Halves and Quarters

'If I share my chocolate equally with my friend, each of us gets half. That is FAIR sharing.'

1. What You Will Learn

• Understanding halves, quarters, and three-quarters
• Understanding one-third and two-thirds
• Writing fractions using numbers
• Finding fractions of a collection
• Comparing fractions

2. What is a Fraction?

A fraction is a PART of a whole. When we divide something EQUALLY, each part is a fraction.

Half (½)

If we divide ONE chapati between TWO people equally, each gets half.

One out of two equal parts = ½

Quarter (¼)

If we divide ONE chocolate among FOUR people equally, each gets one-quarter.

One out of four equal parts = ¼

Three-Quarter (¾)

If you take THREE out of FOUR equal parts, you have three-quarters.

One-Third (⅓)

If you divide ONE among THREE people, each gets one-third.

3. Fractions in Everyday Life

4. Finding a Fraction of a Collection

Half of a Collection

Half of 12 apples = 12 ÷ 2 = 6 apples

Quarter of a Collection

Quarter of 20 toffees = 20 ÷ 4 = 5 toffees

Three-Quarter of a Collection

Three-quarter of 12 eggs = 12 ÷ 4 = 3, then 3 × 3 = 9 eggs

One-Third of a Collection

One-third of 15 marbles = 15 ÷ 3 = 5 marbles

Practice Table

5. Sharing More Than One Item

Example

Ravi has 3 chapatis. He wants to share EQUALLY with his sister. How much does each get?

• 3 chapatis between 2 people
• Each gets 1 full chapati + ½ chapati = 1½ chapatis

Another Example

4 apples shared among 3 friends:

• Each gets 1 full apple + ⅓ apple = 1⅓ apples

6. Comparing Fractions

Which is Bigger?

• ½ or ¼? (½ is BIGGER — half of something is more than a quarter)
• ¾ or ¼? (¾ is BIGGER — three parts are more than one part)
• ⅓ or ¼? (⅓ is BIGGER — dividing into 3 parts gives BIGGER pieces than dividing into 4)

Remember

The SMALLER the bottom number (denominator), the BIGGER each piece is.

• ½ > ¼
• ⅓ > ¼
• ¾ > ½

7. Key Facts

• Half = ½ = one out of TWO equal parts
• Quarter = ¼ = one out of FOUR equal parts
• Three-quarters = ¾ = three out of FOUR equal parts
• Fraction = PART ÷ WHOLE
• To find a fraction of a number: DIVIDE by the bottom number, then MULTIPLY by the top number
• When the WHOLE is the same, a LARGER fraction means a BIGGER piece

8. Common Mistakes

'Do NOT think ¼ is smaller than ⅛. The smaller the denominator, the bigger the piece.' 'Do NOT forget to divide EQUALLY. Unequal parts are NOT fractions.' 'Do NOT confuse 'quarter of' with 'quarter to' — one is division, the other is time.' 'Do NOT write ½ as 2/1. Half is ONE over TWO, not two over one.' 'Do NOT forget the units — ½ of what? Write it clearly.'

9. Fun Activity

Fraction Kitchen Ask your mother for a roti or a piece of bread.

• Fold it in half — you have TWO equal parts
• Fold it in half again — you have FOUR equal parts
• Colour one part — that is ¼
• Colour three parts — that is ¾

Share a Chocolate Take a chocolate bar with 12 pieces. Share it with 3 friends equally. How many pieces does each get? (Answer: 12 ÷ 4 = 3 pieces each = ¼ of the bar)

Fraction Art Draw a rectangle. Divide it into 4 equal parts. Colour ¼ red, ¼ blue, and ½ yellow. What fraction is coloured? (Answer: ALL — ¼ + ¼ + ½ = 1 whole)

10. Self-Test

Q1. What fraction of a pizza do you get if it is divided among 4 people equally? Answer: ¼ (one-quarter)

Q2. Find half of 18. Answer: 18 ÷ 2 = 9

Q3. Find three-quarters of 20. Answer: 20 ÷ 4 = 5, 5 × 3 = 15

Q4. Which is bigger — ½ of a cake or ¼ of the same cake? Answer: ½ is bigger (bigger pieces)

Q5. A ribbon is 12 m long. Neha uses ¼ of it. How much does she use? Answer: 12 ÷ 4 = 3 m

Q6. Share 5 apples equally between 2 children. How much does each get? Answer: Each gets 2½ apples

Q7. Fill in the blanks: ¾ means _____ out of _____ equal parts. Answer: 3 out of 4

11. Key Vocabulary