Unit Fractions
A unit fraction is a fraction where the numerator is 1. It represents one equal part of a whole. Examples include 1/2, 1/3, 1/4, 1/5, 1/6, and so on.
Unit fractions are the building blocks of all other fractions. For example, 3/4 is made of three copies of the unit fraction 1/4.
What is Unit Fractions - Class 3 Maths (Fractions)?
A unit fraction has 1 as its numerator.
Unit fraction = 1/n (where n is a whole number greater than 0)
The denominator tells how many equal parts the whole is divided into. Since the numerator is 1, you take exactly one of those parts.
Types and Properties
Common unit fractions:
| Fraction | Read As | Size (biggest to smallest) |
|---|---|---|
| 1/2 | One-half | Biggest |
| 1/3 | One-third | ↓ |
| 1/4 | One-quarter | ↓ |
| 1/5 | One-fifth | ↓ |
| 1/6 | One-sixth | ↓ |
| 1/8 | One-eighth | ↓ |
| 1/10 | One-tenth | Smallest (in this list) |
Key idea: The larger the denominator, the smaller the unit fraction.
Solved Examples
Example 1: Identify Unit Fractions
Question: Which of these are unit fractions: 1/5, 3/4, 1/8, 2/7, 1/2?
Think:
- Unit fractions have numerator = 1.
- 1/5 ✓, 3/4 ✗, 1/8 ✓, 2/7 ✗, 1/2 ✓
Answer: 1/5, 1/8, and 1/2 are unit fractions.
Example 2: Compare Unit Fractions
Question: Which is larger: 1/3 or 1/6?
Think:
- Both are unit fractions. Smaller denominator = bigger piece.
- 3 < 6, so 1/3 > 1/6.
Answer: 1/3 > 1/6.
Example 3: Order Unit Fractions
Question: Arrange from largest to smallest: 1/4, 1/2, 1/8, 1/3.
Think:
- Smaller denominator = larger fraction.
- 2 < 3 < 4 < 8
Answer: 1/2 > 1/3 > 1/4 > 1/8.
Example 4: Unit Fractions on a Number Line
Question: Mark 1/4 on a number line from 0 to 1.
Think:
- Divide the space between 0 and 1 into 4 equal parts.
- The first mark is 1/4.
0 ——— 1/4 ——— 2/4 ——— 3/4 ——— 1
Answer: 1/4 is at the first mark after 0.
Example 5: Building Fractions from Unit Fractions
Question: How is 3/5 made from unit fractions?
Think:
- 3/5 = 1/5 + 1/5 + 1/5
- It is 3 copies of the unit fraction 1/5.
Answer: 3/5 = 3 × (1/5).
Example 6: Word Problem — Sharing
Question: Ria shares a chocolate bar equally among 4 friends. What fraction does each friend get?
Think:
- 4 equal parts → each part = 1/4
Answer: Each friend gets 1/4 of the chocolate bar.
Example 7: Word Problem — Cooking
Question: A recipe needs 1/3 of a cup of sugar. Is this a unit fraction?
Think:
- Numerator = 1 → yes, it is a unit fraction.
Answer: Yes, 1/3 is a unit fraction.
Example 8: True or False
Question: True or false — 1/100 is larger than 1/10.
Think:
- Larger denominator = smaller fraction.
- 100 > 10, so 1/100 < 1/10.
Answer: False. 1/100 is smaller than 1/10.
Example 9: How Many Unit Fractions Make 1 Whole?
Question: How many copies of 1/6 make 1 whole?
Think:
- 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6 = 1
Answer: 6 copies of 1/6 make 1 whole.
Key Points to Remember
- A unit fraction has numerator 1: 1/2, 1/3, 1/4, 1/5, ...
- Larger denominator = smaller unit fraction.
- 1/2 is the largest unit fraction commonly used; 1/10, 1/100 are very small.
- Every fraction can be built from unit fractions: 3/4 = 1/4 + 1/4 + 1/4.
- n copies of 1/n = 1 whole (e.g., 5 copies of 1/5 = 1).
- Unit fractions are useful for comparing sizes of parts.
Practice Problems
- List all unit fractions with denominators from 2 to 8.
- Which is greater: 1/5 or 1/9?
- Arrange from smallest to largest: 1/7, 1/2, 1/5, 1/10.
- How many copies of 1/8 make 1 whole?
- Express 4/7 as a sum of unit fractions.
- Aman cuts a rope into 5 equal parts. What unit fraction does each piece represent?
- True or false: 1/4 is greater than 1/3.
Frequently Asked Questions
Q1. What is a unit fraction?
A unit fraction has 1 as the numerator. It represents exactly one equal part of a whole. Examples: 1/2, 1/3, 1/4, 1/5.
Q2. Why is 1/2 the largest common unit fraction?
Because dividing a whole into 2 parts gives the biggest pieces. The fewer parts you make, the bigger each part is.
Q3. How do I compare unit fractions?
The unit fraction with the smaller denominator is larger. 1/3 > 1/5 because thirds are bigger pieces than fifths.
Q4. Can I build any fraction from unit fractions?
Yes. Any fraction a/b is equal to a copies of the unit fraction 1/b. For example, 5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
Q5. Is 1 a unit fraction?
1 can be written as 1/1, which is a unit fraction. But it is usually just called 'one whole'.
Q6. How many unit fractions are there?
There are infinitely many unit fractions: 1/2, 1/3, 1/4, 1/5, and so on. There is no end.
Q7. Are unit fractions covered in NCERT Class 3?
Yes. NCERT Class 3 Maths introduces unit fractions like 1/2, 1/3, 1/4 through sharing activities and picture-based questions.
Q8. What is the smallest unit fraction?
There is no smallest unit fraction. As the denominator gets bigger (1/10, 1/100, 1/1000), the fraction gets smaller and smaller, but never reaches 0.
Related Topics
- Introduction to Fractions
- Numerator and Denominator
- Fractions of a Collection
- Comparing Fractions (Grade 3)
- Equivalent Fractions (Grade 3)
- Fractions on a Number Line
- Half, Quarter and Three-Quarter
- Fractions of Shapes
- Adding Like Fractions (Grade 3)
- Subtracting Like Fractions (Grade 3)
- Fraction Word Problems (Grade 3)
