1+1+1+1+1}$$

Since \frac{113}{26216} and \frac{116}{26216} have the same denominator, add them by adding their numerators.

$$\frac{9}{\frac{113+116}{26216}+\frac{1}{232}+\frac{1}{225}+1+1+1+1+1}$$

Add 113 and 116 to get 229.

$$\frac{9}{\frac{229}{26216}+\frac{1}{232}+\frac{1}{225}+1+1+1+1+1}$$

Least common multiple of 26216 and 232 is 26216. Convert \frac{229}{26216} and \frac{1}{232} to fractions with denominator 26216.

$$\frac{9}{\frac{229}{26216}+\frac{113}{26216}+\frac{1}{225}+1+1+1+1+1}$$

Since \frac{229}{26216} and \frac{113}{26216} have the same denominator, add them by adding their numerators.

$$\frac{9}{\frac{229+113}{26216}+\frac{1}{225}+1+1+1+1+1}$$

Add 229 and 113 to get 342.

$$\frac{9}{\frac{342}{26216}+\frac{1}{225}+1+1+1+1+1}$$

Reduce the fraction \frac{342}{26216} to lowest terms by extracting and canceling out 2.

$$\frac{9}{\frac{171}{13108}+\frac{1}{225}+1+1+1+1+1}$$

Least common multiple of 13108 and 225 is 2949300. Convert \frac{171}{13108} and \frac{1}{225} to fractions with denominator 2949300.

$$\frac{9}{\frac{38475}{2949300}+\frac{13108}{2949300}+1+1+1+1+1}$$

Since \frac{38475}{2949300} and \frac{13108}{2949300} have the same denominator, add them by adding their numerators.

$$\frac{9}{\frac{38475+13108}{2949300}+1+1+1+1+1}$$

Add 38475 and 13108 to get 51583.

$$\frac{9}{\frac{51583}{2949300}+1+1+1+1+1}$$

Convert 1 to fraction \frac{2949300}{2949300}.

$$\frac{9}{\frac{51583}{2949300}+\frac{2949300}{2949300}+1+1+1+1}$$

Since \frac{51583}{2949300} and \frac{2949300}{2949300} have the same denominator, add them by adding their numerators.

$$\frac{9}{\frac{51583+2949300}{2949300}+1+1+1+1}$$

Add 51583 and 2949300 to get 3000883.

$$\frac{9}{\frac{3000883}{2949300}+1+1+1+1}$$

Convert 1 to fraction \frac{2949300}{2949300}.

$$\frac{9}{\frac{3000883}{2949300}+\frac{2949300}{2949300}+1+1+1}$$

Since \frac{3000883}{2949300} and \frac{2949300}{2949300} have the same denominator, add them by adding their numerators.

$$\frac{9}{\frac{3000883+2949300}{2949300}+1+1+1}$$

Add 3000883 and 2949300 to get 5950183.

$$\frac{9}{\frac{5950183}{2949300}+1+1+1}$$

Convert 1 to fraction \frac{2949300}{2949300}.

$$\frac{9}{\frac{5950183}{2949300}+\frac{2949300}{2949300}+1+1}$$

Since \frac{5950183}{2949300} and \frac{2949300}{2949300} have the same denominator, add them by adding their numerators.

$$\frac{9}{\frac{5950183+2949300}{2949300}+1+1}$$

Add 5950183 and 2949300 to get 8899483.

$$\frac{9}{\frac{8899483}{2949300}+1+1}$$

Convert 1 to fraction \frac{2949300}{2949300}.

$$\frac{9}{\frac{8899483}{2949300}+\frac{2949300}{2949300}+1}$$

Since \frac{8899483}{2949300} and \frac{2949300}{2949300} have the same denominator, add them by adding their numerators.

$$\frac{9}{\frac{8899483+2949300}{2949300}+1}$$

Add 8899483 and 2949300 to get 11848783.

$$\frac{9}{\frac{11848783}{2949300}+1}$$

Convert 1 to fraction \frac{2949300}{2949300}.

$$\frac{9}{\frac{11848783}{2949300}+\frac{2949300}{2949300}}$$

Since \frac{11848783}{2949300} and \frac{2949300}{2949300} have the same denominator, add them by adding their numerators.

$$\frac{9}{\frac{11848783+2949300}{2949300}}$$

Add 11848783 and 2949300 to get 14798083.

$$\frac{9}{\frac{14798083}{2949300}}$$

Divide 9 by \frac{14798083}{2949300} by multiplying 9 by the reciprocal of \frac{14798083}{2949300}.

$$9\times \frac{2949300}{14798083}$$

Express 9\times \frac{2949300}{14798083} as a single fraction.

$$\frac{9\times 2949300}{14798083}$$

Multiply 9 and 2949300 to get 26543700.

$$\frac{26543700}{14798083}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {4} \cdot 5 ^ {2} \cdot 29 \cdot 113}{2909 \cdot 5087} = 1\frac{11745617}{14798083} = 1.7937255791848175$$