It is frequently required to decide whether a fraction is greater or smaller when comparing fractions. Finding equal fractions and comparing different measurements are very famous cases in mathematics where the ability to order fractions is important. Ordering fractions facilitates meaningful comparisons in mathematical problems and helps us understand the relative sizes of fractions.

In this article, we will address the important term of ordering fractions. We elaborate on its definition and the necessary steps to write these fractions in ascending or descending order. We will also give some examples to understand this concept precisely.

Ordering Fractions:

The technique of writing fractions in a certain order according to their numerical values is known as ordering fractions. The fractions elaborate on how many parts we have out of the total parts or numbers.

Ordering fractions simply means arranging them in a specific order from smallest to largest or largest to smallest. This is similar to ordering numbers on a number line but with fractions and for that purpose, we should understand the relationship between the numerators and denominators.

Consider a cake that is cut into equal slices with each slice representing a portion of the cake as a whole. The fraction indicates the number of slices we have relative to the total number of slices. For example, if we have 2 slices of a cake having 8 total slices of cake. We will write it as 2/8. In simple words we can say that a fraction has two parts:

• Numerator: This is the number of slices we have and in this case, it is the upper part of the line that is 2.
• Denominator: This is the total number of slices and here, in this case, it is below the line which is eight.

Ordering fractions is essential for the following reasons:

• It helps us to compare different quantities precisely.
• It enables us to solve math problems that have fractions.
• It provides the basis for important math concepts such as ratios and proportions

Steps to Order Fractions:

Now we will address the useful steps to arrange the fractions into the required order.

1. Common Denominator:

This is the most important step. Fractions cannot be easily compared unless they have the same denominators. Suppose you have two pizzas. One of the pizzas is cut into four slices and the other one is cut into eight slices. Here we need to have a common denominator for comparing how much pizza each slice represents like cutting both pizzas into 8 slices. There are two ways to find a common denominator:

• Determine LCM: This is the smallest number that is divisible by the denominators of all other fractions.
• Multiplying denominators: We can multiply each denominator by the other denominators unless they are all the same.

2. Comparing Numerators:

Once we have determined the denominator simply compare the numerators. The fraction with the larger numerator represents a larger portion of the whole and hence it is greater such as 4/12 is greater than 3/12 because 4 is larger than 3. It is important to note that the denominator tells us the total number of parts and the numerator elaborates on how many of those parts we have.

3. Order the Fractions:

We arrange the fractions in the desired order based on the comparison of numerators. If we are to arrange them from smallest to largest or start with the fraction with the smallest numerator and move on to the fraction with the next smallest numerator and so on.

• Ascending order: Arrange the fractions from smallest to largest such as 3/12, 4/12.
• Descending order: Arrange the fractions from largest to smallest such as 4/12, 3/12.

4. Rewrite the Fractions:

If we used the multiplication method to find the common denominator, rewrite the fractions with the original denominators. Here it is necessary to understand that practice is the key to mastering any skill. The more you practice ordering fractions, the more confident and efficient you will become.

How to order the fractions?

Example 1: Ordering Fractions with Same Denominators

Determine what will be the order of the following fractions from least to greatest.
1/3
2/3
1/3

Solution:

Step 1: Check Denominators:

Since all fractions have the same denominator (3), we can proceed directly to compare their numerators.

Step 2: Compare Numerators: 1 < 2 < 3.

Step 3: Order Fractions: It helps us to compare different quantities precisely
It enables us to solve math problems that have fractions.
It provides the basis for important math concepts such as ratios and proportions.

1/3, 2/3, 1/3.

Step 4: Find Order:
Step 1/3, 2/3, 1/3 Ans.

Example 2: Ordering Fractions with Unlike Denominators

Determine what will be the order of the following fractions from least to greatest.
1/2, 1/4, and 3/8

Solution:

Step 1: Determine LCM:
8 is the LCM of 2, 4, and 8.

Step 2: Make Denominators Equal:
Multiply 1/2 by 4/4:
1/2 x 4/4 = 4/8.
Multiply 1/4 by 2/2:
1/4 x 2/2 = 2/8.
Multiply 3/8 by 1/1:
3/8 x 1/1 = 3/8.

Step 3: Compare Numerators:
2 < 3 < 4.

Step 4: Order Fractions:
2/8, 3/8, 4/8.

Step 5: Final Order:
2/8, 3/8, 4/8.

Example 3: Ordering Fractions with Mixed Numbers
Determine what will be the order of the following numbers from least to greatest.
11/2
3/4
2

Solution:

Step 1: Convert Mixed Number:
Convert 1 ½ to an improper fraction:
1 + ½ = 2/2 + 1/2 = 3/2.

Step 2: Find LCM:
The LCM of 2, 4, and 2 is 4.

Step 3: Make Denominators Equal:
Multiply 3/2 by 2/2:
3/2 x 2/2 = 6/4.
Multiply 3/4 by 1/1:
3/4 x 1/1 = 3/4.

Step 4: Compare Numbers:
2 < 3 < 6.

Step 5: Order Numbers:
2, 3/4, 6/4.
Final Order: 2, 3/4, 6/4 Ans.
Example 4:Order the following fractions:
1/2
3/4
1/4

Solution:
Step 1: Find the LCM of the denominators, which is 4.
Step 2: Rewrite the fractions with the common denominator: 2/4, 3/4, 1/4
Step 3: Compare numerators: 1 < 2 < 3
Step 4: Order the fractions:
1/4, 2/4, 3/4 Ans.

Wrap Up:

In this article, we have discussed the topic of ordering fractions. We have covered its definition and steps that help us to order the fractions. In the last section, we addressed some solved examples. Hopefully, by reading this article you can easily order the fractions in the required format.