TECH

How to Arrange the Numbers in Ascending & Descending Orders?

What are the ordering fractions?

In mathematics, the arrangements of decimals, fractions, and percentages in ascending or descending orders are known as ordering fractions. The arrangements of decimals, fractions, and percentages in ascending order are said to be least to greatest.

While the arrangements of decimals, fractions, and percentages in descending orders are known as greatest to least. Firstly, you must be familiar with decimals, fractions, and percentages and how to convert them from one form to another.

Fractions

Fractions are the numbers written in the form of x/y where y never be zero. It can be proper, improper, or mixed fractions. The proper fractions are those in which the denominator is greater than the numerator e.g., 2/9, 3/13, 1/21, etc.

Improper fractions are those in which the numerator is greater than the denominator e.g., 12/9, 33/13, 41/21, etc. While the term mixed fraction is the product of an integer and the fraction e.g., 4 * 2/9, 2 * 3/13, 5 * 1/21, etc.

Decimals

Decimals are the numbers written in the form of integers and real numbers with a decimal point e.g., 2.9, 3.13, 1.21, etc.

Percentages

The numbers written along with a “%” sign are said to be the percentages. Each percentage can be written in the form of fractions by dividing that number by hundred e.g., 29% = 29/100, 313% = 313/100, 121% = 121/100, etc.

Now you are able to take any kind of number to arrange them. you can easily understand the concept of the ascending and descending orders by stairs of the house. For example, coming down from the upper step to the lower step is said to be the greatest to least arrangement.

While going upward from the lower step to the upper is said to be the least to the greatest arrangement. Now let us further describe the methods of arranging the numbers, fractions, and percentages in ordering fractions.

Techniques of arranging fractions, numbers, and percentages

For the arrangements of numbers, percentages, and fractions, there are two well-known techniques. Such as:

Making the like fraction technique
Fractions and percentages to decimals conversion technique.

A least to greatest calculator can be used to arrange the fractions, numbers, and percentages according to the above techniques in a couple of seconds. Let us briefly describe the techniques of ordering fractions.

1. Making the like fraction technique

Making like fraction is a well-known technique of ordering fractions in which you have to make all the fractions denominators similar by using a list of multiples or prime factorization. This technique allows you to arrange the fractions in ascending or descending orders easily.

Below are a few steps to make like fractions for the arrangements.

Take the given list of fractions.
Take all the denominators of the list of fractions.
After that calculate the least common multiple of the list of denominators.
Make all the denominators equal to the least common multiple.
After that arrange the calculated list of like fractions either in ascending order or descending order.
Lastly, write the corresponding fractions of each like fraction.

Below is an example of this technique to understand the concept more accurately.

Example

Arrange the given fractions from least to greatest and greatest to least by using the making like fractions technique.

11/2, 5/4, 9/10, 10/5, 15/6, 3/8, 2/11, 1/3

Solution

Step I: Firstly, take the given list of fractions.

11/2, 5/4, 9/10, 10/5, 15/6, 3/8, 2/11, 1/3

Step II: Now find take the denominators of the given list of fractions.

Denominators = 2, 4, 10, 5, 6, 8, 11, 3

Step III: Calculate the least common multiple of the above denominators to make the like fractions.

Least common multiple of 2, 4, 10, 5, 6, 8, 11, and 3 = 1320

Step IV: Now make all the fractions equal to the least common multiple of the denominators.

11/2 = 11 * 660 / 2 * 660 = 7260/1320

5/4 = 5 * 330 / 4 * 330 = 1650/1320

9/10 = 9 * 132 / 10 * 132 = 1188/1320

10/5 = 10 * 264 / 5 * 264 = 2640/1320

15/6 = 15 * 220 / 6 * 220 = 3300/1320

3/8 = 3 * 165 / 8 * 165 = 495/1320

2/11 = 2 * 120 / 11 * 120 = 240/1320

1/3 = 1 * 440 / 3 * 440 = 440/1320

Step V: Now make the arrangement of the above like fractions from least to greatest.

Least to greatest = 240/1320, 440/1320, 495/1320, 1188/1320, 1650/1320, 2640/1320, 3300/1320, 7260/1320

Now take the corresponding fractions:

Least to greatest = 2/11, 1/3, 3/8, 9/10, 5/4, 10/5, 15/6, 11/2

Step VI: Similarly, make the arrangement of the above like fractions from greatest to least and write their corresponding terms.

Greatest to least = 7260/1320, 3300/1320, 2640/1320, 1650/1320, 1188/1320, 495/1320, 440/1320, 240/1320

Their corresponding terms are:

Greatest to least = 11/2, 15/6, 10/5, 5/4, 9/10, 3/8, 1/3, 2/11

2. Fractions and percentages to decimals conversion technique

The conversion of fractions and percentages into decimals technique is another well-known technique for the arrangement of numbers. Follow the below steps to arrange the fractions, numbers, and percentages.

Take the list of percentages, fractions, and numbers.
Calculate the quotient of each fraction by dividing the numerator by the denominator.
After that arrange the decimals from least to greatest and greatest to least.
Lastly, write the corresponding fractions of each decimal.

Below is an example of this technique to understand the concept more accurately.

Example

Arrange the given fractions and percentages from least to greatest and greatest to least by using the fraction to decimal conversion technique.

240/3, 256/6, 450/48, 39%, 54%, 4 * 2/6, 5 * 21/10

Solution

Step I: Take the list of given fractions and percentages.

240/3, 256/6, 450/48, 39%, 54%, 4 * 2/6, 5 * 21/10

Step II: Firstly, convert the improper fractions into decimals.

240/3 = 80

256/6 = 128/3 = 42.67

450/48 = 225/24 = 9.375

Step III: Now change the percentages into fractions and convert them into decimals.

39% = 39/100 = 0.39

54% = 54/100 = 27/50 = 0.54

Step IV: Now convert the mixed fraction into improper fractions and convert them into decimals.

4 * 2/6 = 28/6 = 14/3 = 4.67

5 * 21/10 = 71/10 = 7.1

Step V: Now arrange the calculated decimals from least to greatest and write the corresponding fractions and percentages.

Least to greatest = 0.39, 0.54, 4.67, 7.1, 9.375, 42.67, 80

The corresponding terms are:

Least to greatest = 39%, 54%, 4 * 2/6, 5 * 21/10, 450/48, 256/6, 240/3

Step VI: Now arrange the calculated decimals from greatest to least and write the corresponding fractions and percentages.

Greatest to least = 80, 42,67, 9.375, 7.1, 4.67, 0.54, 0.39

The corresponding terms are:

Greatest to least = 240/3, 256/6, 450/48, 5 * 21/10, 4 * 2/6, 54%, 39%

Conclusion

In this article, we have discussed all the basics of the ascending and descending orders with techniques and solved examples. Now you are witnessing that arranging fractions, numbers, and percentages either in ascending or descending orders.