Solve {l}{110/106*100}{103.77-102.94/102.94}

$$\left. \begin{array} { l } { \frac { 110 } { 106 } \times 100 } \\ { \frac { 103.77 - 102.94 } { 102.94 } } \end{array} \right.$$

Sort

$$\frac{83}{10294},\frac{5500}{53}$$

Solution Steps

Reduce the fraction \frac{110}{106} to lowest terms by extracting and canceling out 2.

$$sort(\frac{55}{53}\times 100,\frac{103.77-102.94}{102.94})$$

Express \frac{55}{53}\times 100 as a single fraction.

$$sort(\frac{55\times 100}{53},\frac{103.77-102.94}{102.94})$$

Multiply 55 and 100 to get 5500.

$$sort(\frac{5500}{53},\frac{103.77-102.94}{102.94})$$

Subtract 102.94 from 103.77 to get 0.83.

$$sort(\frac{5500}{53},\frac{0.83}{102.94})$$

Expand \frac{0.83}{102.94} by multiplying both numerator and the denominator by 100.

$$sort(\frac{5500}{53},\frac{83}{10294})$$

Least common denominator of the numbers in the list \frac{5500}{53},\frac{83}{10294} is 545582. Convert numbers in the list to fractions with denominator 545582.

$$\frac{56617000}{545582},\frac{4399}{545582}$$

To sort the list, start from a single element \frac{56617000}{545582}.

$$\frac{56617000}{545582}$$

Insert \frac{4399}{545582} to the appropriate location in the new list.

$$\frac{4399}{545582},\frac{56617000}{545582}$$

Replace the obtained fractions with the initial values.

$$\frac{83}{10294},\frac{5500}{53}$$

Evaluate

$$\frac{5500}{53},\ \frac{83}{10294}$$