Rational Numbers on Number Line
Rational numbers are defined as any number that can be represented as the ratio of two integers where the denominator is not equal to zero. Rational numbers on a number line are the way of representing positive and negative rational numbers visually. Let us understand more about rational numbers on a number line in this article.
| 1. | Representation of Rational Numbers on a Number Line |
| 2. | How to Represent Rational Numbers on Number Line? |
| 3. | FAQs on Rational Numbers on Number Line |
Representation of Rational Numbers on a Number Line
Rational numbers are defined as a number that can be represented in the form of p/q where p and q are integers and q ≠ 0. Representation of rational numbers on a number line is defined as plotting or graphing positive and negative rational numbers on a number line. Number line helps us to find an infinite number of rational numbers between any two rational numbers by increasing the number of divisions.
How to Represent Rational Numbers on Number Line?
Representation of rational numbers on a number line is very similar to the representation of negative integers or negative fractions on a number line. On a number line, keeping '0' as the reference, the left-hand side of '0' represents the negative region, and the right-hand side of '0' represents the positive region. Let us look into the steps to represent rational numbers on a number line as shown below.
Example: We will plot 4/5 on the number line.
Step I: Draw a number line by marking 0 as the reference.
Step II: Identify the integers between which the rational number lies and mark them. 4/5 lies between 0 and 1.
Step III: Mark the number of divisions between the integers marked in step II equivalent to the denominator of the given rational number. Here, 4/5 has 5 as the denominator. Thus, we will make 5 divisions.
Step IV: Starting from 0, move towards the right by the number of steps equivalent to the numerator of the given rational number. For 4/5 we will be moving 4 units towards the right starting from 0.
Thus, we have represented 4/5 on the number line as encircled above.
Negative Rational Numbers on Number Line
Representing negative rational numbers on the number line is similar to the representation of positive rational numbers except for the fact that the direction of movement is towards the left-hand side of the origin. All the steps described above remain the same performed on the left region of the number line. Let us take an example to understand the representation of negative rational numbers on a number line.
Example: Represent - 3/4 on a number line.
To represent - 3/4 on a number line we will mark the integers 0 and -1 since - 3/4 lies between them. We will then be making 4 divisions as the denominator of - 3/4 is 4. Since the rational number is negative, therefore we will be moving towards the left-hand side starting from 0 by 3 units to plot - 3/4 as shown above.
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Rational Numbers on Number Line Examples
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Example 1: Represent the rational number - 6/7 on the number line.
Solution: To represent - 6/7 on the number line, we will follow the steps to plot rational numbers on a number line.
We will identify the integers between which - 6/7 lies and mark them on the number line.
- 6/7 lies between 0 and - 1. Now we will make 7 divisions as the denominator of the given rational number is 7 followed by making 6 moves towards the left side starting from 0 as the numerator is - 6. Hence the rational number - 6/7 is plotted on the number line as shown above.
FAQs on Rational Numbers on Number Line
What are Rational Numbers on a Number Line?
Rational numbers on a number line are a way of representing positive and negative rational numbers on a number line very similar to integers.
How to Show Rational Numbers on Number Line?
Rational numbers on a number line are represented by identifying the integers between which the rational number lies, followed by making the number of divisions equivalent to the denominator of the rational number. Depending upon the sign of the rational number, we will be moving towards the right or left of 0 on the number line equivalent to the numerator of the rational number. For example: To plot 2/3 on the number line, we will make 3 divisions between 0 and 1 followed by moving 2 steps towards the right-hand side keeping 0 as the reference.
How to Represent Negative Rational Numbers on Number Line?
The representation of negative rational numbers is very similar to the representation of positive rational numbers. All the steps are performed on the left-hand side of the number line. For example: To represent - 1/6 on a number line, 6 divisions will be made between 0 and - 1 as the denominator of - 1/6 is 6 followed by moving 1 step towards the left-hand side by keeping 0 as the reference.
What is the Importance of Locating Rational Numbers on a Number Line?
Locating rational numbers on a number line helps us to visually understand arithmetic operations on rational numbers such as adding, subtracting, multiplying, and dividing rational numbers. It also helps us in understanding comparing and ordering rational numbers.
How do you Represent 3/4 on a Number Line?
To represent 3/4 on a number line, we plot the integers 0 and 1 on the number line as 3/4 falls between these numbers. The number of divisions that will be made between 0 and 1 will be 4 as the denominator of 3/4 is 4. Starting from 0, we will move by 3 units towards the right to get 3/4 on the number line.
How to make a Rational Number Line?
A rational number line is very similar to a regular number line where the right-hand side of '0' denotes the positive side and the left-hand side of '0' denotes the negative side. All the positive rational numbers such as 1/3, 2/3... are marked on the right and the negative rational numbers such as - 1/3, - 2/3... are marked on the left of '0' on the number line.