121 LearnersLast updated on July 5th, 2025
Integers on Number Line
The straight line where the numbers are represented clearly is called the number line. Integers include the positive numbers, negative numbers, and zero. For kids, number lines are used to explain basic mathematical concepts like addition, subtraction, multiplication, and division. In this article, how to represent integers on a number line will be discussed.
What are Integers?
Integers are the set of zero, positive, and negative numbers including zero. It is represented using “Z”,. For example, -5, -2, -1, 0, 1, 5, and 8.
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 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, we first check the sign of the second addend. 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 number line:
The subtraction of integers follows similar steps to addition. When subtracting, we should first check the sign of the subtrahend. If the subtrahend is a positive integer, we move to the left. Move to the right if the subtrahend is a negative number.
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 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.
For example, 5 × (-4)
To multiply 5 and (-4), we start at 0, and then move 4 steps to the left, 5 times. The final position is -20, so 5 × (-4) = -20
Real-world applications of Integers on Number Line
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.
- Thermometers use a number line, with zero degrees as the reference point for temperature
- In geography, the number line is used to measure the elevations above or below sea level.
- To track income and expenses, we can use a number line.
Common Mistakes and How to Avoid Them in Integers on Number Line
Understanding integers on a number line is essential for performing arithmetic operations. Students often make mistakes when working with integers on a number line. To avoid these common mistakes, let’s learn how to avoid them.
Mistake 1
Placing zero in the wrong place
It is a common misconception of not considering zero on the number line. Zero should be placed in the middle of the number line, the left-hand side of zero should represent the negative numbers and the right side should represent the positive numbers.
Mistake 2
Incorrectly labeling the negative and positive directions
Marking the numbers in opposite directions is a common mistake. Pacing negative numbers on the right side is incorrect. To avoid such mistakes, always make sure to mark the negative numbers on the left side of zero and the positive numbers on the right of zero.
Mistake 3
Errors in addition and subtraction
Adding or subtracting integers on the number line is one of the easiest ways to explain mathematical concepts to kids. The basic misconception the students make is in error in counting the integers. So it is important to remember that for adding integers, one has to move on the right-hand side of the number line and for subtraction it is always the left-hand side of the number line.
Mistake 4
Incorrectly ordering negative numbers
When representing a negative number on a number line, one of the common mistakes that students often make is confusing the value of negative numbers. This is because students often think that the number with the greater absolute value is larger, but this is incorrect for negative numbers. For example, -10 is less than -2.
Mistake 5
Errors in multiplication
Misapplying the negative sign in multiplication is a common mistake and leads to errors. Always remember that the product of two numbers with the same sign is positive, while the product of two numbers with opposite signs is negative.
Solved Examples of Integers on Number Line
Problem 1
Represent the integers -4, -1, 0, 3, and 5 on a number line.
NA
Explanation
To represent the integers on a number line, first draw a horizontal line with equal spacing. Identify and label the numbers using circles.
Problem 2
Compare -3 and 2 using a number line.
-3 is less than 2
Explanation
On a number line, the number on the right side is greater. As -3 is on the left of 2, -3 is less than 2.
Problem 3
Find (-2) + 5 using a number line
(-2) + 5 = 3
Explanation
Draw a number line and mark the points in equal intervals. Start from -2 and move 5 units to the right, it ends at point 3. Therefore, (-2) + 5 = 3.
Problem 4
Find (-5) - (-2) using a number line.
(-5) - (-2) = -3
Explanation
Draw a number line and label point -5, and move 2 units to the right, and it lands on -3. So (-5) - (-2) = -3.
Problem 5
Find (-3) × 2 using a number line.
(-3) × 2 = -6
Explanation
Multiplication is the repeated addition of a number. So to multiply -3 with 2, we move 2 groups of -3, that is, move 3 units to the left and 3 units to the right. So, (-3) × 2 = -6.
FAQs on Integers on Number Line
1.What is a number line?
2.What is the importance of the number line?
3.How can you compare two integers using a number line?
4.Can a number line be used for fractions and decimals?
5.What are the real-life applications of number lines?
6.How can children in Australia use numbers in everyday life to understand Integers on Number Line?
7.What are some fun ways kids in Australia can practice Integers on Number Line with numbers?
8.What role do numbers and Integers on Number Line play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Integers on Number Line skills?
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
