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Integers

A line which is used to represent numbers graphically is called a number line. This line can be of any length and it has both positive and negative numbers along with zero. The numbers on number line are marked off at equal distances from each other.

However, we do not know where to mark negative and positive numbers on this number line.

To know where to mark and how to locate integers on a number line, let us learn go through the following video.

We can also find the predecessor and successor of a number using a number line. Let us see how.

1. To find the predecessor of a number using a number line, we have to move 1 unit to the left of the given number. The result of this activity gives us the predecessor of the number.
1. To find the successor of a number using a number line, we have to move 1 unit to the right of the given number. The result of this activity gives us the successor of the number.

Let us discuss some examples based on the location of integers on the number line.

Example 1:

The following figure is a horizontal number line representing integers.

Observe the number line and give answers to the following questions.

(a) If M is 4, then which points represent the integers –4, –6, and 7?

(b) Which point on the number line represents neither a negative number nor a positive number?

(c) Write the integers for the points J, D, R, and Q.

(d) Is X a positive or a negative integer?

Solution:

(a) It is given that point M represents the integer 4 i.e., M represents +4. By moving 1 unit to the left of M, we will reach at point J. This point J represents the location of the integer 3. When we keep on moving 3 units to the left, we will be at point O. This point O represents the location of the integer 0.

To locate the integer –4 on the number line, we will move 4 units to the left of O. On doing so, we will reach at point T. Thus, point T represents the location of the integer –4 on the number line. In this way, we will locate the integers –6 and 7 on the given number line. After doing so, we will obtain point G as –6 and K as 7.

Thus, the points T, G, and K represent the location of the integers –4, –5, and 7 respectively on the number line.

(b) We know that 0 can be written as +0 or –0. Therefore, 0 is such a number that isneither negative nor positive. On the given number line, the position of 0 is represented by point O.

Therefore, O is the only point on the number line that represents neither a negative number nor a positive number.

(c) For the given number line, point O represents the integer 0. In order to reach J…

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