Solve 991/9,100/99,99/99,9999/100,frac{101}{99}

$$99 \frac { 1 } { 9 } , \frac { 100 } { 99 } , \frac { 99 } { 99 } , 99 \frac { 99 } { 100 } , \frac { 101 } { 99 }$$

Sort

$$1,\frac{100}{99},\frac{101}{99},\frac{892}{9},\frac{9999}{100}$$

Solution Steps

Divide 99 by 99 to get 1.

$$sort(\frac{99\times 9+1}{9},\frac{100}{99},1,\frac{99\times 100+99}{100},\frac{101}{99})$$

Multiply 99 and 9 to get 891.

$$sort(\frac{891+1}{9},\frac{100}{99},1,\frac{99\times 100+99}{100},\frac{101}{99})$$

Add 891 and 1 to get 892.

$$sort(\frac{892}{9},\frac{100}{99},1,\frac{99\times 100+99}{100},\frac{101}{99})$$

Multiply 99 and 100 to get 9900.

$$sort(\frac{892}{9},\frac{100}{99},1,\frac{9900+99}{100},\frac{101}{99})$$

Add 9900 and 99 to get 9999.

$$sort(\frac{892}{9},\frac{100}{99},1,\frac{9999}{100},\frac{101}{99})$$

Convert decimal numbers in the list \frac{892}{9},\frac{100}{99},1,\frac{9999}{100},\frac{101}{99} to fractions.

$$\frac{892}{9},\frac{100}{99},1,\frac{9999}{100},\frac{101}{99}$$

Least common denominator of the numbers in the list \frac{892}{9},\frac{100}{99},1,\frac{9999}{100},\frac{101}{99} is 9900. Convert numbers in the list to fractions with denominator 9900.

$$\frac{981200}{9900},\frac{10000}{9900},\frac{9900}{9900},\frac{989901}{9900},\frac{10100}{9900}$$

To sort the list, start from a single element \frac{981200}{9900}.

$$\frac{981200}{9900}$$

Insert \frac{10000}{9900} to the appropriate location in the new list.

$$\frac{10000}{9900},\frac{981200}{9900}$$

Insert \frac{9900}{9900} to the appropriate location in the new list.

$$\frac{9900}{9900},\frac{10000}{9900},\frac{981200}{9900}$$

Insert \frac{989901}{9900} to the appropriate location in the new list.

$$\frac{9900}{9900},\frac{10000}{9900},\frac{981200}{9900},\frac{989901}{9900}$$

Insert \frac{10100}{9900} to the appropriate location in the new list.

$$\frac{9900}{9900},\frac{10000}{9900},\frac{10100}{9900},\frac{981200}{9900},\frac{989901}{9900}$$

Replace the obtained fractions with the initial values.

$$1,\frac{100}{99},\frac{101}{99},\frac{892}{9},\frac{9999}{100}$$

Evaluate

$$\frac{892}{9},\frac{100}{99},1,\frac{9999}{100},\frac{101}{99}$$