Ordering fractions: What is it and how to calculate it?

What is it and how to calculate it?

In algebra, the ordering fractions is a wide concept that is helpful in calculating the arranged data set. The set could contain fractions, decimals, whole numbers, or percentages. The arrangement of these terms could be either in ascending order or descending order.

The terms ascending and descending orders are widely used in mean, median, mode, variance, standard deviation, etc. In this post, we will discuss the basics of arranging the fractions, percentages, and decimals according to ordering fractions with examples.

What is ordering fractions?

The term used to arrange the fractions (proper, improper, or mixed), percentages, and decimals in ascending order and descending order is said to be the ordering fractions. This is a well-known technique to arrange the given data.

The ascending order is that order in which the data is arranged from least to greatest (smallest to largest) while the descending order is that order in which the data is arranged from greatest to least (largest to smallest).

The ascending and descending orders are very helpful to make the calculations easier by arranging the data values in a sequence. Now we are going to discuss which kind of number should involve in this arrangement.

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1. Fractions

The ordering fraction technique is mainly created for the arrangements of the fractional terms. The fraction is that term in which the number is written in the form of u/v where v never be zero. The fraction can be proper, improper, or mixed depending on the condition of the numbers.

The fractions in which the denominator is smaller than the numerator is said to be the improper fractions. For example, 12/5, 34/3, 91/30, 23/4, etc. are the improper fractions. While the fractions in which the numerator is smaller than the denominator are said to be the proper fractions.

For example, 1/6, 12/ 19, 15/ 20, 2/ 4, etc. are the proper fractions. On the other hand, the fractions that are the combination of the whole numbers and the proper fractions are said to be the mixed fraction that is created from the improper fractions. For example, 19/3 can be written as 6 * 1/3.

2. Decimals

The numbers written in with a point “.” Sign among them are said to be the decimal numbers. The decimal numbers can be smaller or larger such as 0.001, 0.3, 5.5, 1234.789, etc. these terms can also be arranged in a sequence with the help of ordering fractions.

For example, arrange 3.1, 4.6, 2.1, 0.4, 12.3, and 12.4 in ascending and descending orders.

Ascending order = 0.4, 2.1, 3.1, 4.6, 12.3, 12.4

Descending order = 12.4, 12.3, 4.6, 3.1, 2.1, 0.4

Similarly, the natural numbers, whole numbers, ad integers can be arranged in ascending or descending orders.

3. Percentages (%)

The terms that are written with a “%” sign are said to be the percentages of the numbers as it indicates the hundredth part of any object. The percentages can be written in the form of u/v by placing 100 at the denominator to each percentage term to remove its sign.

For example, 12% can be written as 12/100 or 0.12.

Now you have a sound knowledge of the fractions, decimals, and percentages such as what are they and how to write them. Now you can easily arrange the terms either in ascending order or descending order with the help of the methods of ordering fractions.

Methods of ordering fractions

There are three methods to arrange the fractions, decimal, and percentages. These methods are helpful in arranging the data values by using technology or manually. Here are these methods.

1. By using a least to greatest calculator

2. Converting fractions to decimals

3. Making like fractions

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

1. By using a Least to Greatest Calculator

An ascending order calculator is a helpful resource to solve the problems of ordering fractions. This tool will arrange the given set of numbers, fractions, and percentages in a couple of seconds.

fractions
Ordering Fractions

2. Making like Fractions

Let’s take an example to understand this method.

Example

Arrange 12/2, 8/4, 11/6, 2/8, 14/10, 12/12, 1/14 ascending and descending orders.

Solution

Step 1: First of all, write the given fractions and percentages.

12/2, 8/4, 11/6, 2/8, 14/10, 12/12, 1/14

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

Denominators of proper and improper fractions = 2, 4, 6, 8, 10, 12, 14

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

LCM of 2, 4, 6, 8, 10, 12, 14 = 840

Step 3: Now make all the denominator of the given fractions equal to 840 to make them like fractions.

12/2 = 12 * 420 / 2 * 420 = 5040/ 840

8/4 = 8 * 210 / 4 * 210 = 1680/ 840

11/6 = 11 * 140 / 6 * 140 = 1540/ 840

2/8 = 2 * 105 / 8 * 105 = 210/ 840

14/10 = 14 * 84 / 10 * 84 = 1176/ 840

12/12 = 12 * 70 / 12 * 70 = 840/ 840

1/14 = 1 * 60 / 14 * 60 = 60/ 840

Step 4: Now arrange the above calculated fractions from least to greatest and after that write the corresponding term of the decimals

Least to greatest = 60/ 840, 210/ 840, 840/ 840, 1176/ 840, 1540/ 840, 1680/ 840, 5040/ 840

Their corresponding terms are:

Ascending order = 1/14, 2/8, 12/12, 14/10, 11/6, 8/4, 12/2

Step 5: Now arrange the above calculated fractions from greatest to least and after that write the corresponding term of the decimals

Greatest to least = 5040/ 840, 1680/ 840, 1540/ 840, 1176/ 840, 840/ 840, 210/ 840, 60/ 840

Their corresponding terms are:

Descending order = 12/2, 8/4, 11/6, 14/10, 12/12, 2/8, 1/14

3. Converting fractions to decimals

Let’s take an example to understand this method.

Example

Arrange 16/8, 54/6, 3 * 18/4, 92%, 42%, 10 * 8/12, 6 * 2/12, 12/16 in ascending and descending orders.

Solution

Step 1: First of all, write the given fractions and percentages.

16/8, 54/6, 3 * 18/4, 92%, 42%, 10 * 8/12, 6 * 2/12, 12/16

Step 2: Now convert the fractional term into decimals.

16/8 = 2

54/6 = 27/3 = 9

12/16 = 6/8 = 3/4 = 0.75

3 * 18/4 = 30/4 = 15/2 = 7.5

10 * 8/12 = 128/12 = 64/6 = 32/3 = 10.67

6 * 2/12 = 74/12 = 37/6 = 6.17

Step 3: Now deals with the percentages and convert them into decimals.

92% = 92/100 = 46/50 = 23/25 = 0.92

42% = 42/100 = 21/50 = 0.42

Step 4: Now arrange the decimals from least to greatest and after that write the corresponding term of the decimals.

Least to greatest = 0.42, 0.75, 0.92, 2, 6.17, 7.5, 9, 10.67

The corresponding terms are:

Ascending order = 42%, 12/16, 92%, 16/8, 6 * 2/12, 3 * 18/4, 54/6, 10 * 8/12

Step 5: Now arrange the decimals from greatest to least and after that write the corresponding term of the decimals.

Greatest to least = 10.67, 9, 7.5, 6.17, 2, 0.92, 0.75, 0.42

The corresponding terms are:

Descending order = 10 * 8/12, 54/6, 3 * 18/4, 6 * 2/12, 16/8, 92%, 12/16, 42%

Wrap up

In this post, we have covered all the basic intent of the ordering fractions along with its definition, working, methods, and solved examples. We also discussed and online calculator that can solve the problems of ordering fractions in a fraction of a second.

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