Ascending Order

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 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   biggest 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 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, arrange 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

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] 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 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 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 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