**Ordered fractions** are fractions that are sorted in ascending order.

# Methods of ordering
The common methods for ordering fractions are:
## Method 1: Common denominator
Find the #key# LCM : least common multiple #key# of the denominators of all fractions. This will be the common denominator of all fractions. 

Multiply and divide a number with all fractions so that their denominator becomes equal to the common denominator, as shown in the figure below:



After all of the fractions have an #key# equal denominator : i.e., the common denominator #key#, sort the fractions on the basis of their numerators. 

The fraction with the largest numerator is the largest fraction, and the fraction with the smallest numerator is the smallest fraction. The ordered fractions after the sorting are the sorted fractions.


**Fractions**: 1/2, 2/5, 5/3

**Common denominators**: 15/30, 12/30, 50/30

**Sorted numerators**: 12/30, 15/30, 50/30

**Ordered fractions**: 2/5, 1/2, 5/3

## Method 2: Common numerators
Find the LCM of the numerators of all fractions. This will be the common numerator of all fractions. 

Multiply and divide a number with all fractions so that their numerator becomes equal to the common numerator, as shown in the figure below:

After all of the fractions have an #key# equal numerator : i.e., the common numerator #key#, sort the fractions on the basis of their denominators. 

The fraction with the largest denominator is the smallest fraction, and the fraction with the smallest denominator is the largest fraction. The ordered fractions after the sorting are the sorted fractions.

**Fractions**: 9/4, 7/2, 2/3, 5/11

**Common numerators**: 630/280, 630/180, 630/945, 630/1386

**Sorted denominators**: 630/1386, 630/945, 630/280, 630/180

**Ordered fractions**: 5/11, 2/3, 9/4, 7/2

## Method 3: Changing to fractions
Change all of the fractions to their decimal equivalents and sort them. The resulting fractions after sorting are the sorted fractions.

**Fractions**: 1/9, 2/7, 5/3, 7/11, 2/9

**Equivalent decimals**: 0.11, 0.29, 1.67, 0.64, 0.22

**Sorted equivalent decimals**: 0.11, 0.22, 0.29, 0.64, 1.67

**Ordered fractions**: 1/9, 2/9, 2/7, 7/11, 5/3

What are ordered fractions?

Ordered fractions are fractions that are sorted in ascending order. 

Fractions	Equivalent Decimals
9/4	630/280
7/2	630/180
2/3	630/945
5/11	630/1386

Fractions	Equivalent Decimals
1/9	0.11
2/7	0.29
5/3	1.67
7/11	0.64
2/9	0.22

Fractions	Common Denominator
1/2	15/30
2/5	12/30
5/3	50/30