Solve {l}{6*10^2+3*10+8/10+5/10000}{1+1/10+1/100+frac{1}{1000}+frac{1}{10000}}

$$\left. \begin{array} { l } { 6 \times 10 ^ { 2 } + 3 \times 10 + \frac { 8 } { 10 } + \frac { 5 } { 10000 } } \\ { 1 + \frac { 1 } { 10 } + \frac { 1 } { 100 } + \frac { 1 } { 1000 } + \frac { 1 } { 10000 } } \end{array} \right.$$

Sort

$$\frac{11111}{10000},\frac{1261601}{2000}$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$sort(6\times 100+3\times 10+\frac{8}{10}+\frac{5}{10000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Multiply 6 and 100 to get 600.

$$sort(600+3\times 10+\frac{8}{10}+\frac{5}{10000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Multiply 3 and 10 to get 30.

$$sort(600+30+\frac{8}{10}+\frac{5}{10000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Add 600 and 30 to get 630.

$$sort(630+\frac{8}{10}+\frac{5}{10000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$sort(630+\frac{4}{5}+\frac{5}{10000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Convert 630 to fraction \frac{3150}{5}.

$$sort(\frac{3150}{5}+\frac{4}{5}+\frac{5}{10000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Since \frac{3150}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$sort(\frac{3150+4}{5}+\frac{5}{10000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Add 3150 and 4 to get 3154.

$$sort(\frac{3154}{5}+\frac{5}{10000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Reduce the fraction \frac{5}{10000} to lowest terms by extracting and canceling out 5.

$$sort(\frac{3154}{5}+\frac{1}{2000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Least common multiple of 5 and 2000 is 2000. Convert \frac{3154}{5} and \frac{1}{2000} to fractions with denominator 2000.

$$sort(\frac{1261600}{2000}+\frac{1}{2000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Since \frac{1261600}{2000} and \frac{1}{2000} have the same denominator, add them by adding their numerators.

$$sort(\frac{1261600+1}{2000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Add 1261600 and 1 to get 1261601.

$$sort(\frac{1261601}{2000},1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Convert 1 to fraction \frac{10}{10}.

$$sort(\frac{1261601}{2000},\frac{10}{10}+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Since \frac{10}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$sort(\frac{1261601}{2000},\frac{10+1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Add 10 and 1 to get 11.

$$sort(\frac{1261601}{2000},\frac{11}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Least common multiple of 10 and 100 is 100. Convert \frac{11}{10} and \frac{1}{100} to fractions with denominator 100.

$$sort(\frac{1261601}{2000},\frac{110}{100}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Since \frac{110}{100} and \frac{1}{100} have the same denominator, add them by adding their numerators.

$$sort(\frac{1261601}{2000},\frac{110+1}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Add 110 and 1 to get 111.

$$sort(\frac{1261601}{2000},\frac{111}{100}+\frac{1}{1000}+\frac{1}{10000})$$

Least common multiple of 100 and 1000 is 1000. Convert \frac{111}{100} and \frac{1}{1000} to fractions with denominator 1000.

$$sort(\frac{1261601}{2000},\frac{1110}{1000}+\frac{1}{1000}+\frac{1}{10000})$$

Since \frac{1110}{1000} and \frac{1}{1000} have the same denominator, add them by adding their numerators.

$$sort(\frac{1261601}{2000},\frac{1110+1}{1000}+\frac{1}{10000})$$

Add 1110 and 1 to get 1111.

$$sort(\frac{1261601}{2000},\frac{1111}{1000}+\frac{1}{10000})$$

Least common multiple of 1000 and 10000 is 10000. Convert \frac{1111}{1000} and \frac{1}{10000} to fractions with denominator 10000.

$$sort(\frac{1261601}{2000},\frac{11110}{10000}+\frac{1}{10000})$$

Since \frac{11110}{10000} and \frac{1}{10000} have the same denominator, add them by adding their numerators.

$$sort(\frac{1261601}{2000},\frac{11110+1}{10000})$$

Add 11110 and 1 to get 11111.

$$sort(\frac{1261601}{2000},\frac{11111}{10000})$$

Least common denominator of the numbers in the list \frac{1261601}{2000},\frac{11111}{10000} is 10000. Convert numbers in the list to fractions with denominator 10000.

$$\frac{6308005}{10000},\frac{11111}{10000}$$

To sort the list, start from a single element \frac{6308005}{10000}.

$$\frac{6308005}{10000}$$

Insert \frac{11111}{10000} to the appropriate location in the new list.

$$\frac{11111}{10000},\frac{6308005}{10000}$$

Replace the obtained fractions with the initial values.

$$\frac{11111}{10000},\frac{1261601}{2000}$$

Evaluate

$$\frac{1261601}{2000},\ \frac{11111}{10000}$$