How to Arrange the Numbers in Ascending & Descending Orders?
In algebra, the arrangements of the numbers either in ascending or descending orders can be done by using various methods. The arrangements of the numbers can also know as least to greatest or greatest to least.
The arrangements of the numbers are frequently used in central tendencies and other algebraic expressions. In this article, we will learn how to arrange numbers, fractions, and percentages with solved examples.
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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%
FAQs
How do I arrange numbers in ascending order?
To arrange numbers in ascending order, start by comparing each number with the one next to it. If the first number is smaller than the second, they’re already in the correct order. If not, swap their positions. Continue this process until all numbers are arranged from smallest to largest.
What’s the easiest way to arrange numbers in descending order?
The easiest way to arrange numbers in descending order is to reverse the process used for ascending order. Begin by comparing each number with the one next to it. If the first number is greater than the second, they’re already in the correct order. If not, swap their positions. Repeat this process until all numbers are arranged from largest to smallest.
Is there a quick method to arrange numbers in ascending or descending order without comparing each pair?
Yes, there is a quick method known as sorting algorithms. One of the most commonly used sorting algorithms is the “Bubble Sort.” In Bubble Sort, the algorithm repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order. This process is repeated until the list is sorted. Other sorting algorithms such as Selection Sort, Insertion Sort, and Quick Sort can also efficiently arrange numbers in ascending or descending order.
Are there any tools or software available to automatically arrange numbers in ascending or descending order?
Yes, there are many tools and software available online that can help you arrange numbers in ascending or descending order quickly and effortlessly. Spreadsheet programs like Microsoft Excel and Google Sheets have built-in functions for sorting data. Additionally, there are numerous online calculators and programming libraries that offer sorting functionalities. You can simply input your numbers, select the desired order (ascending or descending), and the tool will arrange them accordingly.
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.
