In mathematics, ordering fractions is a technique used to arrange fractions, numbers, and percentages in ascending order or descending order. This technique is helpful for applying arithmetic operations on two or more factional terms.

In this blog post, we will learn how to arrange fractions, numbers, and percentages along with examples.

## What is ordering fractions?

Ordering fraction is a well-known method that is frequently used in mathematics to write fractions, numbers, and percentages in a sequence. This sequence could be ascending or descending.

Ascending order is the order in which a list of fractions, numbers, or percentages is arranged from least to greatest. That is why the ascending order is also known as least to greatest. While descending order is the order in which a list of fractions, numbers, or percentages are arranged from greatest to least.

That is why the ascending order is also known as greatest to least. These arrangements of numbers, fractions, and percentages are necessary for solving various kinds of problems in mathematics and statistics.

Before going to discuss the methods of ordering fractions, let us briefly describe fractions and percentages.

### Fractions

In mathematics, a fraction is a numerical value that represents a part of a whole. In order to evaluate it, we divide a whole into a number of parts. An example would be 1/2 representing half of something or a whole number.

The fractions are further divided into three types.

- Proper fraction
- Improper fraction
- Mixed fraction

In fractions, a proper fraction has a smaller numerator than a denominator. While an improper fraction has a larger numerator than a denominator. A mixed fraction is a combination of a whole number and a proper fraction.

For example, 2/7 is a proper fraction, 7/3 is an improper fraction, and 2 3/5 is a mixed fraction.

### Percentages

An expression indicating the hundredth part of any quantity is known as a percentage. In this case, one percent is equivalent to one-hundredth of the whole; thus, 100 percent represents the whole, while 200 percent specifies twice the given amount.

It is denoted by “%”. For example, 10%, 20%, 100%, etc.

## Methods of arranging fractions

There are two well-known methods of arranging fractions.

- Making like fractions
- Turning fractions into decimals

Let us further describe the above methods briefly.

### Making like fractions

Making like fractions is a well-known technique for the arrangement of fractions. In this technique, you have to take the denominators of all the given fractions. Then calculate the least common multiple of denominators.

After that make all the denominators equivalent to the least common multiple. In the end arrange the numerators according to the desired condition i.e., from least to greatest or greatest to least.

The mixed fraction method is also helpful for calculating the sum and difference of two or more fractions. For performing the sum and difference, you have to followsimilar steps and in the last step, you have to add or subtract the numerators after making the like denominators.

### Turning fractions into decimals

Turning fractions into decimals is another technique for arranging fractions. In this technique, you have to divide the numerators by denominators to calculate the decimal values. After that arrange the values either in ascending order or descending order.

## How to arrange the fractions and percentages?

The methods of arranging fractions play a vital role in the arrangement of numbers, percentages, and fractions in ascending or descending orders. A least to greatest calculator is also a helpful and time-saving way to arrange the given data according to the methods.

### Example 1: For making like fractions

Arrange the given data in ascending and descending orders by using the making like fraction method.

3/7, 12/4, 19/2, 35/6, 22/5, 11/10, 100/3

**Solution **

**Step 1: **First of all, take the denominators of the given fractions.

3/7, 12/4, 19/2, 35/6, 22/5, 11/10, 100/3

Denominators = 7, 4, 2, 6, 5, 10, 3

**Step 2:** Now calculate the least common multiple of the above denominators.

Prime factors of 7 = 7

Prime factors of 4 = 2 x 2

Prime factors of 2 = 2

Prime factors of 6 = 2 x 3

Prime factors of 5 = 5

Prime factors of 10 = 2 x 5

Prime factors of 3 = 3

Common factors = 2, 3, 5

Non common factors = 7, 2

Least common multiple = products of common factors x product of non-common factors

Least common multiple = (2 x 3 x 5) x (7 x 2)

Least common multiple = 30 x 14 = 420

**Step 3:** Now make all the denominators equal to 420.

3/7 = 3 x 60 / 7 x 60 = 180/420

12/4 = 12 x 105 / 4 x 105 = 1260/420

19/2 = 19 x 210 / 2 x 210 = 3990/420

35/6 = 35 x 70 / 6 x 70 = 2450/420

22/5= 22 x 84 / 5 x 84 = 1848/420

11/10= 11 x 42 / 10 x 42 = 451/420

100/3 =100 x 140 / 3 x 140 = 14000/420

**Step 4:** Now arrange the above like fractions from least to greatest and write their corresponding fractions.

180/420, 451/420, 1260/420, 1848/420, 2450/420, 3990/420, 14000/420

Corresponding fractions are:

3/7, 11/10, 12/4, 22/5, 35/6, 19/2, 100/3

**Step 5:** Now arrange the above like fractions from greatest to least and write their corresponding fractions.

14000/420, 3990/420, 2450/420, 1848/420, 1260/420, 451/420, 180/420

Corresponding fractions are:

100/3, 19/2, 35/6, 22/5, 12/4, 11/10, 3/7

An ordering factions calculator can be used to solve the above problem to save time. This calculator will calculate the result in ascending and descending orders with steps in a couple of seconds.

### Example 2: for turning fractions into decimals

Arrange the given data in ascending and descending orders by using the turning fractions into decimals method.

12/3, 18/6, 50/5, 2 * 4/6, 110/11, 60/3, 120/2, 10%

**Solution **

**Step 1:** First of all, convert the given numbers into fractions.

12/3, 18/6, 50/5, 2 * 4/6, 110/11, 60/3, 120/2, 10/100

**Step 2:** Now divide the numerators by the denominators to calculate the decimal value.

12/3 = 4

18/6 = 3

50/5 = 10

2 * 4/6= 16/6 = 8/3 = 2.67

121/11= 11

60/3= 20

120/2 = 60

10/100 = 5/50 = 1/10 = 0.1

**Step 3:**Now arrange the above decimal values from least to greatest and write their corresponding fractions.

0.1, 2.67, 3, 4, 10, 11, 20, 60

Corresponding fractions are:

10%, 16/6, 18/6, 12/3, 50/5, 121/11, 60/3, 120/2

**Step 4:** Now arrange the above decimal values from greatest to least and write their corresponding fractions.

60, 20, 11, 10, 4, 3, 2.67, 0.1

Corresponding fractions are:

120/2, 60/3, 121/11, 50/5, 12/3, 18/6, 16/6, 10%

## Summary

Now you can grab all the basics of ordering fractions from this post. We have covered all the basics of ordering fractions such as definition, explanation, methods and solved examples. This topic is not difficult just a little effort is required.