Introduction to ordering fractions: Explained with Examples

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Ordering fractions means arranging them from smallest to largest or largest to smallest based on their values. To order fractions, we need to compare their values.

To compare the values of fractions, we need to have a common denominator. A common denominator is a number that is a multiple of both denominators of the fractions being compared.

Once we have a common denominator, we can compare the numerators of the fractions. The fraction with the greater numerator is larger than the other fraction. If the numerators are equal, then we need to compare the denominators. The fraction with the smaller denominator is larger than the other fraction.

In this article, we discuss ordering fractions definition, ways to finding to ordering fractions, methods of Ordering fractions, real-life applications of ordering fractions, and some examples of ordering fractions.  

Definition of Ordering of fraction 

Ordering of fractions refers to the process of comparing two or more fractions to determine which one is larger or smaller than the others. When comparing fractions, it is important to find a common denominator so that the numerators can be compared directly.

How to Order Fractions?

To order fractions, you can follow these steps: 

  1. Find a common denominator for all fractions you want to order.
  2. Convert each fraction to an equivalent fraction with the same denominator as found in step 1.
  3. Order the fraction by comparing their numerators.
  4. Simplify the ordered fraction fractions if possible.

 For example, let’s say you want to order the fractions 3/4, 1/2, and 2/3.

Step 1: Find a common denominator.

The least common multiple of 4, 2, and 3 is 12.

Step 2: Convert each fraction to an equivalent fraction with a denominator of 12.

3/4 = 9/12

1/2 = 6/12

2/3 = 8/12

Step 3: Order the fractions by comparing their numerators.

6/12 < 8/12 < 9/12

Step 4: Simplify the ordered fractions if possible.

6/12 = 1/2

8/12 = 2/3

9/12 = 3/4

Therefore, the ordered fractions are 1/2, 2/3, and 3/4. 

Methods of ordering fractions:

There are two common methods for ordering fractions:

Method 1: Find a common denominator

To find a common denominator for ordering fractions, you first need to identify the denominators of all the fractions you want to order.

For example, let’s say we want to order the fractions 1/3, 2/5, and 3/8. The denominators are 3, 5, and 8, respectively.

To find a common denominator, you need to find the least common multiple (LCM) of these denominators. One way to do this is to list out the multiples of each denominator and find the smallest multiple that they all have in common.

Using the first method:

  • Multiples of 3: 3, 6, 9, …
  • Multiples of 5: 5, 10,15, …
  • Multiples of 8: 8, 16,24, …

The smallest multiple that all three denominators have in common is 120. Therefore, we can convert each fraction to an equivalent fraction with a denominator of 120:

  • 1/3 = 40/120
  • 2/5 = 48/120
  • 3/8 = 45/120

Now, we can compare the numerators of these fractions to determine their order. In this case, the order is:

1/3 < 3/8 < 2/5

Method 2: Convert the fractions to decimals:

To convert fractions to decimals, you need to divide the numerator by the denominator using a long division or a calculator. Once you have converted all the fractions to decimals, you can compare them to order the fractions from least to greatest.

For example, let’s say we want to order the fractions 2/3, 1/4, and 5/6 in decimal form:

To order fractions, we first need to find a common denominator for all the fractions we want to compare.

2/3 = 0.666666…

1/4 = 0.25

5/6 = 0.833333…

Now that we have converted the fractions to decimals, we can see that the order from least to greatest is:

1/4 = 0.25

 < 2/3 = 0.666666… 

< 5/6 = 0.833333…

Now,

1/4 < 2/3< 5/6

Real-life application of Ordering fractions:

  • Dividing a bill while eating at a restaurant.
  • Finding the discounted price of an object on sale.
  • Arranging a recipe.
  • Ordering fractions are frequently used to analyze the performance of a particular player and team.

Example section:

Here is an example to order numbers from least to greatest and vice versa. 

Example:

Write the following fractions in order of size:

4/3, 3/2, 5/6, 7/12

Step 1:

The fractions have different denominators. 

The denominators of the fractions are 3, 2, 6, and 12. For solving to-order fractions with different denominators, you need to find a common denominator. The LCM (Least Common Multiple) method is one way to find the smallest common denominator.

The LCM of two or more numbers is the smallest positive number that is a multiple of all of them.

33-2-6-12
21-2-2-4
21-1-1-2
11-1-1

Now: 

LCM = 3 × 2 × 2 = 12

4 × 4 / 3 × 4 = 16 / 12

3 × 6 / 2 x 6= 18 / 12

5 × 2/6 × 2= 10/ 12

7/12= 7/ 12

Step 2:

Find the smallest fraction by comparing the numerators and order the fractions

Here are the fractions with their common denominator of 12

16/ 12, 18/12, 10/12, 7/12

Writing them in the least to greatest order would give 

7/ 12, 10/12, 16/12, 18/12

Now write their original fractions

7/ 12, 5/6, 4/3, 3/2

Step 3:

Find the greatest to least order of fractions by comparing the numerators.

Here are the fractions with their common denominator of 12

16/ 12, 18/12, 10/12, 7/12

Writing them in the greatest to least order would give 

18/ 12, 16/12, 10/12, 7/12

Now write their original fractions

3/2, 4/3, 5/6, 7/12

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Summary:

In this article, a basic definition of Ordering fractions, their finding step, methods of Ordering fractions, and also real-life use of Ordering fractions will be discussed. Moreover, with the help of examples, the topic is explained. After a complete understanding of this article, anyone can defend this topic.

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