Solve {l}{1.1/2}{2.1/9}{3.5/9}{4.4/9}

$$\left. \begin{array} { l } { 1.1 / 2 } \\ { 2.1 / 9 } \\ { 3.5 / 9 } \\ { 4.4 / 9 } \end{array} \right.$$

Sort

$$\frac{7}{30},\frac{7}{18},\frac{22}{45},0.55$$

Solution Steps

Expand \frac{1.1}{2} by multiplying both numerator and the denominator by 10.

$$sort(\frac{11}{20},\frac{2.1}{9},\frac{3.5}{9},\frac{4.4}{9})$$

Expand \frac{2.1}{9} by multiplying both numerator and the denominator by 10.

$$sort(\frac{11}{20},\frac{21}{90},\frac{3.5}{9},\frac{4.4}{9})$$

Reduce the fraction \frac{21}{90} to lowest terms by extracting and canceling out 3.

$$sort(\frac{11}{20},\frac{7}{30},\frac{3.5}{9},\frac{4.4}{9})$$

Expand \frac{3.5}{9} by multiplying both numerator and the denominator by 10.

$$sort(\frac{11}{20},\frac{7}{30},\frac{35}{90},\frac{4.4}{9})$$

Reduce the fraction \frac{35}{90} to lowest terms by extracting and canceling out 5.

$$sort(\frac{11}{20},\frac{7}{30},\frac{7}{18},\frac{4.4}{9})$$

Expand \frac{4.4}{9} by multiplying both numerator and the denominator by 10.

$$sort(\frac{11}{20},\frac{7}{30},\frac{7}{18},\frac{44}{90})$$

Reduce the fraction \frac{44}{90} to lowest terms by extracting and canceling out 2.

$$sort(\frac{11}{20},\frac{7}{30},\frac{7}{18},\frac{22}{45})$$

Least common denominator of the numbers in the list \frac{11}{20},\frac{7}{30},\frac{7}{18},\frac{22}{45} is 180. Convert numbers in the list to fractions with denominator 180.

$$\frac{99}{180},\frac{42}{180},\frac{70}{180},\frac{88}{180}$$

To sort the list, start from a single element \frac{99}{180}.

$$\frac{99}{180}$$

Insert \frac{42}{180} to the appropriate location in the new list.

$$\frac{42}{180},\frac{99}{180}$$

Insert \frac{70}{180} to the appropriate location in the new list.

$$\frac{42}{180},\frac{70}{180},\frac{99}{180}$$

Insert \frac{88}{180} to the appropriate location in the new list.

$$\frac{42}{180},\frac{70}{180},\frac{88}{180},\frac{99}{180}$$

Replace the obtained fractions with the initial values.

$$\frac{7}{30},\frac{7}{18},\frac{22}{45},\frac{11}{20}$$

Evaluate

$$0.55,\ \frac{7}{30},\ \frac{7}{18},\ \frac{22}{45}$$