Rational Numbers on Number Line
Every rational number can be represented as a point on the number line. Positive rational numbers lie to the right of 0, and negative rational numbers lie to the left.
To plot a fraction like 3/4 on the number line, divide the segment from 0 to 1 into 4 equal parts and mark the 3rd part. For −2/5, divide the segment from 0 to −1 into 5 equal parts and mark the 2nd part from 0.
What is Rational Numbers on Number Line - Grade 7 Maths (Rational Numbers)?
Plotting rational numbers on a number line:
- Identify the two consecutive integers between which the number lies.
- Divide the segment between those integers into as many equal parts as the denominator.
- Count from the lower integer as many parts as the numerator.
- Mark the point.
Rational Numbers on Number Line Formula
Key fact:
Between any two rational numbers, there are infinitely many rational numbers.
This means the number line is densely packed with rational numbers — you can always find another one between any two.
Types and Properties
Types of rational numbers on the number line:
- Proper fractions (0 < p/q < 1): Lie between 0 and 1.
- Improper fractions (p/q > 1): Lie beyond 1 (convert to mixed number to locate).
- Negative fractions: Lie to the left of 0.
- Integers: Special rational numbers at whole-number positions (e.g., 3 = 3/1).
Solved Examples
Example 1: Plotting 3/5
Problem: Plot 3/5 on the number line.
Solution:
- 3/5 lies between 0 and 1.
- Divide the segment from 0 to 1 into 5 equal parts.
- Mark the 3rd part from 0.
Answer: 3/5 is at the 3rd mark when 0 to 1 is divided into 5 equal parts.
Example 2: Plotting −2/3
Problem: Plot −2/3 on the number line.
Solution:
- −2/3 lies between −1 and 0.
- Divide the segment from −1 to 0 into 3 equal parts.
- From 0, move 2 parts to the left.
Answer: −2/3 is at the 2nd mark to the left of 0 when −1 to 0 is divided into 3 parts.
Example 3: Plotting 7/4
Problem: Plot 7/4 on the number line.
Solution:
- 7/4 = 1 3/4. It lies between 1 and 2.
- Divide the segment from 1 to 2 into 4 equal parts.
- Mark the 3rd part from 1.
Answer: 7/4 is at the 3rd mark between 1 and 2 when divided into 4 parts.
Example 4: Finding Rational Numbers Between Two Numbers
Problem: Find 3 rational numbers between 1/2 and 3/4.
Solution:
- Convert to equivalent fractions with a larger denominator.
- 1/2 = 4/8, 3/4 = 6/8
- Only 5/8 between them. Need more: use denominator 16.
- 1/2 = 8/16, 3/4 = 12/16
- Between them: 9/16, 10/16, 11/16
Answer: Three rational numbers: 9/16, 10/16 (= 5/8), 11/16.
Example 5: Ordering on Number Line
Problem: Arrange on a number line: −1, 1/2, −1/4, 3/4.
Solution:
- From left to right: −1, −1/4, 1/2, 3/4
- −1 is leftmost, then −1/4 (closer to 0), then 1/2, then 3/4.
Answer: Order: −1 < −1/4 < 1/2 < 3/4.
Real-World Applications
Real-world uses:
- Temperature scales: Thermometers are number lines with decimal/fractional readings.
- Maps: Coordinates often involve rational numbers.
- Measurement: Rulers show fractions of centimetres or inches.
Key Points to Remember
- Every rational number has a unique position on the number line.
- Positive rationals are right of 0, negative rationals are left of 0.
- To plot p/q: divide the appropriate unit segment into q parts and count p parts.
- Between any two rational numbers, there are infinitely many more.
- The number line is dense with rational numbers.
Practice Problems
- Plot 2/7 on the number line.
- Plot −5/3 on the number line.
- Find 5 rational numbers between 0 and 1.
- Find 3 rational numbers between 1/3 and 1/2.
- Mark these on a number line: −3/2, 0, 1/4, 5/4.
Frequently Asked Questions
Q1. How do you plot a rational number on the number line?
Find which two integers it lies between. Divide that segment into as many parts as the denominator. Count from the lower integer as many parts as the numerator.
Q2. Can every rational number be plotted?
Yes. Every rational number p/q corresponds to exactly one point on the number line.
Q3. How many rational numbers are between 0 and 1?
Infinitely many. For example, 1/2, 1/3, 1/4, 2/5, 3/7, ... There is no end to the list.
Q4. What about irrational numbers?
Irrational numbers (like √2 or π) also have positions on the number line but cannot be expressed as p/q. Together, rational and irrational numbers fill the entire number line.
Related Topics
- Rational Numbers
- Comparing Rational Numbers
- Number Line Representation
- Rational Numbers Between Two Numbers
- Equivalent Rational Numbers
- Standard Form of Rational Number
- Operations on Rational Numbers
- Properties of Rational Numbers
- Additive Inverse of Rational Numbers
- Multiplicative Inverse of Rational Numbers
- Density Property of Rational Numbers
