How to Order Integers Using Number Line and Comparison Rules
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)
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
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 on the Number Line
1. What is ordering of integers in maths?
The ordering of integers means arranging integers from smallest to largest or largest to smallest based on their position on the number line. Integers include negative numbers, zero, and positive numbers (…, −3, −2, −1, 0, 1, 2, 3, …).
- Numbers to the right on the number line are greater.
- Numbers to the left are smaller.
- Example (ascending order): −5, −2, 0, 3, 7.
2. How do you arrange integers in ascending order?
To arrange integers in ascending order, list them from the smallest value to the largest value. Follow these steps:
- Place all negative numbers first (more negative means smaller).
- Then place 0 (if included).
- Finally, list positive numbers in increasing order.
Ascending order: −7, −3, 0, 2, 4.
3. How do you arrange integers in descending order?
To arrange integers in descending order, list them from the largest value to the smallest value. Use the number line idea:
- Start with the greatest positive number.
- Then smaller positive numbers.
- Then 0.
- Finally, negative numbers (closer to zero first).
Descending order: 6, 1, −2, −4.
4. How do you compare two negative integers?
When comparing two negative integers, the number with the greater absolute value is actually smaller. This is because it lies further left on the number line.
- Compare −3 and −8.
- Since 8 > 3, −8 is farther from zero.
- Therefore, −8 < −3.
5. What is the rule for ordering integers on a number line?
The rule for ordering integers on a number line is that numbers increase as you move to the right and decrease as you move to the left. Key points:
- Right side numbers are always greater.
- Left side numbers are always smaller.
- Zero separates negative and positive integers.
6. How do you order positive and negative integers together?
To order positive and negative integers together, place negative numbers first, then zero, and then positive numbers. Steps:
- Arrange negative integers from smallest (most negative) to largest.
- Place 0 after negatives (if included).
- Arrange positive integers in increasing order.
Ordered (ascending): −6, −1, 3, 5.
7. What is the difference between ascending and descending order of integers?
The difference is that ascending order arranges integers from smallest to largest, while descending order arranges them from largest to smallest.
- Ascending example: −4, −1, 2, 6.
- Descending example: 6, 2, −1, −4.
8. Can you give an example of ordering integers step by step?
Yes, ordering integers step by step involves comparing their positions relative to zero and each other. Example: Arrange 7, −9, 4, −2, 0 in ascending order.
- Step 1: Identify negative numbers → −9, −2.
- Step 2: Order negatives → −9 < −2.
- Step 3: Place 0 after negatives.
- Step 4: Order positives → 4 < 7.
9. Why is zero important when ordering integers?
Zero is important because it separates negative integers from positive integers on the number line. Key facts:
- All negative numbers are less than 0.
- All positive numbers are greater than 0.
- Zero itself is neither positive nor negative.
10. What are common mistakes when ordering integers?
A common mistake when ordering integers is thinking that a number with a larger digit is always greater, especially with negative numbers. Watch out for:
- Assuming −10 is greater than −2 (actually −10 < −2).
- Ignoring zero in mixed sets of integers.
- Not using the number line for comparison.
