Integers on Number Line

Integers are whole numbers, including positive numbers, negative numbers, and zero, represented by the symbol “Z”. Positive integers are greater than zero, negative integers are less than zero, and zero is the central reference point. For example, -5, -2, -1, 0, 1, 5, and 8 are all integers, with positive numbers to the right and negative numbers to the left of zero.

How to Represent Integers on a Number Line?

Let us now understand how to represent integers on a number line. As we know, the integers consist of positive numbers such as 1, 2, 3, 4, …, and negative numbers such as -1, -2, -3, -4, …, and 0. When representing integers on the number line, we mark zero at the center of the number line. Positive numbers are marked to the right of zero, and negative numbers to the left.
 

Addition and Subtraction of Integers on the Number Line

The numbers are used to perform basic arithmetic operations. Now, let’s learn how to add or subtract integers using the number line. We start from 0 and move to the right if the numbers are positive and to the left if the numbers are negative.

Addition of Integers on the Number Line:

When adding integers using a number line, start at the position of the first addend. Then move right if adding a positive number or left if adding a negative number.  Then we mark the first addend on the number line and move towards the right side if the second addend is positive. Move to the left if the second addend is a negative number
For example, 8 + (-3):
First, mark 8 on a number line. As the second addend is a negative number, we move 3 steps towards the left. So, 8 + (-3) = 5. 

Subtraction of Integers Using the Number Line:

Subtraction on a number line that involves adding the opposite of the number being subtracted. Move left for positive subtrahends and right for negative subtrahends. For example, 8 - 5 starts at 8, moves five steps left, landing at 3, while -5 - (-2) moves two steps right to -3. This approach clarifies subtraction and number relationships.

For example, 8 - 5:

To find the difference, first mark 8 on the number line. Then, move 5 steps to the left. So, 8 - 5 = 3

Multiplication of Integers on the Number Line

Multiplication is the process of repeatedly adding a number to itself. When multiplying an integer by a number, we start from zero. Then move to the right if the multiplier is positive, and if the multiplier is negative, we move left. When multiplying by a negative number, we reverse direction. For example, (-5) × 4 would mean moving 5 units to the left 4 times.

For example, 5 × (-4)
For 5 × (-4), start at 0 and make 5 jumps of 4 units each to the left, landing on -20.

In our real life, integers on the number line are used to represent concepts like temperature, elevation, sports, and so on. Here are real-world applications of integers on the number line. 

Temperature Measurement: Thermometers use integers to represent temperature, with zero degrees as a reference point. Positive numbers indicate temperatures above zero, while negative numbers show temperatures below zero.

Elevation in Geography: Integers measure heights above or below sea level. Positive numbers indicate mountains or hills, while negative numbers indicate valleys, basements, or ocean trenches.

Finance and Money Management: Integers track income and expenses. Positive numbers show earnings or profits, and negative numbers represent losses or debts, helping individuals and businesses manage budgets efficiently.

Engineering Applications: In engineering, integers represent quantities like voltage, force, and displacement, including positive and negative directions. They are essential for calculations in mechanical, civil, and electrical projects.

Robotics: Robotics uses integers to control movement and positioning. Positive and negative integers help define forward/backward or left/right motions, ensuring precise control of robotic arms and machines.