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Ordering of Integers

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Last updated date: 17th Apr 2024
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How Do You Perform Integer Ordering?

Integers are numbers that are not fractions but whole numbers. Integers are of two types-negative and positive integers. The numbers are classified as positive and negative integers only according to their placement on the number line.


If the numbers are placed on the left side of 0 on the number line, the integers are called negative integers. If the integers are placed on the right side of 0 on a number line, they are called positive integers. Apart from this difference, the negative integers always have a negative sign in front of the number, while the positive integers don’t have one. Let us know how to put these integers in order.

Ordering Integers

Ordering integers means one has to arrange the integers in a particular sequence. To order the integers, one has to put them on a number line. The most basic rule you should remember is that the integer on the left on a number line is always smaller.

A Number Line(self-made)


A Number Line(self-made)

Have a look at the picture of the number line in the above image.

You can see that $- 1$ is placed on the left side of 0. This means that 0 is greater than $- 1$; hence, $0 > - 1$. Have a look on the right side of 0. Since 1 is placed before 2, you can write that 2 is greater than 1, $2 > 1$. Therefore, wherever you go from left to right on the numberline, the numbers keep increasing. This rule applies to all integers. Now you may understand the meaning of the temperatures in a thermometer with a minus sign.


A Thermometer


A Thermometer


Things to Remember While Ordering Integers

  • Positive integers are always greater than negative integers.

  • Zero is greater than every negative integer but smaller than every positive integer.

  • The greater the number, the lesser is the value of its negative integer. For example, 5 is greater than 0, but $- 5$ is much less than 0.


Solved Questions on the Ordering of Integers

1. Arrange the given integers from greater to lesser. $“9, 2, 0, -5, -7, -1, -2”$.

Solution: The question says that you have to order the integers from greater to lesser. Negative integers are always less than positive integers, so you must write the largest integer first. Hence, the order is $9, 2, 0, - 1, - 2, - 5, - 7$.


2. Arrange the given integers in lesser to greater. $"2,-4,5,8,-10,-3,3"$.

Solution: The question says that the order of the integers must be from lesser to greater. As the negative integers are always less than the positive integers, the negative integers will be written first while ordering the integers. Hence, the order of the given integers is $- 10, - 4, - 3, 2, 3, 5, 8$.


3. Arrange in ascending order. $"20, -10, 0, 12, -13"$.

Solution: As the question says that the given integers must be in ascending order, one has to arrange them in a lesser to greater order. The negative integers are always less than the positive integers. Hence, the order of the given integers is $- 13, - 10,0,12,20$.


4. Arrange in descending order. $"17,16,-13,-14,12"$.

Solution: According to the question, one has to solve the given integers in descending order or from greater to lesser. Since the positive integers are greater than the negative integers, one has to write the greater positive integers first. Hence, the order of the integers is $"17,16,12,-13,-14"$.


Conclusion

In this article, you have learnt about positive and negative integers, the representation of integers on a number line, and ordering integers from greater to lesser. You have also learnt that the numbers on the right are always greater than the ones on the left on a number line. According to this simple rule, you can arrange the numbers in either ascending order or descending order as per the questions.

FAQs on Ordering of Integers

1. Are comparing integers and ordering integers the same thing?

No, comparing and ordering integers are two different things. While comparing integers, one has to identify the greater or smaller integer between two integers. However, in the ordering of integers, there are multiple integers that are arranged in either ascending or descending order. 

2. If the negative integers have a “-” sign in front of the number, is it necessary that subtraction be performed?

No. When a negative integer has a “-”, it doesn’t always mean that it is getting subtracted. For example, when one says that the temperature of a place is $- {1^ \circ }C$, it does not get subtracted but gives an idea of the temperature. But when we write that, $3 – 2$, it means the subtraction is being performed. Hence, there is a difference, and one must be careful while writing negative integers.

3. Does ordering integers help plot them on a number line?

Ordering integers into greater and lesser gives you an idea of the placement of the integer on a number line. Hence, to plot the particular integers, you can first draw a number line, like the one in this article, and then mark a dot on top of the numbers. This is called the plotting of integers on a number line.