Fractions on Number Line
You know how to show whole numbers like 0, 1, 2, 3 on a number line. But what about numbers between them, like 1/2 or 3/4? Fractions can also be shown on a number line.
Placing fractions on a number line helps you understand their size and compare them. You can see which fractions are closer to 0, which are closer to 1, and how fractions relate to each other.
In Class 6 NCERT Maths, you will learn how to represent proper fractions, improper fractions, and mixed numbers on a number line.
What is Fractions on Number Line - Grade 6 Maths (Fractions)?
How fractions appear on a number line:
- The space between 0 and 1 is divided into equal parts based on the denominator.
- If the denominator is 4, divide the space into 4 equal parts. Each part represents 1/4.
- The numerator tells you how many parts to count from 0.
Example: To show 3/4 on a number line:
- Draw a number line with 0 and 1 marked.
- Divide the space between 0 and 1 into 4 equal parts.
- Count 3 parts from 0. That point is 3/4.
Fractions on Number Line Formula
Steps to represent a fraction on a number line:
- Look at the denominator — it tells you how many equal parts to divide each unit into.
- Look at the numerator — it tells you how many parts to count from 0 (or from the start of the unit).
- Mark the point.
For improper fractions and mixed numbers:
- Convert the improper fraction to a mixed number (or vice versa).
- An improper fraction like 7/4 = 1 and 3/4. So it lies between 1 and 2 on the number line.
- Divide the space between 1 and 2 into 4 parts and count 3 parts from 1.
Types and Properties
Types of fractions on the number line:
- Proper fractions (numerator < denominator): Always lie between 0 and 1. Examples: 1/3, 2/5, 4/7.
- Improper fractions (numerator ≥ denominator): Lie at 1 or beyond 1. Examples: 5/3 lies between 1 and 2. 8/4 = 2 lies at 2.
- Mixed numbers: Same as improper fractions. 2 and 1/3 lies between 2 and 3.
- Unit fractions (numerator = 1): 1/2 is at the middle of 0 and 1. 1/3 is at the first third mark. 1/4 is at the first quarter mark.
Solved Examples
Example 1: Representing 1/2 on a Number Line
Problem: Show 1/2 on a number line.
Solution:
Step 1: Draw a number line with 0 and 1.
Step 2: Denominator = 2. Divide the space between 0 and 1 into 2 equal parts.
Step 3: Numerator = 1. Count 1 part from 0.
Answer: 1/2 is at the midpoint between 0 and 1.
Example 2: Representing 3/5 on a Number Line
Problem: Show 3/5 on a number line.
Solution:
Step 1: Draw a number line with 0 and 1.
Step 2: Denominator = 5. Divide the space into 5 equal parts.
Step 3: Numerator = 3. Count 3 parts from 0.
Answer: 3/5 is at the third mark out of 5 between 0 and 1.
Example 3: Representing 7/4 on a Number Line
Problem: Show 7/4 on a number line.
Solution:
Step 1: 7/4 = 1 and 3/4. It lies between 1 and 2.
Step 2: Divide the space between 1 and 2 into 4 equal parts.
Step 3: Count 3 parts from 1.
Answer: 7/4 is at the third mark between 1 and 2.
Example 4: Representing 2 and 1/3 on a Number Line
Problem: Show 2 1/3 on a number line.
Solution:
Step 1: 2 1/3 lies between 2 and 3.
Step 2: Divide the space between 2 and 3 into 3 equal parts.
Step 3: Count 1 part from 2.
Answer: 2 1/3 is at the first mark between 2 and 3.
Example 5: Comparing Fractions on a Number Line
Problem: Using a number line, which is greater: 2/5 or 3/5?
Solution:
Divide the space between 0 and 1 into 5 equal parts.
2/5 is at the 2nd mark. 3/5 is at the 3rd mark.
3/5 is further to the right than 2/5.
Answer: 3/5 > 2/5. On a number line, the fraction further to the right is greater.
Example 6: Showing 0/4 and 4/4
Problem: Where do 0/4 and 4/4 lie on a number line?
Solution:
0/4 = 0. It lies at the point 0.
4/4 = 1. It lies at the point 1.
Answer: 0/4 is at 0 and 4/4 is at 1.
Example 7: Equivalent Fractions on Number Line
Problem: Show that 1/2 and 2/4 are at the same point on a number line.
Solution:
For 1/2: Divide 0 to 1 into 2 parts. Mark the 1st part = 1/2.
For 2/4: Divide 0 to 1 into 4 parts. Mark the 2nd part = 2/4.
Both points are at the same location (the midpoint of 0 and 1).
Answer: 1/2 and 2/4 are equivalent fractions — they represent the same point.
Example 8: Placing Multiple Fractions
Problem: Place 1/6, 3/6, and 5/6 on a number line.
Solution:
Step 1: Divide the space between 0 and 1 into 6 equal parts.
Step 2:
- 1/6 is at the 1st mark.
- 3/6 is at the 3rd mark (this is also 1/2).
- 5/6 is at the 5th mark.
Answer: The fractions are at the 1st, 3rd, and 5th marks on a number line divided into sixths.
Real-World Applications
Why fractions on a number line matter:
- Understanding size: Seeing fractions on a number line helps you understand which fractions are bigger and which are smaller.
- Comparing fractions: The fraction further to the right on the number line is always greater.
- Equivalent fractions: Fractions that land on the same point are equivalent (like 1/2 and 2/4).
- Building towards decimals: Decimals are just fractions with denominators of 10, 100, etc. Placing them on a number line is the same process.
- Measurement: Rulers and measuring tapes divide units into fractions (halves, quarters, eighths).
Key Points to Remember
- Fractions can be shown on a number line by dividing each unit into equal parts.
- The denominator tells you how many equal parts to make.
- The numerator tells you how many parts to count.
- Proper fractions (less than 1) lie between 0 and 1.
- Improper fractions (1 or more) lie at 1 or beyond.
- A fraction further to the right on the number line is greater.
- Equivalent fractions land on the same point.
- 0/n = 0 and n/n = 1 for any positive number n.
Practice Problems
- Show 2/3 on a number line.
- Show 5/8 on a number line.
- Place 1/4, 2/4, and 3/4 on the same number line.
- Show 9/5 on a number line. (Hint: convert to a mixed number first.)
- Using a number line, which is greater: 3/7 or 5/7?
- Show that 2/3 and 4/6 are at the same point on a number line.
Frequently Asked Questions
Q1. How do you show a fraction on a number line?
Divide the space between two whole numbers into equal parts based on the denominator. Count from the left whole number as many parts as the numerator says. That point represents the fraction.
Q2. Where do proper fractions lie on the number line?
Proper fractions (where numerator is less than denominator) always lie between 0 and 1.
Q3. Where do improper fractions lie on the number line?
Improper fractions lie at 1 or beyond. For example, 5/3 lies between 1 and 2, and 8/4 = 2 lies at the point 2.
Q4. How can a number line help compare fractions?
On a number line, a fraction that is further to the right is greater. So if you place two fractions on the same number line, you can instantly see which is bigger.
Q5. Do equivalent fractions go to the same point?
Yes. Equivalent fractions like 1/2 and 3/6 represent the same value, so they are at the same point on the number line.
Q6. Can negative fractions be shown on a number line?
Yes. Negative fractions are shown to the left of 0 on the number line. For example, −1/2 is halfway between 0 and −1.
Related Topics
- Introduction to Fractions
- Comparing Fractions
- Equivalent Fractions
- Number Line Representation
- Proper and Improper Fractions
- Mixed Numbers
- Simplest Form of a Fraction
- Like and Unlike Fractions
- Addition of Fractions
- Subtraction of Fractions
- Unit Fractions
- Word Problems on Fractions
- Types of Fractions
- Addition and Subtraction of Fractions
