Solve {l}{2/3}{2,5/3}{3,4/5,3}{9/3}

$$\left. \begin{array} { l } { \frac { 2 } { 3 } } \\ { \frac { 2,5 } { 3 } } \\ { \frac { 3,4 } { 5,3 } } \\ { \frac { 9 } { 3 } } \end{array} \right.$$

Sort

$$\frac{34}{53};\frac{2}{3};\frac{5}{6};3$$

Solution Steps

Expand \frac{2,5}{3} by multiplying both numerator and the denominator by 10.

$$sort(\frac{2}{3};\frac{25}{30};\frac{3,4}{5,3};\frac{9}{3})$$

Reduce the fraction \frac{25}{30} to lowest terms by extracting and canceling out 5.

$$sort(\frac{2}{3};\frac{5}{6};\frac{3,4}{5,3};\frac{9}{3})$$

Expand \frac{3,4}{5,3} by multiplying both numerator and the denominator by 10.

$$sort(\frac{2}{3};\frac{5}{6};\frac{34}{53};\frac{9}{3})$$

Divide 9 by 3 to get 3.

$$sort(\frac{2}{3};\frac{5}{6};\frac{34}{53};3)$$

Convert decimal numbers in the list \frac{2}{3};\frac{5}{6};\frac{34}{53};3 to fractions.

$$\frac{2}{3};\frac{5}{6};\frac{34}{53};3$$

Least common denominator of the numbers in the list \frac{2}{3};\frac{5}{6};\frac{34}{53};3 is 318. Convert numbers in the list to fractions with denominator 318.

$$\frac{212}{318};\frac{265}{318};\frac{204}{318};\frac{954}{318}$$

To sort the list, start from a single element \frac{212}{318}.

$$\frac{212}{318}$$

Insert \frac{265}{318} to the appropriate location in the new list.

$$\frac{212}{318};\frac{265}{318}$$

Insert \frac{204}{318} to the appropriate location in the new list.

$$\frac{204}{318};\frac{212}{318};\frac{265}{318}$$

Insert \frac{954}{318} to the appropriate location in the new list.

$$\frac{204}{318};\frac{212}{318};\frac{265}{318};\frac{954}{318}$$

Replace the obtained fractions with the initial values.

$$\frac{34}{53};\frac{2}{3};\frac{5}{6};3$$

Evaluate

$$\frac{2}{3},\ \frac{5}{6},\ \frac{34}{53},\ 3$$