Half, Quarter and Three-Quarter
The fractions half (1/2), quarter (1/4), and three-quarter (3/4) are among the first fractions children learn. These fractions appear everywhere in daily life — from sharing food to telling time.
Understanding these three fractions builds a strong base for all fraction work in higher classes. In Class 3, you learn to recognise them, write them, and use them to solve simple problems.
What is Half, Quarter and Three-Quarter - Class 3 Maths (Fractions (Grade 3))?
Half (1/2) means dividing something into 2 equal parts and taking 1 part.
Quarter (1/4) means dividing something into 4 equal parts and taking 1 part.
Three-Quarter (3/4) means dividing something into 4 equal parts and taking 3 parts.
| Fraction | In Words | What It Means |
|---|---|---|
| 1/2 | One-half | 1 out of 2 equal parts |
| 1/4 | One-quarter | 1 out of 4 equal parts |
| 3/4 | Three-quarters | 3 out of 4 equal parts |
The bottom number (denominator) tells how many equal parts the whole is divided into. The top number (numerator) tells how many parts are taken.
Half, Quarter and Three-Quarter Formula
Half of a number = Number ÷ 2
Quarter of a number = Number ÷ 4
Three-quarters of a number = (Number ÷ 4) × 3
Types and Properties
Understanding Each Fraction
1. Half (1/2)
- Cut a chapati into 2 equal pieces — each piece is 1/2.
- Half of 10 = 10 ÷ 2 = 5
- Half of 20 = 20 ÷ 2 = 10
2. Quarter (1/4)
- Fold a paper into 4 equal parts — each part is 1/4.
- Quarter of 12 = 12 ÷ 4 = 3
- Quarter of 20 = 20 ÷ 4 = 5
3. Three-Quarters (3/4)
- If a pizza has 4 slices and you eat 3, you ate 3/4.
- Three-quarters of 8 = (8 ÷ 4) × 3 = 2 × 3 = 6
- Three-quarters of 20 = (20 ÷ 4) × 3 = 5 × 3 = 15
Relationship Between Them
- 1/2 = 2/4 (half is the same as two-quarters)
- 1/4 + 1/4 = 2/4 = 1/2
- 1/4 + 3/4 = 4/4 = 1 (whole)
Solved Examples
Example 1: Example 1: Finding Half
Question: What is half of 16?
Think:
- Half means divide by 2
- 16 ÷ 2 = 8
Answer: Half of 16 = 8
Example 2: Example 2: Finding a Quarter
Question: What is one-quarter of 24?
Think:
- Quarter means divide by 4
- 24 ÷ 4 = 6
Answer: One-quarter of 24 = 6
Example 3: Example 3: Finding Three-Quarters
Question: What is three-quarters of 20?
Think:
- First find one-quarter: 20 ÷ 4 = 5
- Then multiply by 3: 5 × 3 = 15
Answer: Three-quarters of 20 = 15
Example 4: Example 4: Word Problem – Sharing Mangoes
Question: Aman has 12 mangoes. He gives half to his sister. How many mangoes does he give?
Think:
- Half of 12 = 12 ÷ 2 = 6
Answer: Aman gives 6 mangoes.
Example 5: Example 5: Shading a Shape
Question: A square is divided into 4 equal parts. 3 parts are shaded. What fraction is shaded?
Think:
- Total equal parts = 4
- Shaded parts = 3
- Fraction shaded = 3/4 (three-quarters)
Answer: 3/4 of the square is shaded.
Example 6: Example 6: Time Connection
Question: What fraction of an hour is 15 minutes?
Think:
- 1 hour = 60 minutes
- 60 ÷ 4 = 15
- So 15 minutes = 1/4 of an hour (quarter of an hour)
Answer: 15 minutes is 1/4 (a quarter) of an hour.
Example 7: Example 7: Word Problem – Stickers
Question: Priya has 40 stickers. She uses three-quarters of them for her project. How many stickers did she use?
Think:
- One-quarter of 40 = 40 ÷ 4 = 10
- Three-quarters of 40 = 10 × 3 = 30
Answer: Priya used 30 stickers.
Example 8: Example 8: Comparing Fractions
Question: Which is more: 1/2 of 20 or 1/4 of 20?
Think:
- 1/2 of 20 = 20 ÷ 2 = 10
- 1/4 of 20 = 20 ÷ 4 = 5
- 10 > 5
Answer: 1/2 of 20 (= 10) is more than 1/4 of 20 (= 5).
Example 9: Example 9: Equivalent Fractions
Question: Show that 1/2 = 2/4.
Think:
- 1/2 of 8 = 8 ÷ 2 = 4
- 2/4 of 8 = (8 ÷ 4) × 2 = 2 × 2 = 4
- Both give 4 — they are the same fraction
Answer: 1/2 = 2/4 (they are equivalent fractions).
Example 10: Example 10: Money Problem
Question: Kavi saves ₹100. He spends a quarter on a book. How much does he spend?
Think:
- Quarter of ₹100 = 100 ÷ 4 = ₹25
Answer: Kavi spends ₹25 on the book.
Real-World Applications
Where Do We See Halves, Quarters, and Three-Quarters?
- Time: Quarter past (1/4 hour = 15 min), half past (1/2 hour = 30 min), quarter to (3/4 hour = 45 min).
- Food: Half a chapati, a quarter of a pizza, three-quarters of a glass of milk.
- Money: Half of ₹10 = ₹5, quarter of ₹100 = ₹25.
- Sports: Half-time in a football match, quarter-finals in a tournament.
- Measurement: Half a metre = 50 cm, quarter of a kilogram = 250 g.
Key Points to Remember
- 1/2 (half) = divide into 2 equal parts, take 1.
- 1/4 (quarter) = divide into 4 equal parts, take 1.
- 3/4 (three-quarters) = divide into 4 equal parts, take 3.
- Half of a number = number ÷ 2.
- Quarter of a number = number ÷ 4.
- Three-quarters of a number = (number ÷ 4) × 3.
- 1/2 is the same as 2/4 (equivalent fractions).
- 1/4 + 3/4 = 4/4 = 1 whole.
Practice Problems
- Find half of 30.
- Find one-quarter of 36.
- Find three-quarters of 16.
- Meera has 18 beads. She gives half to her friend. How many beads does she give?
- What is a quarter of an hour in minutes?
- Rahul has ₹80. He saves three-quarters. How much does he save?
- A rectangle is divided into 4 equal parts. 1 part is coloured. What fraction is coloured?
- Which is greater: 3/4 of 12 or 1/2 of 12?
Frequently Asked Questions
Q1. What does half mean in maths?
Half means dividing something into 2 equal parts and taking 1 part. It is written as 1/2. Half of 10 is 5.
Q2. What is the difference between a quarter and a half?
A half (1/2) is one of 2 equal parts. A quarter (1/4) is one of 4 equal parts. A half is always bigger than a quarter of the same number.
Q3. How do I find three-quarters of a number?
First divide the number by 4 to find one-quarter. Then multiply by 3. For example, three-quarters of 24: 24 ÷ 4 = 6, then 6 × 3 = 18.
Q4. Is 1/2 the same as 2/4?
Yes, 1/2 and 2/4 are equivalent fractions. They represent the same amount. If you divide a shape into 2 parts and shade 1, or divide it into 4 parts and shade 2, the shaded area is the same.
Q5. What is a quarter of 100?
A quarter of 100 = 100 ÷ 4 = 25.
Q6. How are these fractions used in telling time?
Quarter past means 15 minutes after the hour (1/4 of 60). Half past means 30 minutes (1/2 of 60). Quarter to means 45 minutes past (3/4 of 60).
Q7. What do 1/4 and 3/4 add up to?
1/4 + 3/4 = 4/4 = 1 whole. Together, a quarter and three-quarters make a complete whole.
Q8. Can I find half of an odd number?
Yes, but the answer will not be a whole number. Half of 7 is 3 and a half (3½). In Class 3, most problems use even numbers to keep answers simple.
Q9. Where do we see quarters in daily life?
Quarters appear in time (quarter hour = 15 min), money (quarter of ₹100 = ₹25), measurement (quarter kg = 250 g), and food (a quarter of a pizza or cake).
Related Topics
- Introduction to Fractions
- Half and Quarter
- Numerator and Denominator
- Fractions of a Collection
- Comparing Fractions (Grade 3)
- Equivalent Fractions (Grade 3)
- Unit Fractions
- Fractions on a Number Line
- Fractions of Shapes
- Adding Like Fractions (Grade 3)
- Subtracting Like Fractions (Grade 3)
- Fraction Word Problems (Grade 3)
