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Chapter 6: Integers

    Introduction

    How Negative Numbers Arise?

    Some Uses of Negative Numbers

    Representation of integers on a number line

    Ordering of integers

    Addition And Subtraction of Integers

    Exercise 6.1

    Exercise 6.2

    Exercise 6.3

    Exercise 6.4

    What Have We Discussed

    Enhanced Curriculum Support

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 6: Integers > Ordering of integers

Ordering of integers

Raman and Imran live in a village where there is a step well. There are in all 25 steps down to the bottom of the well.

One day Raman and Imran went to the well and counted 8 steps down to water level. They decided to see how much water would come in the well during rains. They marked at the existing level of water and marked 1,2,3,4,... above that level for each step.

Step Well

After the rains they noted that the water level rose up. Lets represent the step well as below.

Step Well

As you can see, the water rose to the step.

After a few months, they noticed that the water level had fallen three steps below the zero mark.

Now, they started thinking about marking the steps to note the fall of water level.

Let's help them. Suddenly, Raman remembered that at one big dam he saw numbers marked even below zero. Imran pointed out that there should be some way to distinguish between numbers which are above and below .

Then Raman recalled that the numbers which were below zero had sign in front of them.

So they marked one step below zero as and two steps below zero as and so on.

So the water level is now at (3 steps below zero).

After that due to further use, the water level went down by 3 step and it was at . You can see that –6 –3.

Representation of the step well numbering on a graph

Fill in the boxes using > and < signs

We know that 7 4 and from the number line shown above, we observe that 7 is to the right of 4.

Similarly, 4 > 0 and 4 is to the of 0. Now, since 0 is to the right of

so, 0 – 3.

Again, – 3 is to the right of so, – 3 – 8.

Thus, we see that on a number line the number as we move to the right and as we move to the left.

Therefore, – 3 < – 2, – 2 < – 1, – 1 < 0, 0 < 1, 1 < 2, 2 < 3 so on.

Hence, the collection of integers can be written as...,–5, –4, – 3, – 2, – 1, 0, 1, 2, 3, 4, 5...

Compare the following pairs of numbers using > or <

Now, that we have understood the ordering of integers, let's cement our understanding by answering the following questions below: