Fractions of a Collection
So far, you have seen fractions of a single shape (like a circle or rectangle). But fractions can also describe parts of a group or collection.
For example, if you have 12 mangoes and give away 1/3 of them, you need to find 1/3 of 12. This is called finding a fraction of a collection.
What is Fractions of a Collection - Class 3 Maths (Fractions)?
A fraction of a collection means dividing a group of objects into equal parts and taking some of those parts.
Fraction of a collection = (Numerator / Denominator) × Total number of objects
Steps:
- Divide the total by the denominator (to find the size of one part).
- Multiply by the numerator (to find the required number of parts).
Solved Examples
Example 1: 1/2 of a Collection
Question: Find 1/2 of 16 pencils.
Think:
- Divide 16 by 2 = 8
- Take 1 part = 8
Answer: 1/2 of 16 = 8 pencils.
Example 2: 1/3 of a Collection
Question: Find 1/3 of 15 marbles.
Think:
- Divide 15 by 3 = 5
- Take 1 part = 5
Answer: 1/3 of 15 = 5 marbles.
Example 3: 2/3 of a Collection
Question: Find 2/3 of 18 flowers.
Think:
- Divide 18 by 3 = 6 (one-third)
- Two-thirds = 2 × 6 = 12
Answer: 2/3 of 18 = 12 flowers.
Example 4: 1/4 of a Collection
Question: Find 1/4 of 20 books.
Think:
- Divide 20 by 4 = 5
Answer: 1/4 of 20 = 5 books.
Example 5: 3/4 of a Collection
Question: Find 3/4 of 24 apples.
Think:
- 1/4 of 24 = 24 ÷ 4 = 6
- 3/4 = 3 × 6 = 18
Answer: 3/4 of 24 = 18 apples.
Example 6: Word Problem — Sharing Sweets
Question: Priya has 30 sweets. She gives 1/5 to her brother. How many does she give?
Think:
- 1/5 of 30 = 30 ÷ 5 = 6
Answer: Priya gives 6 sweets to her brother.
Example 7: Word Problem — Cricket
Question: A cricket team has 15 players. 1/3 are bowlers. How many bowlers are there?
Think:
- 1/3 of 15 = 15 ÷ 3 = 5
Answer: There are 5 bowlers.
Example 8: Finding the Remaining Part
Question: Aman has 12 crayons. He gives 1/4 to his friend. How many does he keep?
Think:
- 1/4 of 12 = 12 ÷ 4 = 3 (given away)
- Remaining = 12 − 3 = 9
Answer: Aman keeps 9 crayons.
Example 9: 2/5 of a Collection
Question: Find 2/5 of 25 students.
Think:
- 1/5 of 25 = 5
- 2/5 = 2 × 5 = 10
Answer: 2/5 of 25 = 10 students.
Key Points to Remember
- To find a fraction of a collection, divide by the denominator, then multiply by the numerator.
- 1/2 of a group = divide by 2.
- 1/3 of a group = divide by 3.
- 1/4 of a group = divide by 4.
- For fractions like 2/3 or 3/4, find one part first, then multiply.
- The remaining fraction = 1 − the fraction given away.
- The collection must be divisible by the denominator for whole-number answers.
Practice Problems
- Find 1/2 of 20 stickers.
- Find 1/3 of 21 mangoes.
- Find 2/5 of 35 beads.
- Kavi has 24 toy cars. He gives 1/4 to his cousin. How many does he give?
- Find 3/4 of 16 chapatis.
- There are 30 students in a class. 1/6 are absent. How many are absent?
- Neha has 28 bangles. She wears 1/7 of them. How many does she wear? How many are left?
Frequently Asked Questions
Q1. What does fraction of a collection mean?
It means finding a part of a group. For example, 1/4 of 20 buttons means dividing 20 buttons into 4 equal groups and taking 1 group, which is 5.
Q2. How do I find 1/3 of a number?
Divide the number by 3. For example, 1/3 of 12 = 12 ÷ 3 = 4.
Q3. How do I find 2/3 of a number?
First find 1/3 by dividing by 3, then multiply by 2. For 2/3 of 18: 18 ÷ 3 = 6, then 6 × 2 = 12.
Q4. What if the number does not divide evenly by the denominator?
In Class 3, the problems are designed so the total is divisible by the denominator. In higher classes, you learn to handle non-whole-number answers.
Q5. Is fraction of a collection different from fraction of a shape?
The idea is the same — dividing into equal parts. But for a shape, you shade parts. For a collection, you count objects in each group.
Q6. How do I find the remaining fraction?
If you give away 1/4, the remaining fraction is 1 − 1/4 = 3/4. Then find 3/4 of the total.
Q7. Can I use multiplication to find a fraction of a number?
Yes. To find 3/5 of 20, calculate (3 × 20) ÷ 5 = 60 ÷ 5 = 12. Or divide first: 20 ÷ 5 = 4, then 4 × 3 = 12.
Q8. Is this covered in NCERT Class 3?
Yes. NCERT Class 3 Maths includes finding fractions of collections using everyday objects like fruits, pencils, and stickers.
