Adding Integers with the Help of Number Line: Except for fractions, the set of integers consists of zero, positive numbers, and negative numbers. When arithmetic operations are applied to integers, integer addition and subtraction rules are not the same.

A number line is a tool for comparing and organising numbers. Each number on a number line is plotted in relation to the origin (zero), and the position of a number on a number line defines its value. The numerals on the number are negative or positive depending on where they are in relation to zero 0.  This indicates that every number from one to zero is a positive number, and any number from one to zero is a negative number.

Integers on Number Line Definition

On a number line, integers are written at equal intervals. The integers are categorised as positive integers and negative integers. If you observe the number line shown below, you can see that the origin is \(0\) (zero), which stands in the middle of the number line. There are positive numbers are on the right side of zero, and on the left side, there are negative numbers.

So, this number line represents the integers which include positive and negative numbers. The integers extend endlessly in both directions, which is why the arrows are marked at both ends to show that the line is infinite.

If you see the above number line carefully, the numbers increase and decrease as the direction changes. This is because any number on the left side is always less than the number to its right. 

For example, \(3\) is less than \(4;\, – 5\) is less than \( – 2.\)
Similarly, any number on the right side is always more than the number to its left.
Example: \(5\) is greater than the number \(3;\, – 1\) is greater than \( – 4.\)

Representing Integers on Number Line

The number line is a straight line with numbers placed at equal intervals along its length. However, a number line can be extended infinitely in any direction and represented horizontally.
The integers are marked on the number line as given below:

The positive integers are marked on the right side of zero on the number line, and negative integers are placed on the left.

The farther numbers move to the right from zero on the number line, the value of the numbers increases, and the more distant the numbers move to the left on the number line from zero, the value decreases.

When we compare any two numbers on a number line, the number on the right side of the number line will be more significant.

Operations on the Number Line

The four fundamental operations of mathematics are addition, subtraction, multiplication and division. There are different methods to perform these operations.
The arithmetic operations of integers can be explained in a better way on the number line.

Addition of Integers on Number Line

Addition on number line for integers is explained below:

Positive Integers: When you add any two positive numbers, the result will always be positive. Thus, while adding positive numbers, the direction of the movement will always be to the right side.
Example: Addition of \(4\) and \(4\left( {4 + 4 = 8} \right)\)

So the first number is \(4,\) and the second number is also \(4;\) both are positive numbers.
Locate the number \(4\) on a number line, then move \(4\) steps to the right side to reach \(8.\)

Negative Integers: When you add two negative numbers, the result you get is always negative. Thus, when you add negative numbers, the direction of the move will always be on the left side.
Example: The addition of the negative numbers \( – 3\) and \( – 5\)

The first number is \( – 3,\) and the second number is \( – 5;\) both are negative. Now, point out the number \( – 3\) on a number line, then move \(5\) steps to the left side to reach \( – 8.\)

Uses of Number Line

A number line can be used to carry out addition, subtraction, multiplication etc. You always have to move right to add the numbers, move the left side to subtract the numbers and skip count to multiply the numbers.

Types of Number Line

There are three types of the number line, and they are given below:

1. Real Number Line: The real number line, or simply called the number line, allows you to visually represent the real numbers by associating them with the unique points on the line.
2. Imaginary Number Line: In mathematics, a line of imaginary numbers exists like the real number line. The two lines sit at right angles to each other, like the ?x and ?−y− axis of the graph. These two intersect at the zero points of each line. These number lines help you imagine how real and imaginary numbers work.
3. Circular Number Line: The union of the real number line and the imaginary line is known as the circular number line.

We hope this article on Adding Integers with the Help of Number Line has provided you with an idea about the addition of integers on the number line. Stay tuned to Embibe for more informative articles.