Mathematical Algorithms Mathematics

How to order fractions from least to greatest and vice versa?

Fraction is a topic that most of the students don’t like because of the complexity involved in understanding and solving them. Most of the time, we need to convert the fractions into decimals in order to proceed with our calculations. That’s where students begin to dislike it.

In this post, we will guide you about how to order fractions from least to greatest (ascending) and greatest to least (descending) along with the definition of the fraction.

Arranging or ordering fractions involve converting fractions into decimals sometimes. But, don’t worry, we will demonstrate the concept in a way that you will find very easy to comprehend. Moreover, we will use practical examples to make the idea of ordering fractions crystal clear for you.

What is a Fraction?

Since everybody enjoys pizza, let’s say we’ve ordered a big pizza from our local pizza shop. One big pizza is sliced into 8 slices at the shop. As soon as the pizza arrives, you take four yummy hot slices and cram them into your mouth as the cheese slides off the slice. You’ve just finished a 4/8 or 1/2 of the pizza which is a fraction used to represent the part of the pizza that you ate.

A fraction is just one part of a whole. You have less than whole, but more than 0 of the same thing. You just have a portion of it.


A fraction simply indicates how much of the part you have. It’s literally the quantity or number between two whole quantities or numbers. It’s not quite one whole number, but it’s also not quite another. It lies between both of them.

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In the case of pizza, you just consumed a portion of the pizza, but you only ate a fraction of it. You can see that mastering fractions for beginners aren’t so difficult when you use food examples, right?

Forming a Fraction

A fraction consists of two numbers. One at the top and one at the bottom, having a slash “/” between them. If you have eaten 4 slices out of 8, the fraction would be:


1.   Numerator

The numerator is the number written at the top of the division sign. It indicates how much of each component you have. In our previous pizza case, the numerator is 4 because you ate four slices of that hot cheesy pizza.


2.   Denominator

The number below the slash is referred to as the denominator. It shows us how many pieces the whole has been broken down into. In our previous pizza case, the denominator is eight since the whole pizza was split into eight slices.


What fraction of the pizza would you have eaten if there were six slices and you just ate five? The total number of slices in the whole pizza is six. As a result, six is the denominator in this case.

When you consumed five slices of pizza, the numerator would be five. So, the fraction would become 5/6. If you have eaten 7 slices of pizza out of 8, the fraction would be 7/8.

Ordering Fractions from Least to Greatest and Greatest to Least

Now that you know what exactly a fraction is and how to form a fraction, let’s go through how to order fractions in ascending and descending order. It is pretty simple to put whole numbers in order, but, in the case of fractions, we don’t really know which one is greater or smaller by just looking at them.

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Before we move onto explaining the ordering method, check out this least to greatest calculator. It is a very useful resource for students to order fractions in the least to greatest order and vice versa.

Note: Ascending order is usually referred to as least to greatest and descending order is referred to as greatest to least.

Let’s arrange a set of fractions by using an example.

Method 1: By Converting to Decimals

The first method of ordering fractions is to convert all fractions into decimals. After converting, compare all decimals as it would be easy to comprehend the value of fractions in the form of a decimal.


Arrange the following fractions in the least to greatest and greatest to least order.

3/4, 5/2, 4/5, 7/2, 6/5

  • Convert all fractions to decimals to put these numbers in order.

3/4 = 0.75

5/2 = 2.5

4/5 = 0.8

7/2 = 3.5

6/5 = 1.2

  • Compare all decimal values and arrange in the least to greatest and vice versa.

Least to Greatest Order = 0.75, 0.8, 1.2, 2.5, 3.5

  • Now write the corresponding fractions in the same order.

Least to Greatest Order = 3/4, 4/5, 6/5, 5/2, 7/2

Greatest to Least Order = 3.5, 2.5, 1.2, 0.8, 0.75

Write the corresponding fractions.

Greatest to Least Order = 7/2, 5/2, 6/5, 4/5, 3/4

Method 2: By Finding LCD

The second method of ordering fractions involves finding the LCD – least common denominator. In this method, we find the LCD of all fractions and multiply those fractions with the least common denominator.


Order the following fractions using the LCD method.

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1/4, 3/2, 4/6

  • Use denominators of all fractions to find the LCD. You can also use an online least common denominator calculator to find the LCD. To find it manually, list multiples of all denominators and find the smallest common number in all of them.

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

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

Multiples of 6 = 6, 12, 18, 24, 30, 36…

Least Common Denominator (LCD) = 12

  • Multiply all fractions with the least common denominator which is 12 in this case.

12 × 1/4, 12 × 3/2, 12 × 4/6

3, 18, 8

  • Arrange the numbers in both orders.

Least to Greatest = 3, 8, 18

Greatest to Least = 18, 8, 3

Both of the above methods can be used to order fractions. You can use either method you are comfortable with. If you are good to go with decimals, you can choose to get the least common denominator.

Wrapping Up

You may have learned a few new things in this post, but, it will only help you if you practice these methods with a couple of examples. Understanding fractions is not rocket science. You only need consistency with the practice to master the concept of fractions. So, grab a pen and paper, and start solving fractions if you want to give your best in the next exams.

About the author

Venkatesan Prabu

Venkatesan Prabu

Wikitechy Founder, Author, International Speaker, and Job Consultant. My role as the CEO of Wikitechy, I help businesses build their next generation digital platforms and help with their product innovation and growth strategy. I'm a frequent speaker at tech conferences and events.