The ordering of fractions is frequently used in mathematics for various purposes. It is mainly used to arrange the given set of data either from least to greatest or greatest to least. The whole numbers, percentages, decimals, and fractions can be arranged in both ways with the help of ordering fractions.

In central tendencies, the ascending and descending order is widely used to arrange the data to calculate the various results. In this post, we are going to explain the ordering of fractions along with their techniques and examples.

**What are the ordering fractions?**

In mathematics, the ordering fraction is a technique of arranging the proper, improper, & mixed fractions from least to greatest (ascending order) or greatest to least (descending order). This term can also arrange percentages, whole numbers, and decimals.

The term ascending order is that order in which the smallest value is taken first and goes up to the largest value. While the descending order is the order in which the largest value is taken first and then goes up to the smallest value.

The numbers that are mixed or scattered can be arranged in a sequence either from largest to smallest or smallest to largest easily with the help of ascending and descending orders. Let us briefly discuss the numbers that can be arranged in a sequence.

**Whole numbers**

The numbers in which the digits start from zero and go onward are said to be the whole numbers i.e., 0, 1, 2, 3, 4, 5, 6, … if these numbers are given in an unordered manner, then they can be arranged easily with the help of ordering fractions such as:

5, 7, 3, 2, 9, and 0 can be arranged in ascending and descending order.

Ascending order = 0, 2, 3, 5, 7, 9

Descending order = 9, 7, 5, 3, 2, 0

Similarly, decimal numbers can be arranged easily.

**Percentages**

The percentage is a relative term that indicates the hundredth part of any quantity. It is denoted by a “%” sign. For example, if a student takes 150 marks out of three hundred it means the student square 50% marks.

The percentages can be arranged either in ascending order or descending order by converting percentages into fractions or decimals.

**Fractions**

The most commonly used and main term for ordering fractions is a fraction. The fraction is written in the form of p/q where q is not equal to zero. There are further three kinds of fractions e.g., proper fraction, improper fraction, and mixed fraction.

A proper fraction is a subtype of fraction in which the denominator is greater than the numerator. Such as ½, 4/5, 9/11, etc. The improper fractions are those fractions in which the numerator is greater than the denominator. Such as 3/2, 5/3, 6/2, etc.

While the mixed fraction is the combination of natural numbers and proper fractions. Such as 17/2 can be written as 8 * 1/2.

All the above-mentioned numbers can be arranged easily from least to greatest or greatest to least with the help of the technique of the ordering fraction. In this post, now we are further going to explain the techniques of ordering fractions.

**Techniques of ordering fractions**

The techniques of calculating the ordering fraction are two while one is the by using an online calculator. Here are the techniques for ordering fractions.

- By using a least to greatest calculator
- Converting fractions to decimals
- Making like fractions

Let us describe these techniques of ordering fractions with the help of examples.

**By using a least to greatest calculator**

The online tools are very helpful in solving numerical problems with steps to avoid time-consuming calculations in a fraction of a second. A least to greatest calculator is a helpful tool for arranging whole numbers, percentages, fractions, and decimals either in ascending or descending orders.

Here are the steps to use this calculator.

- First of all, select the term that you want to calculate such as least to greatest or greatest to least.
- Enter the comma-separated fraction, numbers, or percentages into the input box.
- Hit the calculate button.
- Press show more to view the solution with steps.

**Converting fractions to decimals**

Let’s understand this technique with the help of an example.

**Example **

Arrange the given fractions, percentages, and whole numbers in ascending or descending orders.

9, 96/8, 55/6, 3 * 18/48, 29%, 41%, 12 * 8/9, 5 * 1/12, 1/2

**Solution **

**Step 1:** First of all, write the given comma-separated values.

9, 96/8, 55/6, 3 * 18/48, 29%, 41%, 12 * 8/9, 5 * 1/12, 1/2

**Step 2:** Convert the improper and proper fractions into decimals

1/2 = 0.5

96/8 = 48/4 = 24/2 = 12

55/6 = 18/5 = 9.2

**Step 3:** Now convert the given numbers in percentages to fractions and then in decimals.

29% = 29/100 = 0.29

41% = 41/100 = 0.41

**Step 4:** Now convert the mixed fraction into improper fractions and then in decimals.

12 * 8/9 = 116/9 = 12.89

5 * 1/12 = 61/12= 5.08

3 * 18/48 = 162/48 = 81/24 = 3.375

**Step 5:** Now write the calculated decimals in ascending order and after that take the corresponding terms.

Ascending order = 0.29, 0.41, 0.5, 3.375, 5.08, 9, 9.2, 12, 12.89

The corresponding terms are:

Ascending order = 29%, 41%, 1/2, 3 * 18/48, 5 * 1/12, 9, 55/6, 96/8, 12 * 8/9

**Step 6:** Now write the calculated decimals in descending order and after that take the corresponding terms.

Descending order = 12.89, 12, 9.2, 9, 5.08, 3.375, 0.5, 0.41, 0.29

The corresponding terms are:

Descending order = 12 * 8/9, 96/8, 55/6, 9, 5 * 1/12, 3 * 18/48, 1/2, 41%, 29%

**Making like fractions**

Let’s understand this technique with the help of an example.

**Example **

Arrange the given fractions in ascending and descending orders by using the like fractions technique.

1/5, 12/4, 19/2, 5/3, 1/8, 2/6, 1/12

**Solution **

**Step 1:** First of all, take the given list of comma-separated proper and improper fractions.

1/5, 12/4, 19/2, 5/3, 1/8, 2/6, 1/12

**Step 2:** Now calculate the least common multiple by taking the denominators of the proper and improper fractions.

Denominators of proper and improper fractions = 5, 4, 2, 3, 8, 6, 12

Use any method of least common multiple to find the LCM of the above numbers.

LCM of 5, 4, 2, 3, 8, 6, 12 = 120

**Step 3:** Now take the LCM of the denominators and make all the proper and improper fraction’s denominators the same.

1/5 = 1 * 24 / 5 * 24 = 24/120

12/4 = 12 * 30 / 4 * 30 = 360/120

19/2 = 19 * 60 / 2 * 60 = 1140/120

5/3 = 5 * 40 / 3 * 40 = 200/120

1/8 = 1 * 15 / 8 * 15 = 15/120

2/6 = 2 * 20 / 6 * 20 = 40/120

1/12 = 1 * 10 / 12 * 10 = 10/120

**Step IV:** Arrange the like fractions from least to greatest and after that take the corresponding terms.

Least to greatest = 10/120, 15/120, 24/120, 40/120, 200/120, 360/120, 1140/120

Their corresponding terms are:

Ascending order = 1/12, 1/8, 1/5, 2/6, 5/3, 12/4, 19/2

**Step V:** Similarly, Arrange the like fractions from greatest to least and after that take the corresponding terms.

Greatest to least = 1140/120, 360/120, 200/120, 40/120, 24/120, 15/120, 10/120

Their corresponding terms are:

Descending order = 19/2, 12/4, 5/3, 2/6, 1/5, 1/8, 1/12

**Final Words **

In this post, we have discussed all the basics of ordering fractions and how to arrange numbers, fractions, and percentages either in ascending order or descending order. We have also discussed the techniques of ordering fractions with examples.