# Order of Fractions: Defined and Explained with Examples

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We know very well about “fractions”, the value in the form of “p/q” is called a fraction. There are many types of fractions in mathematics i.e. proper fractions, improper fractions, and mixed fractions, like a fraction, unlike fractions, and equivalent fractions, etc.

The “Flemish pamphlet De Thiende”, printed in Leyden in 1585, is credited with popularizing decimal fractions as a calculating tool. In this article, we’ll discuss fractions and how to order fractions with the help of solved examples.

## What is a Fraction?

A fraction is defined as p / q.

Example:

1/2, 3/7, and 5/11 are examples of fractions, etc.

## Advantages of fraction:

There are the following advantages of fractions in our daily life:

• It is easy to implement
• It is highly “effective” and “efficient”
• One of the best is that it is easy to use.

## Oder of Fractions:

There are the following methods of arranging values, fractions, and numbers. Normally there are two methods of arranging fractions or numbers.

• Ascending order
• Descending Order

## Ascending order:

The method of arranging values in which small values are first and greatest value after the small is called ascending order of values.

## Descending order:

The method of arranging values in which large values are the first and small values after the large is called the descending order of values.

## How to write percentages in the fractional form?

We can write percentage value as a fraction by dividing 100 i.e. 40% can be written in fraction form as 40/100. We easily understand the idea of ordering fractions by doing this conversion on the percentage values.

## Methods of ordering fractions:

We already discuss types of arranging values now we describe the method of arranging fractions, normally two basic methods of arranging fractions can be used following.

• Making like fraction
• Conversion method

## Making like fractions:

There is the following step for making like fractions.

• Write the fraction
• Write denominators separately
• Find the LCM of all denominators of fractions
• Now make all denominators equal
• After making an equal denominator arrange nominators in the order you want.

## Conversion method of fraction:

There are the following steps of the conversion method.

• Write the fraction
• Write each fraction into a percentage by multiplying 100
• Arrange the number by desired order.

## How to order fractions?

Here are a few examples to understand how to order fractions.

### Example 1:

Using the making-like fraction method arrange the following.

12/5, 13/7, 2/9, 1/17, 21/4, 16/3

Solution:

Step 1: Write the fraction
12/5, 13/7, 2/9, 1/17, 21/4, 16/3

Step 2: Separately Write denominators
Denominators separately = 5, 7, 9, 17, 4, 3

Step 3: Find the LCM of all denominators
LCM = 21420

Step 4: Now make all denominators equal
12 / 5 = ( 12 × 4284 ) / ( 5 × 4284 ) = 51408 / 21420
13 / 7 = ( 13 × 3060 ) / ( 7 × 3060 ) = 39780 / 21420
2 / 9 = ( 2 × 2380 ) / ( 9 × 2380 ) = 4760 / 21420
1 / 17 = ( 1 × 1260 ) / ( 17 × 1260 ) = 1260 / 21420
21 / 4 = ( 21 × 5355 ) / ( 4 × 5355 ) = 112455 / 21420
16 / 3 = ( 16 × 7140 ) / ( 3 × 7140 ) = 114240 / 21420

Step 5: Arrange nominators in the order you want
Ascending order = 1260 / 21420, 4760 / 21420, 39780 / 21420, 51408 / 21420, 112455 / 21420, 114240 / 21420

“The corresponding terms of the above terms are”:

Least to greatest = 1 / 17, 2 / 9, 13 / 7, 12 / 5, 21 / 4, 16 / 3

Descending order = 114240 / 21420, 112455 / 21420, 51408 / 21420, 39780 / 21420, 4760 / 21420, 1260 / 21420

“The corresponding terms of the above terms are”:

Greatest to least = 16 / 3, 21 / 4, 12 / 5, 13 / 7, 2 / 9, 1 / 17

An ordering fractions calculator is a helpful way to order the fractions in ascending order and descending order to avoid time consuming calculations.

### Example 2:

Arrange into ascending and descending order the following by using the conversion method:

7 / 13, 9 / 4, 5 / 12, 2 / 9, 16 / 3, 1 / 14

Solution:

Step 1: Write the fraction
7 / 13, 9 / 4, 5 / 12, 2 / 9, 16 / 3, 1 / 14

Step 2: Write the fraction into a percentage by multiplying 100
7 / 13 = (7 × 100) / 13 = 53.8 %
9 / 4 = (9 × 100) / 4 = 225 %
5 / 12 = (5 × 100) / 12 = 41.6 %
2 / 9 = (2 × 100) / 9 = 22.2 %
16 / 3 = (16 × 100) / 3 = 533.3 %
1 / 14 = (1 × 100) / 14 = 7.1 %

Step 3: Arrange the number by desired order
Ascending order = 7.1 %, 22.2 %, 41.6 %, 53.8 %, 225 %, 533.3 %

“The corresponding terms of the above terms are”:

Least to greatest = 1 / 14, 2 / 9, 5 / 12, 7 / 13, 9 / 4, 16 / 3

Descending order = 533.3 %, 225 %, 53.8 %, 41.6 %, 22.2 %, 7.1 %

“The corresponding terms of the above terms are”:

Greatest to least = 16 / 3, 9 / 4, 7 / 13, 5 / 12, 2 / 9, 1 / 14

## Final words

In this article, we’ve discussed the order of fractions methods with examples and steps. What is a fraction how many types of fraction, we also discussed the Advantages of a fraction in our daily life? The procedure of finding the order of fractions i.e. making-like fraction method and conversion method.

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## Vijay Gupta

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