Ascending Order Definition
Ascending means increasing in simple language. In Mathematics, Ascending Order means arranging the numbers in order from smallest to largest. It means to write the number from the smallest one to the largest one in order.
For example, 3, 5, 7, 9, 13, 19, 21, 24, 26, 27, 28, and 29 are written in Ascending Order as the number that comes after the previous is larger than that.
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In different fields of Mathematics, it has great importance. The numbers written in this order give a better approach to reaching different values. For example, you can easily find the mode and median of the numbers written in this order.
Note:
Read about Mode and Median in detail.
The reverse of this order is called Descending Order. In this order, the numbers are written in the reverse direction.
Note:
You can read about Descending Order here.
How to arrange different terms in Ascending Order?
To arrange the whole numbers in this order, you only have to compare them. First of all, you have to write the smallest number in the first place. After that, you should keep writing the numbers higher than the previous one.
Arranging Whole Numbers
To arrange the whole numbers in this order, you only have to compare them. First of all, you have to write the smallest number in the first place. After that, you should keep writing the numbers higher than the previous one.
Example 1:
Write the following numbers in Ascending Order.
2, 3, 4, 9, 5, 11, 7, 12, 21, 13.
Solution:
To arrange these numbers in Ascending Order, we will start writing from the smallest term as mentioned above.
2, 3, 4, 5, 7, 9, 11, 12, 13, 21
As you can see that all numbers are written in proper order and the coming number is bigger than the previous one.
Arranging Fractions
It is a little bit complicated to arrange fractions in order. There are two different conditions in this regard that we are going to discuss in the following section.
With Same Denominator
If you have got a set of fractions with the same denominator, you only have to arrange them from smallest to largest order according to their numerators. Let us explain it with an example.
Example 2:
Write the following fractions in Ascending Order.
2/7 ,5/7 ,3/7 ,9/7 ,4/7 ,11/7
Solution:
As you can see the denominator of all fractions is the same. So, we only have to arrange the numbers by comparing their numerators.
2/7,3/7 ,4/7 ,5/7 ,9/7 ,11/7
The above fractions have now been arranged in Ascending Order.
With Same Numerator
Sometimes, you may have to arrange the fractions with the same numerator in order. The process is similar to the above but a little bit reversed. To arrange such fractions, the fraction with the largest denominator will come first while the fraction with the smallest denominator comes at the end of the list.
Example 3:
Write the following fractions in the Ascending order
7/2 ,7/5 ,7/3 ,7/9 ,7/4 ,7/11
Solution:
As you can see numerator of all fractions is the same. So we have to arrange these numbers from largest to smallest with respect to the denominator to arrange them in Ascending Order.
7/11 ,7/9 ,7/5 ,7/4 ,7/3 ,7/2Now, the fractions have been arranged in Ascending Order.
Arranging Decimals
When it comes to arranging decimals in Ascending Order, you can follow two steps mainly.
- Compare the whole part of the decimals to arrange them in increasing order.
- If their whole part is the same, compare the decimal part to arrange them in this order.
FAQ's
How can we arrange fractions with the different numerators and denominators in Ascending Order?
We can arrange such fractions in order by taking the LCM of those fractions.
Can we arrange decimals in Ascending Order?
Yes, we can arrange decimals in an increasing or decreasing order.
Can we arrange integers in Ascending Order?
Yes, we can arrange integers in this order too. But you should first understand that the higher number with a negative sign is actually smaller because the number line moves from left to right in increasing order.
