Order of Fractions: Defined and Explained with Examples

By Vijay Gupta

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Order of fractions

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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Thank you.

Vijay Gupta

Hello everyone, My name is Vijay Gupta and I belong to a very small town that is situated in district Hardoi, which is in Uttar Pradesh. 1. Education – I’ve completed my primary education from a private school that is situated in my hometown and upper primary, matric and higher secondary education have been completed from a government college. Well, I was an average student till class 5th, but I accelerated my preference towards studies from class six. Consequently, I passed out many classes with good positions. Even I passed out 12th with good marks ( 405/500 ) and topped my college. Due to getting good marks, I got a cheque of 500 rupees and was rewarded by the Principal of my college. After completing my 12th, I prepared twice for IIT ( Indian Institute of Technology ) from Aakash institute, but unfortunately, I failed to get selected into the best IIT colleges. But during the preparation, I was being graduated from CSJMU Kanpur. I completed my graduation in 2016 and now I’m pursuing an educational degree ( B.Ed. ). 2. Profession – Although I love teaching, but I also do blogging. Both are my favorite jobs.

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