How to Order Fractions: An Easy Guide (2 Methods)

how to order fractions

In algebra, the least to greatest is frequently used to make the ordering of percentages, fractions, and integers. This term is simply said to be the ordering fraction or order of fractions. The order of fractions can also order the given terms from greatest to least.

In this article, we’ll learn about how to order fractions (or, the basics of ordering fractions) with a lot of examples. This is going to be an easy and complete guide for you so, hold your sit and be with me till the end.

Read also: How to get better at maths?

Let’s start with an important question…

What is the Order of Fractions?

In mathematics, ordering fractions or order of fractions means arranging the fractions in ascending or descending order. In other words, arranging the fractions from greatest to least or least to greatest is known as the order of fractions.

Example:

12/3, 21/5, 17/7, 23/16, 22/12, 13/9 (random order of fractions)

The right order of fractions = 23/16, 13/9, 22/12, 17/7, 12/3, 21/5 (will tell you later how I did it.)

Note: When we say just Order of fractions we take it as Ascending order of fractions i.e. we have to arrange the fractions in ascending order.

What is Ascending Order?

Ascending order means when we arrange the numbers, fractions, or anything from smallest to largest from left to right.

What is Ascending order

Here are some examples of ascending order:

0, 2, 5, 12, 54, 100 (Integers in ascending order) 0.01, 0.4, 0.8, 0.85 (Decimals in ascending order) 1/4, 2/4, 5/4, 8/4, 9/4 (Fractions in ascending order)

Descending order is just the opposite of ascending order where we arrange the numbers, fractions, or anything from largest to smallest from left to right.

What is Descending order

Examples of descending order:

100, 54, 12, 5, 2, 0 (Integers in descending order) 94%, 75%, 42%, 18% (percentages in descending order)

The order of fractions can also arrange the percentages and decimal numbers because the percentages and decimals are also written in the form of fractions. The fractions can be proper, improper, or mixed.

The fractions are written in the form of p/q where p & q are integers. The decimals are written in the form of 0.25, 0.125, 1.6, etc. while the percentages are written with a % sign or in the form of fractions by taking 100 as a denominator. For example, 12% = 12/100.

How to Order Fractions?

To arrange the fractions, decimals, and percentages in ascending order or descending order, there are two methods of the order of fractions. These two methods of ordering fractions are:

  1. Using a common denominator or making like fractions.
  2. Converting the fractions into decimals and then ordering.

The above two methods are frequently used to arrange the fractions. You can use any method to arrange the given terms in ascending order or descending order.

To order the mixed fractions, first of all, make them improper fractions and then apply any method of ordering fractions.

For example, 2 ¾ = 11/4

You can also use the ordering fractions calculator to arrange the fractions by using the above methods of the order of fractions.

Let’s dive into each method of ordering fractions with examples:

Remember, the fractions, whole numbers, percentages, and mixed numbers can be arranged either in ascending or descending order by applying the methods of ordering fractions.

Method 1: By using the common denominator method

In this method, we follow the 4 steps to order the fractions (in ascending/descending order)

  • Step-1. Find the least common multiple of the denominators of the given fractions
  • Step-2. Make the common denominator of the given fractions
  • Step-3. Arrange the like fractions from least to greatest (or, greatest to least) as the question says
  • Step-4. Rewrite the fractions as they appear in the questions

Example:

Q. Find the order of fractions of the given fractions, 12/3, 21/5, 17/7, 23/16, 22/12, 13/9 by using the common denominator method.

Solution: We will follow the above four steps to order the given fractions.

Fractions are: 1/2, 2/8, 7/4, 8/16, 6/8

Step-1: In these fractions, the dominators are 3, 5, 7, 16, 12, and 9 while the least common multiple of the denominators is 5040.

  • The multiples of 3 = (3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, …)
  • The multiples of 5 = (5, 10, 15, 20, 25, 30, 35, 40, 45, 50, …)
  • The multiples of 7 = (7, 14, 21, 28, 35, 42, 49, 56, 63. 70, …)
  • The multiples of 16 = (16, 32, 48, 64, 80, 96, 112, 128, 144, 160, …)
  • The multiples of 12 = (12, 24, 36, 48, 60, 72, 84, 96, 108, 120, …)
  • The multiples of 19 = (9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …)

Hence, the least common multiple of 3, 5, 7, 16, 12, 9 = 5040]

Step-2: Make the common dominators.

  • 12/3 = (12 x 1680) / (3 x 1680) = 20160/5040
  • 21/5 = (21 x 1008) / (5 x 1008) = 21168/5040
  • 17/7 = (17 x 720) / (7 x 720) = 12240/5040
  • 23/16 = (23 x 315) / (16 x 315) = 7245/5040
  • 22/12 = (22 x 420) / (12 x 420) = 9240/5040
  • 13/9 = (13 x 560) / (9 x 560) = 7280/5040

i.e. 20160/5040, 21168/5040, 12240/5040, 7245/5040, 9240/5040, 7280/5040

Step-3: Arrange the like fractions from least to greatest.

= 7245/5040, 7280/5040, 9240/5040, 12240/5040, 20160/5040, 21168/5040

Step-4: Rewrite the fractions as they appear in the questions

Least to greatest = 23/16, 13/9, 22/12, 17/7, 12/3, 21/5

and, Greatest to least = 21/5, 12/3, 17/7, 22/12, 13/9, 23/16

Method 2: By converting the fractions into decimals.

This is the best and easy method for ordering fractions. In this method, we only follow the 3 steps to get the order of fractions.

  • Step-1. Convert the given fractions (proper and improper) into decimals.
  • Step-2. Arrange the decimals from least to greatest (or, greatest to least) as the question says
  • Step-3. Rewrite them into fractions as they appear in the questions

How about an example in this method?

Q. Find the order of fractions of the given terms, 128/8, 42/9, 9/81, 10%, 0,12, 14%, 2 3/6, 5 8/2 by using the Converting the fractions into decimals method.

Solution: We will follow the above three steps to order the given fractions.

These proper and improper fractions are: 128/8, 42/9, 9/81, 10%, 0.12, 14%, 2 3/6, 5 8/2

Step-1: First, convert all the fractions into decimals.

  • 128/8 = 64/4 = 32/2 = 16
  • 42/9 = 14/3 = 4.67
  • 9/81 = 3/27 = 1/9 = 0.12
  • 10% = 10/100 = 5/50 =1/10 = 0.1
  • 0.12
  • 14% = 14/100 = 7/50 = 0.14
  • 2 3/6 = 15/6 = 5/2 = 2.5
  • 5 8/2 = 18/2 = 9/1 = 9

i.e. 16, 4.67, 0.12, 0.1, 0.12, 0.14, 2.5, 9

Step-2: Arrange these decimals from least to greatest.

= 0.1, 0.12, 0.12, 0.14, 2.5, 4.67, 9, 16

Step-3: Rewrite the fraction order as they gave in the question.

Least to greatest = 10%, 0.12, 9/81, 14%, 2 3/6, 42/9, 5 8/2, 128/8

and, Greatest to least = 128/8, 5 8/2, 42/9, 2 3/6, 14%, 9/81, 0.12, 10%

If you don’t want to do these calculations then you can also use a least to greatest calculator. This tool provides the result in ascending and descending order with steps.

However, I’d suggest you do the calculations by yourself it will not only make you fast at calculations but also in exams or test you won’t need to rely on any calculator tool.

Summary:

Now you are witnessed that ordering fractions are not a difficult topic. In this post, we’ve discussed all the basics of ordering fractions and how you can order fractions with the two methods.

You can easily arrange the terms from least to greatest and greatest to least just by learning this post.

Now, I’d like to hear from you:

Which methods do you like most and find it easy for ordering fractions?

Let me know in the comment. I’m all ears.

This article is written by Angela L. Harper. However, all views in this content are mine.

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