Ascending Order
The students are taught the concept of Orders to develop a better logical, analytical, and practical thinking approach towards things in general. Ascending Order is a concept of arranging the numbers which are helpful for the students in a number of ways which have been discussed later here. Also, it is imperative for the students to take good care of the Mathematical concepts by memorizing them over a period of time by regularly practicing so that the students are regained in the long term memory.
Vedantu provides the students with all the study material required by the students for practicing these concepts from Class 1 to 12 in a manner that is comprehendible, easy, and well to learn through them. Also, we provide the students with the solutions for the textbooks of various boards and educational institutes to help the students clear their doubts at the earliest.
What is Ordering?
Arranging the numbers one by one is considered as Ordering. There are two types of Ordering.
1. Ascending Order: In this Order, the numbers are arranged from lowest to highest.
2. Descending Order: In this Order, the numbers are arranged from highest to lowest.
Tricks Applied to Arrange the Numbers in Ascending Order
Count the digits of the numbers. A one-digit number is smaller than a two-digit number.
E.g., In 8, 15 the smallest number comes first i.e., 8 and then 15
If all the numbers have an equal number of digits, then the numbers whose first digit is greater will be a higher number.
E.g., In 15, 28. The number 15 is smaller than 28. So, it comes first.
If the numbers have an equal number of digits and the first digits are the same then compare the last digits.
E.g., in 18 and 11, the first digit 1 is the same in both. 8 is more than 1. So 18 is bigger than 11.
Ascending Order Symbol
For Ascending Order mostly we use the upward arrow or the arrow towards the right. The word “Ascending” means go upwards, so the symbol is the arrow directed upwards.
In a number line, the negative numbers are denoted at left, while the positive numbers are denoted at right. So in Ascending format, the numbers continuously increase in magnitude from left to right. The symbol will be a right arrow.
Example: 2 > 5, -20 > 10
What Does Ascending Order Mean?
When we access huge amounts of data to work, it is difficult to put it in a particular Order. Ordering helps us to sort and filter the data in an organized form. When data are arranged from the smallest to the largest manner, it is called Ascending Order.
Use of Ascending Order
It is used mostly in Mathematics, data sorting, date calculation, numerical calculation, and alphabetical arrangement of words and letters. It helps to make data simpler and easy to understand.
When using such an Order some important rules are always to be followed.
Always start with the smallest number or amounts
Numbers should be sorted in Ascending Order
The last number should always be the highest number
For letters or words, arranged alphabetically
For alpha-numeric first, the numbers sorted from “0” to “9” and then the letters followed from “a” to “z”
For dates and places, the oldest dates should come first.
Ascending Order in Math
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Ascending Order means Increasing Order. When we arrange or Order numbers from the smallest to the greatest we call it Ascending Order. Let us see how to put the numbers 23, 12, 41, 62, 19 in Ascending Order. i.e., 12, 19, 23, 41, 62
Example: Write the missing numbers in Ascending Orders?
2, _, 4, _, 6, _
Answer: 2, 3, 4, 5, 6and 7
Ascending Order may be sequential Ascending Order, which can be counted by adding 1 in each number.
Example: 2 + 1 =3
3 + 1 = 4
The Order may skip counting by adding any arbitrary number.
e.g., 10, 15, 25, 35, 48, 55, 65, 70
An integer on a number line is always greater than every integer on its left and lesser than every integer on its right.
Example: -5 < -4
->A negative number is less than any positive number.
Example: 15 > -41
->Integers increase in value, as we go to the right on the number line.
Example: -1> -3, 7 > -8, 9 > 2
->Integers decrease in value, as we go to the left on the number line.
Example: -3<5, - 9 < 0
Example: Arrange the integers
−3,0,−5,5,4,−1
−3,0,−5,5,4,−1 in Ascending Order.
Solution: Arrange the numbers on a number line.
-5 -4 -3 -2 -1 0 1 2 3 4 5
Integers to the right of zero in the increasing Order- (0, 4, 5)
Integers to the left of zero in the increasing Order- (-5, -3, -1, 0)
So, Ascending Order: (-5, -3, -1, 0, 4, 5)
Ascending Order and Descending Order
Ordering requires a comparison between the largest and smallest. When numbers are sorted from lowest to the highest Order, the Order is called an Ascending Order. While the numbers are sorted from highest to lowest Order, the Order is called a Descending Order.
Example: Arrange the numbers in Descending Order.
52, 16, 32, 89, 65, 76
Solution:
89, 76, 65, 52, 32, 16
Example: Write 22 to 26 in Ascending Order.
Answer: 22, 23, 24, 25, 26
Example: Write 45 to 40 in Descending Order.
Answer: 45, 44, 43, 42, 41 and 40
Ascending or Descending Order is required for the arrangement of data from oldest to newest and vice-versa in the data arrangement system.
Ascending Order of Alphabets
When we make an arrangement of data in alphabetical Order, Ascending Order is most useful. In a dictionary, when we search a particular word from a huge amount of data, such Ordering is required.
Searching any particular word from the dictionary has been made possible due to the arrangement of data in Ascending form.
Ascending Order in Fractions
A fraction is a ratio between numerator and denominator. While Ordering the fraction, we follow different rules.
A Fraction Having Same Denominators
By comparing the numerators having the same denominators; numbers are arranged in Order. The smallest numerator is recognized as the smallest fraction having the same denominator.
Example: Write the numbers in Ascending Order 3/7, 8/7, 9/7, 4/7
Answer: First compare the numerators as all these numbers have the same denominators 7
We get, 3 < 4 < 8 < 9
So, 3/7, 4/7, 8/7, 9/7
A Fraction Having Same Numerators
By comparing the denominators having the same numerator; numbers are arranged in Order. The fraction with the highest denominator is recognized as the smallest fraction having the same numerator.
Example: Write the numbers in Descending Order 3/8, 3/5, 3/4, 3/7
Answer: First compare the denominator, as all these numbers have the same numerators 3
So on comparing the denominator,
4 < 5 < 7 < 8
So, 3/8, 3/7, 3/5, 3/4
A Fraction Having Different Numerators and Denominators
First, equal the denominators of every fraction. Then compare them accordingly, as described earlier.
Example: Arrange the numbers in Ascending Order
2/5, 4/6, 3/5, 1/3
Answer: First, find out the LCM of all denominators in the given numbers. That is 30
To make a similar fraction, convert each number into equivalent fractions.
2/5× 2/6 = 12/30
4/6 × 5/5 = 20/30
3/5 × 6/6 = 18/30
1/3 × 10/10 = 10/30
The equivalent fractions are arranged in Ascending Order, we get:
10/30 < 12/30 < 18/30 < 20/30
So, 1/3 < 2/5 < 3/5 < 4/6
FAQs on Ascending Order
1. What is meant by Ascending Order?
For the knowledge of students, it is answered that the concept of Ascending Order hails from the subject of Mathematics and it means the process of arranging numbers from smallest to largest from left to right. This can also mean arranging the letters or the words in alphabetical Order from A to Z. The word Ascending means “going up”, so Ascending Order means that the numbers are going up in increasing Order of weight. So, in simple terms, we can say that It is a way of Ordering numbers.
2. What does Ascending mean to move up or down?
The terms Ascend, mount, and climb mean to move upward or towards the top. The word ‘Ascend’ articularly is used for a gradual upward movement. So, Ascending is to move up. However, the difference between the terms Ascending and Descending is that Ascending refers to moving up or climbing up or moving ahead of the path of a given event whereas Descending means going down or climbing down or moving backward the path of a given event. Thus, this clarifies us with the role of Ascending as a term.
3. What is the purpose of teaching Ascending Order to the students?
In the subject of Mathematics, the term Ascending Order means the process of arranging numbers from smallest to largest or from left to right. The purpose of teaching Ascending Order to the students is to teach them the logic behind the numbers, the uses of the Orders and such other concepts. This helps the students to improve their thinking skills and ability by understanding the concepts well. This way the students learn the concepts with ease and hence, are able to perform well not only in the immediate exams but also in higher standards when the topics become complicated.
4. When will it be useful for me to sort the data in Ascending Order?
For the students of Maths, arranging the data in Order of Ascending sequence is an easy question but the timing of the same needs to be noted. So, the students can sort a file or a question in Ascending (A-Z, 0-9) or Descending (9-0, Z-A) Order when the question needs rearranging or solving the saem in a particular way. The sorting of data makes it easier for the students to find and use information in a way that makes it easier for them to solve a question. Also, it makes it easier for them to analyze the information in a sorted way and calculate the answer faster.
5. Where Can I understand the Ascending Order concept of Maths?
The students can easily download the concept of Ascending Order from the website of Vedantu for free which is available with examples for their easy understanding. The students can also find more such Mathematical concepts explained in a simplified manner by the experts at Vedantu who have years of experience and expertise in the relevant fields, so the students can easily rely on the material and learn from the saem. The site also provides other study material like sample papers, revision notes, practice questions, important questions, worksheets, etc. to enhance and upgrade the level of preparation.