Fractions on a Number Line
A number line is a straight line where numbers are placed at equal distances. You can show fractions on a number line just like whole numbers.
Fractions fit between whole numbers. For example, 1/2 sits exactly halfway between 0 and 1. This helps you see the size of fractions and compare them easily.
What is Fractions on a Number Line - Class 3 Maths (Fractions)?
To place a fraction on a number line:
- Look at the denominator — it tells you how many equal parts to divide the space between 0 and 1.
- Look at the numerator — it tells you which mark to point to.
Divide the segment 0 to 1 into equal parts (= denominator), then count to the numerator.
Solved Examples
Example 1: Plot 1/2
Question: Show 1/2 on a number line.
Think:
- Divide the space 0 to 1 into 2 equal parts.
- The first mark is 1/2.
0 ———— 1/2 ———— 1
Answer: 1/2 is at the middle of 0 and 1.
Example 2: Plot 3/4
Question: Show 3/4 on a number line.
Think:
- Divide 0 to 1 into 4 equal parts: 0, 1/4, 2/4, 3/4, 1.
- Count to the 3rd mark.
0 —— 1/4 —— 2/4 —— 3/4 —— 1
Answer: 3/4 is at the third mark.
Example 3: Plot 2/5
Question: Show 2/5 on a number line.
Think:
- Divide 0 to 1 into 5 equal parts.
- The marks are: 0, 1/5, 2/5, 3/5, 4/5, 1.
- 2/5 is the second mark.
0 — 1/5 — 2/5 — 3/5 — 4/5 — 1
Answer: 2/5 is at the second mark.
Example 4: Identify a Fraction from a Number Line
Question: A number line from 0 to 1 is divided into 6 equal parts. An arrow points to the 5th mark. What fraction is it?
Think:
- 6 equal parts → denominator = 6
- 5th mark → numerator = 5
Answer: The fraction is 5/6.
Example 5: Compare Using a Number Line
Question: Using a number line, which is greater: 2/3 or 1/3?
Think:
- Divide 0 to 1 into 3 equal parts: 0, 1/3, 2/3, 1.
- 2/3 is to the right of 1/3.
- Numbers to the right are larger.
Answer: 2/3 > 1/3.
Example 6: Fraction Greater Than 1
Question: Where does 5/4 go on a number line?
Think:
- 5/4 is more than 1 (since 4/4 = 1).
- Divide 1 to 2 into 4 parts.
- 5/4 is the first mark after 1.
0 —— 1/4 —— 2/4 —— 3/4 —— 1 —— 5/4 —— 6/4 —— 7/4 —— 2
Answer: 5/4 is between 1 and 2, at the first mark after 1.
Example 7: Word Problem
Question: Ria walks 3/8 of the way from home to school. Show her position on a number line from 0 (home) to 1 (school).
Think:
- Divide 0 to 1 into 8 equal parts.
- Ria is at the 3rd mark = 3/8.
Answer: Ria is at 3/8 of the way — less than halfway.
Example 8: Equivalent Fractions on a Number Line
Question: Show that 1/2 and 2/4 are at the same point on the number line.
Think:
- 1/2: divide 0-1 into 2 parts, mark at the 1st point.
- 2/4: divide 0-1 into 4 parts, mark at the 2nd point.
- Both points are at the same location (the middle).
Answer: 1/2 = 2/4. They are the same point on the number line.
Example 9: Ordering Fractions on a Number Line
Question: Place 1/6, 4/6, and 3/6 on a number line and order them.
Think:
- Divide 0 to 1 into 6 parts.
- 1/6 (1st mark), 3/6 (3rd mark), 4/6 (4th mark).
0 — 1/6 — 2/6 — 3/6 — 4/6 — 5/6 — 1
Answer: 1/6 < 3/6 < 4/6.
Key Points to Remember
- To plot a fraction, divide the segment into parts equal to the denominator, then count to the numerator.
- Fractions closer to 1 are larger; fractions closer to 0 are smaller.
- A number line helps you compare and order fractions visually.
- Equivalent fractions appear at the same point on the number line.
- Fractions greater than 1 (like 5/4) go beyond the 1 mark.
- 0/n is at 0, and n/n is at 1.
Practice Problems
- Draw a number line and plot 1/3 and 2/3.
- Show 3/5 on a number line from 0 to 1.
- A number line from 0 to 1 is divided into 8 equal parts. An arrow points to the 5th mark. What fraction is it?
- Use a number line to show that 2/4 = 1/2.
- Place 1/4, 3/4, and 2/4 on a number line and arrange them from smallest to largest.
- Where does 7/6 go on a number line? Is it between 0 and 1 or between 1 and 2?
- Aman walks 5/8 of the way from home to the park. Is he past the halfway point?
Frequently Asked Questions
Q1. How do I show a fraction on a number line?
Divide the space between 0 and 1 into as many equal parts as the denominator. Then count from 0 to the numerator. That is where the fraction goes.
Q2. What if the fraction is more than 1?
Extend the number line past 1. For example, 5/3 is between 1 and 2. Divide each whole-number segment into 3 parts and count 5 parts from 0.
Q3. How does a number line help compare fractions?
The fraction that is farther to the right is larger. Placing fractions on the same number line makes it easy to see which is greater.
Q4. Do equivalent fractions appear at the same spot?
Yes. 1/2 and 2/4 are at exactly the same point on the number line, even though they have different numbers.
Q5. Where is 0/5 on the number line?
0/5 = 0. It is at the very start of the number line, at 0.
Q6. Where is 5/5 on the number line?
5/5 = 1. It is at the point marked 1.
Q7. Can I show different denominators on the same number line?
It is easier to use separate number lines for different denominators, or use a common denominator so the spacing is the same.
Q8. Is this topic in the NCERT Class 3 textbook?
Yes. NCERT Class 3 Maths introduces fractions on the number line to help students visualise and compare fractions.
