Ordering fractions is a pretty simple topic. When we have given two or more fractions, we have to order them as in ascending or descending order. We can easily understand that the given input is in fraction or not.

In this post we will learn about fractions, ordering fraction, the least to the greatest arrangement of fractions, basic rules along with lot of examples.

## What is ordering fractions?

In order to learn about ordering fractions, you must have some sound knowledge about fractions.

**Fractions **are numbers that represent a part of the whole. When an object or group of objects is divided into equal parts then each individual part is a **fraction**. A fraction is basically written as 2/3, 8/15, 9/19 and so on.

**Ordering fractions** means arranging fractions from the smallest to greatest (ascending order) or greatest to smallest (descending order).

These fractions can be a proper fraction, improper fraction or mixed fractions, let us learn about these fractions.

### Proper fraction

When the numerator is smaller than the denominator, it is a proper fraction. These fractions are less than one and none of them lies beyond one on the number line. The denominator represents the number of equal parts in which the whole is divided. Proper fractions are written as 2/3, 8/15, 9/19, and so on.

### Improper Fraction

When the numerator is larger than the denominator, it is an improper fraction. These fractions are greater than one and lies beyond one on the number line. The denominator represents the number of equal parts required. The numerator is the number of objects available.

Improper fractions are written as 12/3, 8/5, 19/9, and so on.

### Mixed fraction

A number which is written as the product of a whole number with a proper fraction is known as a mixed fraction. Written as

1 2/5, 2 5/7, 9 10/23, and so on.

An improper fraction can be expressed as a mixed fraction by dividing the numerator by the denominator and obtaining the quotient and remainder.

#### Rules of Ordering Fraction

There are two common rules of ordering fraction.

- Using a common denominator
- Changing fraction to decimal and then ordering

#### Using a common denominator

Fractions can compare and ordered by finding their common denominator as to form equivalent fractions. A common denominator is created by using the common multiples of two numbers. In order to create the common denominator, take all the denominators of the fraction and find the least common multiples of those denominators that LCM value of those denominator is referred as common denominator then make each fraction’s denominator equal to that LCM value by multiplying and dividing by the same number.

**Example 1**

Order the fraction 1/2, 1/4, 1/6 ?

**Solution**

**Step 1:**Take the denominators of the fraction.

2, 4, 6

**Step 2:**Find the LCM of these numbers.

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, …

Multiples of 4 = 4, 8, 12, 16, 20, 24, ….

Multiples of 6 = 6, 12, 18, 24, 30, ….

Common multiples of 2, 4 and 6 = 12, 24, …

LCM of 2, 4 and 6 = 12

**Step 3:**Make the denominator of each fraction equal to 12.

(1/2)(6/6) = 6/12

(1/4)(3/3) = 3/12

(1/6)(2/2) = 2/12

**Step 4:**Write in order.

Ascending order = 2/12, 3/12, 6/12

Descending order = 6/12, 3/12, 2/12

**Step 5:**Write the corresponding fractions in the same order.

Ascending order = 1/6, 1/4, 1/2

Descending order = 1/2, 1/4, 1/6

**Example 2**

Order the fraction 1/3, 4/6, 5/9 ?

**Solution**

**Step 1:**Take the denominators of the fraction.

3, 6, 9

**Step 2:**Find the LCM of these numbers.

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, …

Multiples of 6 = 6, 12, 18, 24, 30, ….

Multiples of 9 = 9, 18, 27, 36, 45, ….

Common multiples of 3, 6 and 9 = 18, 36 …

LCM of 3, 6 and 9 = 18

**Step 3:**Make the denominator of each fraction equal to 18.

(1/3)(6/6) = 6/18

(4/6)(3/3) = 12/18

(5/9)(2/2) = 10/18

**Step 4:**Write in order.

Ascending order = 6/18, 10/18, 12/18

Descending order = 12/18, 10/18, 6/18

**Step 5:**Write the corresponding fractions in the same order.

Ascending order = 1/3, 5/9, 4/6

Descending order = 4/6, 5/9, 1/3

#### Changing fraction to decimal then ordering

It is the second method of ordering fraction in which first convert the fraction into decimal by dividing the numerator on denominator and then order the fraction.

**Example 1**

Order the fraction 1/2, 1/4, 1/6 ?

**Solution**

**Step 1:**convert fraction into decimal.

1/2 = 0.5

1/4 = 0.25

1/6 = 0.167

**Step 2:**write in order.

Ascending order = 0.167, 0.25, 0.5

Descending order = 0.5, 0.25, 0.167

**Step 3:**write the corresponding fractions in the same order.

Ascending order = 1/6, 1/4, 1/2

Descending order = 1/2, 1/4, 1/6

**Example 2**

Order the fraction 1/3, 4/6, 5/9 ?

**Solution**

**Step 1:**Convert fraction into a decimal.

1/3 = 0.333

4/6 = 0.667

5/9 = 0.556

**Step 2:**Write in order.

Ascending order = 0.333, 0.556, 0.667

Descending order = 0.667, 0.556, 0.333

**Step 3:**Write the corresponding fractions in the same order.

Ascending order = 1/3, 5/9, 4/6

Descending order = 4/6, 5/9, 1/3

#### How to arrange fraction from least to greatest

The least toLeast to greatest is the form or ordering fraction in which we arrange the fraction from **least to greatest** simply in ascending order. In order to arrange the fraction from least to greatest we use two basic rules of ordering fraction one is to converts the fraction into decimal and then arrange the other is to make common denominator.

Let us take some examples to arrange the fraction from least to greatest.

**Example 1**

Find least to greatest of the fraction 1/2, 1/4, 1/6?

**Solution**

**Step 1:**Take the denominators of the fraction.

2, 4, 6

**Step 2:**Find the LCM of these numbers.

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, …

Multiples of 4 = 4, 8, 12, 16, 20, 24, ….

Multiples of 6 = 6, 12, 18, 24, 30, ….

Common multiples of 2, 4 and 6 = 12, 24, …

LCM of 2, 4 and 6 = 12

**Step 3:**Make the denominator of each fraction equal to 12.

(1/2)(6/6) = 6/12

(1/4)(3/3) = 3/12

(1/6)(2/2) = 2/12

**Step 4:**Write in order.

Ascending order = 2/12, 3/12, 6/12

= 2/12< 3/12< 6/12

**Step 5:**Write the corresponding fractions in the same order.

Ascending order = 1/6, 1/4, 1/2

= 1/6< 1/4< 1/2

**Example 2**

Find least to greatest of the fraction 1/3, 4/6, 5/9 ?

**Solution**

**Step 1:**Convert fraction into decimal.

1/3 = 0.333

4/6 = 0.667

5/9 = 0.556

**Step 2:**Write in order.

Ascending order = 0.333, 0.556, 0.667

= 0.333< 0.556< 0.667

**Step 3:**Write the corresponding fractions in the same order.

Ascending order = 1/3, 5/9, 4/6

= 1/3< 5/9< 4/6

**Summary**

In this post we have learnt about fractions, ordering fraction, least to the greatest arrangement of fractions, basic rules along with a lot of examples. Once you grabbed the knowledge about this topic you will master it. Now you are witnessed that this topic is not difficult. Just little effort is required to be master in this topic.