What Does Order Mean in Maths? Simple Explanation & Examples

What is Ordering in Maths?

Ravi bought 30 bags from Nitya Bags Pvt. Ltd. shop for Rs. 1000 and decided to sell them for Rs. 1200 to Riya. After Riya received the package of 30 bags, she opened it to check the items before paying. She found that the bags were not of the same size (as desired to have bags of the same size). Like some bags were of size 13, some of 16, some of 8, and some of 9. Now, she continued keeping all the bags randomly after checking those.

She desired to have bags of a larger size. Now, she got confused about which bag was of this much size or that much size. The delivery guy was still waiting for the payment. Tired of waiting for Riya, he suggested she pile up the bags of respective sizes in a line. For example, the bags of size ‘8’ in one line, bags of size ‘9’ in the secound line, size ‘13’ in the third line, and the last size ‘16’ in the last line.

So, what the delivery guy suggested to Riya is, ordering. Here, ordering means arranging the bags or items or any entity as per their order or size.

So, What Does Order in Maths mean? Well, here, the bag's size order is: 8 is lesser than 9, 9 is lesser than 13, and 13 is lesser than 16.

Now, let us discuss more about order in Maths with two important ordering signs. We will understand all these things with basic examples for your everlasting remembrance of the concept.

Ordering in Maths with Signs

From the above text, we can see the order is arranging the items in a sequence as per their sizes. Like in the above example for bags, we notice the order as 8 is lesser than 9, 9 is lesser than 13, and 13 is lesser than 16.

Now, if we wish to represent this order in Maths, we write it as 8 < 9 < 13 < 16. Here ‘<’ sign stands for ‘less than’ in Maths. We try to simplify every statement in English with minimal effort in Maths with mathematical relational operators like here we used ‘<’ sign to specify the relationship between the sizes of bags.

(Please note that whenever we start with a lesser number and proceed with the larger numbers, it becomes an ascending order, because we are ascending or increasing numbers each step after a ‘<’ sign).

Ascending Order

Now, if we reverse the order of items that we did above as

16 is greater than 13, 13 is greater than 9, and 9 is greater than 8.

Like we study parts of speech in English, we try to stop the repetition of nouns by using pronouns to make our sentences look prettier. Similarly, in the above statement, we used ‘greater than’ multiple times. Now, consider ‘greater than’ as a noun and replace it with a pronoun ‘>’, to make our statement which is as follows:

16 > 13 > 9 > 8

Here, ‘>’ in Maths has the same meaning as ‘greater than’ in Maths and English both. However, we prefer to use signs to minimise our efforts.

(Please note that whenever we start with a greater number and proceed with the decreasing numbers, it becomes a descending order, because we are descending or decreasing numbers each step after a ‘>’ sign).

Descending Order

Examples of Order in Maths

From the above example, we can understand what order in Maths means. Now, let us assume that you are given a list of roll numbers for Class 5 and being the monitor of the class, you are required to order these roll numbers as per the ascending and descending order both. Now, what you will do is, start with standard 5th and the roll numbers are as follows:

{51, 15, 23, 48, 19, 17, 21, 34, 54}

Now, let us order these numbers in ascending order:

So, the order is: 15, 17, 19, 21, 23, 34, 48, 51, 54.

Or, 15 < 17 < 19 < 21 < 23 < 34 < 48 < 51 < 54

Now, the reverse order will be: 54 > 51 > 48 > 34 > 23 > 21 > 19 > 17 > 15.

So, this is how we do ordering in Maths and we can arrange anything in our real life as per the requirement, be it ascending or descending. These examples will give you a clear idea of what order in Maths means and apply the same to your questions as well.