Ascending Order

What is Ascending Order

It is the arrangement of numbers or other items in ascending order from the smallest to the largest. The numbers we see on the number line from left to right exemplify a rising order. We usually represent it by pausing between numbers or using a 'less than sign (<)' between numbers. For example, 1, 2, 3, 4, 5 or 1 <2 <3 <4 <5.

Have you ever had situations where you had a lot of essential folders/files/documents that might be helpful to you, but because there are so many of them, you can't find the right one? However, many of the problems can be solved if you plan accordingly. Climbing order is one of the ways to collect and represent data.

There’re some rules you need to keep in mind while representing the numbers in the ascending order:

1. The values should always be in smallest to largest form.
2. The first value is always the smallest and last is always the largest value.

For example: 20,68,30,48,56,44

Then, the sequence will be 20<30<44<48<56<68 In this example you can see that the first number is the smallest and the last number is the largest one.

Ascending Order Symbol

Ascending order is represented by the symbol (<) or we can use comma as well. The most common way to represent ascending order is to put a less than symbol between themm which shows the series of number from the smallest to the largest. This symbol all shows that the succeeding number is greater than the preceding number. For example- 11<12<13<14<15<16<17<18.

Fractions in Ascending Order

It means arranging the fractions in the increasing order, from smallest to largest. In the case of fractions there are two ways through which you can arrange it in the ascending order and the answer will be the same from both of the methods.

(a) Convert the fractions into decimals

(b) Convert the given fractions into like fractions

Also check: Fractions and decimal

Convert the fractions into decimals

• Step 1: Convert the series of given fractions into decimals.
• Step 2: Find out the increased order according to decimal values.
• Step 3: Replace all the fractions with the decimal values, you’ll get the result.

For example convert the following into ascending order: 1/2, 2/3, 3/4, 4/5, 5/6

1. So if go with the steps, the first step will be convert them into decimals which means: 0.5, 0.66, 0.75, 0.8, 0.83
2. The second step is to find out the increased order according to the decimal value which is 0.66, 0.5, 0.75, 0.8, 0.83
3. Now replace the fraction with decimals and the final result will be: 1/2< 2/3< 3/4< 4/5< 5/6

Convert the given fractions into like fractions

• Step 1: Find out the L.C.M of denominators.
• Step 2: Divide the value of L.C.M by the denominator of the fraction.
• Step 3: Multiply both the number and the denominator of the part by the value of the result of step 2.
• Step 4: As a result of steps 2 and step 3, compare the same fractions.
• Step 5: Lastly, arrange the values in the order in which they appear.

Let’s take the above example only

Q. Convert the following into ascending order: 1/2, 2/3, 3/4, 4/5, 5/6

Ans. Step 1 will be find out the lcm of the denominator of (2,3,4,5,6) which will be 60

Now in,

Step 2 we’ve to divide the value of lcm by the denominator of the fraction which is

(30, 20,15,12,10)

In step 3 multiply both of the numerator and denominator with the which results in: 30/60, 40/60, 45/60, 48/60, 50/60

On comparing the result will be the same and if we arrange it, the final value will be: 1/2< 2/3< 3/4< 4/5< 5/6

Ascending Order of Negative Numbers

• The subsequent increase in negative numbers means arranging the negative numbers given from the smallest to the largest numbers. It is very important to read as in the case of negative numbers whole numbers are bigger than whole numbers, which creates confusion.
• With negative numbers, the highest number with a negative symbol has the least value. Therefore, if you have to set -38, -59, -7 in the rising order, then it is arranged in the following order: -59 <-38 <-7
• -7 is the largest number and -59 is the smallest of the three given numbers. Look at the picture given below to understand the rising order and the falling of numbers in the number line.

Examples

Q1. Arrange the following numbers 3,7,2,8,1,9 in ascending order?

Ans. The increased order of the numbers will be 1,2,3,7,8 and 9

Q2. Jane counted the number of doors in each of the houses in the neighborhood. She made a list as follows (15, 12, 19, 11, 18). Arrange the numbers in ascending order?

Ans. The number list in the ascending order will be 11,12,15,18,19.