Integers on Number Line
Integers are a set of positive and negative numbers including zero. Integers on a number line are defined as a pictorial representation of integers on a number line. Integers on a number line help us to perform different arithmetic operations. We will be studying more about it in this article.
| 1. | Representing Integers on a Number Line |
| 2. | Addition and Subtraction of Integers on a Number Line |
| 3. | FAQs on Integers on Number Line |
Representing Integers on Number Line
Representation of integers is done using a number line. A number line is a visual representation of numbers on a straight line. It consists of positive integers such as 1, 2,.., negative integers such as - 1, - 2, ... and 0 which is neither a positive nor a negative integer. Let's look into the representation of integers on a number line in the diagram as shown below.
In the above diagram, we have seen the representation of integers on the number line. Let's understand the placing of integers on the number line as described below.
- The integer 0 is taken as the reference on a number line marked at the center.
- The right-hand side of 0 represents the positive integers as they are greater than 0.
- The left-hand side of 0 represents negative integers as they are lesser than 0.
Addition and Subtraction of Integers on Number Line
We will now be understanding the arithmetic operations - addition and subtraction of integers on a number line.
Key Points to perform Arithmetic Operations of Integers on a Number Line:
- Always start from "0".
- Move to the right side, if the number is positive.
- Move to the left side, if the number is negative.
Addition of Integers on Number Line
Adding integers on a number line is done by looking at the sign of the second addend. If we add a positive number to the given integer, we move towards the right side, and if we add a negative integer to the given integer, we move towards the left side. Let us take a few examples to add integers on a number line.
Example 1: Perform the operation 1 + 2 using a number line.
Let us look into the steps given below to understand the problem.
- Step 1: Consider the first number (1) as the starting point on the number line. In order to add 1 + 2, mark 1 on the number line.
- Step 2: Now, from the first number jump by the number of units equivalent to the second number towards the right. This is because the values on a number increase as we move towards the right-hand side. In this case, we are adding 1 + 2, therefore, we will move 2 steps to the right. This will bring us to number 3. So, 1 + 2 = 3.
Example 2: Perform the operation 3 + (-4) using a number line.
The steps remain the same as earlier except for the direction of movement as the addition operation is with a negative number. Here, we take 3 as the starting number and move 4 units towards the left on the number line since the second number is -4 which gives the result as -1.
Subtraction of Integers using Number Line
Subtracting integers on a number line is done by looking at the sign of the subtrahend. To subtract a positive integer, we move towards the left on a number line, and to subtract a negative integer we move towards the right on the number line. Let us take a few examples to subtract integers on a number line.
Example 1: Perform the operation 5 - 3 using a number line.
Let us look into the steps given below to understand the problem.
- Step 1: Mark the first number (5) on the number line.
- Step 2: Move towards the left-hand side of the number line according to the second number given. In this case, the second number is 3, so we will move 3 units to the left as shown by the arrows. Hence, we land on 2, which is the answer.
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Integers on Number Line Examples
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Example 1: Subtract 3 from -4 using a number line.
Solution: We will follow the steps of subtracting integers on number line to solve the problem.
We start with the first number -4 on the number line as shown and move by the number of units equivalent to the second number that is 3 units towards the left and reach on -7. Thus, we see that the subtraction of - 4 - 3 = - 7 is shown on the number line.
FAQs on Integers on Number Line
What are Integers on a Number Line?
Integers on a number line are a way to represent integers visually where all the positive and negative integers including 0 are plotted. It helps us to compare integers and to perform arithmetic operations on them.
How to Represent Integers on Number Line?
Integers are marked on a number line as follows:
- The integer 0 is marked at the center of the number line.
- All the positive integers are marked towards the right of 0 and all the negative integers are plotted towards the left of 0 on the number line.
For example, we will represent the integer 5 on the right of 0, and - 9 will be represented on the left of 0.
How to Multiply Integers on Number Line?
To multiply integers on a number line, start from 0 and count by the first number given in the problem as many times as indicated by the second number. For example, to multiply 2 × 5, take 0 as a reference, count by twos a total of five times that gives the result as 10.
How to Divide Integers on Number Line?
To perform the division of integers on a number line, select a particular segment of the number line from 0 to the first number given in the problem. Then divide this segment evenly into the number of parts indicated by the second number. The length of each part is the result of the division. For example, to perform 12 ÷ 4, select a segment of the number line from 0 to 12. Now divide this segment evenly into four smaller parts. Each part is of length 3 units hence the result is 3.
How to Plot Integers on Number Line?
Integers are plotted on a number line by following basic rules as follows: The integer 0 is plotted exactly at the center, all the positive integers which are greater than 0 such as 1, 2, 3... are plotted towards the right of 0 and all the negative integers which are lesser than 0 such as - 1, - 2, - 3,... are plotted towards the left of 0. For example, 3 is plotted towards the right of 0 and the integer - 4 is plotted towards the left of 0.
How to Add and Subtract Integers on Number Line?
To add integers, we always start with the first number and move towards the right (if positive) or left (if negative) by equivalent units of the second number. For example, to perform 5 + (- 4), we start from 5 and move by 4 units towards the left landing at 1. To subtract integers, we always start with the first number and move towards the left (if positive) or right (if negative) by equivalent units of the second number. For example, to perform - 8 - (- 3), we start from - 8 and move by 3 units towards the right landing at - 5.