A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally. The number line is also used to perform primary operations like addition, subtraction, division, and multiplication. As we move towards the right side of a number line, the numbers increase; as we move towards the left, the numbers decrease.
|1.||How to Represent Numbers on a Number Line?|
|2.||Operations on a Number Line|
|3.||Solved Examples on Number Line|
|4.||Practice Questions on Number Line|
|5.||FAQs on Number Line|
How to Represent Numbers on a Number Line?
There are various types of numbers that can be represented on a number line, such as integers, fractions, rational numbers, and so on. Let us discuss how to represent these various types of numbers on a number line in detail.
Integers on a Number Line
On a number line, integers are marked at equal intervals. These are categorized as positive numbers and negative numbers. If we observe the number line shown below, we see that the origin is 0 (zero), which stands in the middle. To the right, there are positive numbers and to the left, there are negative numbers. Hence, this number line represents integers which include positive and negative numbers. It extends endlessly in both directions and that is why the arrows are marked at both ends to show that the line is infinite.
If we observe the number line carefully, the numbers increase and decrease as we change the directions. Any number to the left is always less than the number to its right. For example, 2 is less than 4; -3 is less than -1
Similarly, any number to the right is always more than the number to its left. For example, 5 is greater than 3; -1 is greater than -3. Similarly, fractions and rational numbers can also be represented on the number line.
Operations on a Number Line
The fundamentals of mathematics revolve around the four basic operations- addition, subtraction, multiplication and division; and there are various methods to perform these operations. The number line is one of the easiest methods to represent such arithmetic operations. Let us see how we perform the four basic operations on a number line with the help of illustrations.
Addition on Number line
Let us understand how to add numbers using the number line with the help of an example. If we need to solve 2 + 3, we start by marking the number 2 on the number line. When we perform addition using a number line, we count by moving one number at a time towards the right side. Since we are adding 2 and 3, we will move 3 steps to the right. This brings us to 5. Hence, 2 + 3 = 5.
Subtraction on Number Line
To perform subtraction using a number line we count by moving one number at a time towards the left side. Let's say, you have 7 oranges and you give 3 to your friend. Find the number of oranges you have now. How will you solve this using a number line? We know that numbers decrease as we go to the left. Starting from 7, take 3 steps to the left to get the answer. This brings us to 4, therefore, you have 4 oranges now.
Multiplication on Number Line
Multiplication is also known as repeated addition. To perform multiplication using a number line we move towards the right side of the number line for a given number of times. Let us consider an example.
Example: Multiply: 4 × 3 using a number line.
Solution: Since this is multiplication, we will move towards the right side of the number line. Starting from zero, four groups of 3 equal intervals need to be formed on the number line. This way we will reach 12 forming 4 individual groups. Observe the following number line that shows 4 × 3 = 12.
Division on Number Line
To perform division using a number line we move towards the left side of the number line dividing a given number into equal groups. We know that the numbers decrease as we go to the left. Let us consider an example.
To solve 12 ÷ 4, we count how many jumps of 4 it takes from 0 to get to 12. These groups or jumps of 4 mean 12 ÷ 4 = 3. The number line shows that it takes 3 groups of 4 to reach 12.
Important Notes on Number line:
Note the following important points about a number line.
- We can represent various numbers on the number line, according to our requirements. For example, they can be only positive numbers, or integers between -4 and 3, or even fractions between -2 and 2.
- Number lines can help us in real-life situations. For example, they read the altitude (height) which is shown on a GPS device's screen, and can tell you how high or low you are below sea level!
Topics Related to Addition
Check out these interesting pages to know about the number line and its related topics.
Solved Examples on Number Line
Example 1: A flower is hidden behind an integer which is at a position 7 less than the spot where the butterfly is placed. Can you find the integer?
From the above figure, it is clear that the butterfly is placed at 4.
7 steps less than 4 means: 7 steps to the left of number 4 will take the butterfly to the flower.
This can also be understood as: + 4 − 7 = −3
This brings us to -3.
Thus, the flower is hidden behind -3.
∴ The integer is -3
Example 2: Show the following addition on a number line.
To perform addition on a number line we first look for the numbers from where we have to start. Here, the starting number is 300 and we need to add 500 to it. The addition of 300 + 500 is shown in the following number line:
Example 3: Represent two times four on a number line.
Two times four can be written as 2 × 4 = 8
This can be easily represented on the number line as:
The number line shows 2 groups with 4 equal intervals.
FAQs on Number Line
What is the Definition of a Number Line?
A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.
What is a Number Line Model?
A number line model is a representation of numbers plotted on an infinite line that extends at both ends.
What all Operations can be Performed Using Number Line?
The four primary operations of addition, subtraction, multiplication, and division can be easily performed using a number line. For addition and multiplication, we move towards the right side and for subtraction and division, we move towards the left side of the number line.
What all Numbers can be Represented on a Number Line?
We can represent integers (positive and negative numbers), fractions, rational numbers, and real numbers on the number line.
How to Perform Addition Using Number Line?
When we perform addition using a number line, we count by moving one number at a time towards the right side. For example, if we need to solve 4 + 5, we start by marking the number 4 on the number line. Since we are adding 4 and 5, we will move 5 steps to the right. This brings us to 9. Hence, 4 + 5 = 9.