NCERT Class 4 Maths · Chapter 5

Sharing and Measuring

Halves, quarters, and other fractions: equal parts, sharing food, fractions of a group, and equal fractions made by folding paper.

📌 What you’ll learn in this chapter
  • What equal parts are
  • Half (½), quarter (¼), one-third (⅓), and other fractions
  • Why sharing among more people gives each person a smaller piece
  • Fractions like ⅖ or ¾ (more than one part)
  • Fractions of a group: ¼ of 12 cookies
  • Equal fractions: ½ = 2/4 = 4/8

🍕 Let’s Begin: The Paratha Problem

Mummy made one big paratha for Rohit and Neha. Rohit tore it quickly, and one piece was big and one was small! “Not fair!” shouted Neha.

Mummy folded the next paratha exactly in the middle and cut along the fold. Now both pieces were the same size. Each child got one half (½).

✂️ Part 1: Equal Parts

A fraction only makes sense when the parts are equal.

  • 2 equal parts → each part is one half, written ½
  • 4 equal parts → each part is one quarter (one-fourth), written ¼
  • 3 equal parts → each part is one-third, written ⅓
  • 5 equal parts → each part is one-fifth, written ⅕

In a fraction, the bottom number tells how many equal parts the whole is cut into, and the top number tells how many parts we are talking about.

⚠️ Common mistake Calling any piece of 2 pieces “a half”, even if one is bigger. ❌
✅ It’s only a half if both parts are exactly the same size.

Many ways to halve: A rectangular paper can be folded in half along its length, across its width, or corner to corner (diagonally). All give 2 equal halves!

🎂 Part 2: More People, Smaller Pieces

A cake shared by 2 friends → each gets ½. When a 3rd friend comes, each gets ⅓. With 4 friends, each gets ¼. With 8 friends, each gets ⅛.

The more people share, the smaller each piece. So ½ > ⅓ > ¼ > ⅛.

⚠️ Common mistake “⅛ is bigger than ¼ because 8 is bigger than 4.” ❌
✅ The cake is cut into more pieces, so each piece is smaller. ¼ > ⅛.

🌸 Part 3: More Than One Part

If a garden is divided into 5 equal beds and roses grow in 3 of them, roses cover ⅗ (three-fifths) of the garden.

⅕ + ⅕ + ⅕ = ⅗  ·  All 5 parts = 5/5 = the whole garden!

🍪 Part 4: Fraction of a Group

To find a fraction of a group, share the group into equal parts.

¼ of 20 marbles: Make 4 equal groups → 5 in each. So ¼ of 20 = 5.

⅓ of 15 bangles: Make 3 equal groups → 5 in each.

¾ of 8 diyas: ¼ of 8 = 2, so ¾ = 3 × 2 = 6 diyas.

📄 Part 5: Equal Fractions (Folding Fun)

Fold a paper in half and colour one part: ½. Fold it again: now the coloured part covers 2 of 4 parts, so 2/4. Fold again: 4 of 8, so 4/8.

½ = 2/4 = 4/8  ·  ⅓ = 2/6 = 4/12

These show the same amount with different names.

✏️ Practice Time

Try these on your own first, then check your answer below each question.

Q1. A roti is cut into 6 equal pieces. What fraction is one piece?
✅ Answer⅙
Q2. Which is bigger, ⅓ or ⅕ of the same pizza?
✅ Answer⅓ (fewer pieces, so bigger pieces)
Q3. What is ½ of 18 pencils?
✅ Answer9 pencils
Q4. What is ¼ of 24 laddoos?
✅ Answer6 laddoos
Q5. A ribbon is cut into 4 equal parts, and 3 parts are used. What fraction is used?
✅ Answer¾

📘 NCERT Textbook Activity Help

Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!

Pages 62–65 · Parts and wholes

Half or two quarters?

✅ AnswerOne half and two quarters are the same amount (½ = 2/4), so it doesn’t matter which you choose. Ikra shared equally. You can check by folding: the parts match exactly. Samina chose two quarters because “two” sounded like more, but it isn’t!
Colour only the shapes whose two parts are exactly the same size and shape. If a whole is cut into 5 equal parts, each is ⅕. A rectangle can be halved in at least 3 ways, and quartered in many ways (4 strips, a 2 × 2 grid, 2 diagonals, and more).
Pages 66–69 · Ding Dong Bell!

Sharing dhokla

✅ Answer 1. Her share keeps getting smaller as more people come (½ → ⅓ → ¼ → ⅕).
When Idha gives her share, Sumedha gets ⅕ + ⅕ = ⅖.
2. She gets more when it’s shared among 9 people (1/9 > 1/11).
3. 6 pieces of ⅙ make a whole.
4. ⅕ + ⅕ + ⅕ = ⅗
Let Us Do: 6 people → ⅙ each, and 8 people → ⅛ each. The 6 people get bigger pieces. Shares: 4 people = ¼ · 5 people = ⅕ · 8 people = ⅛ · 9 people = 1/9. The fraction gets smaller because the same dhokla is cut into more pieces.
Page 70 · Compare fractions

Fill in the blanks

✅ Answer1. ¼ is greater than ⅕ 2. ⅙ > 1/9 3. ⅙ > ⅛ 4. Your own example, like ⅛ is smaller than ⅓.
Pages 70–72 · My Flower Garden

Fifths and sevenths

✅ AnswerFirst plan: Marigold ⅕, Jasmine ⅕. Next: Mogra ⅕, Marigold ⅕ (Rose ⅗). Next: Marigold ⅕ (Rose ⅘).
Seven-part garden: (a) colour 1 box for marigold, 3 for rose, and 3 for hibiscus (1 + 3 + 3 = 7) (b) 3 lily + 2 marigold + 2 periwinkle = 7 (c) 5 mogra + 2 hibiscus = 7
Pages 72–73 · Dream Dosa Designer

Fractions of toppings

✅ AnswerCount the numbered slices of each topping:
Dosa 1 (6 slices): Chilli paneer = 4/6 (= ⅔), Classic potato = 2/6 (= ⅓)
Dosa 2 (6 slices): Tangy tomato = 2/6, Classic potato = 2/6, Spicy onion = 2/6 (⅓ each)
Dosa 3 (8 slices): Spicy onion = 4/8, Tangy tomato = 4/8 (½ each)
Dosa 4 (6 slices): Tangy tomato = ⅙, Classic potato = 2/6, Spicy onion = 3/6
To make the ⅔ + ⅓ dosa, cut it into 3 equal parts: 2 for onion and 1 for potato. For ⅜ + ⅛ + 4/8, cut it into 8 slices: 3 potato, 1 paneer, and 4 tomato.
Diyas: ¼ of 8 = 2 diyas
Pages 74–75 · Fractions of a group

Cookies, hairbands, and barfis

✅ Answer12 cookies: (a) 3 children → ⅓ each = 4 cookies (b) 6 → ⅙ = 2 (c) 2 → ½ = 6 (d) 4 → ¼ = 3
Hairbands: split the friends into 3 equal groups and give hairbands to one group. Flowers: split the pots into 5 equal groups and fill one group.
¼ of 16 barfis = 4 barfis. Rohan’s ribbon is 4 times as long as Mohan’s, so draw 4 copies of Mohan’s ribbon joined end to end.
Pages 76–77 · Folding and fraction chart

Equal fractions

✅ Answer⅓ = 2/6 = 4/12 = 8/24 · ½ = 2/4 = 4/8 = 8/16 = 16/32
1. 2 quarters make ½ 2. ⅔ is greater than ½ 3. True 4. Not true: 3/6 = ½, but 2/8 = ¼ 5. 2 pieces of ⅛ make ¼ 6. For example, two ¼ pieces make ½, three ⅓ pieces make 1, and two ⅙ pieces make ⅓.
Pages 78–79 · Let Us Do

Equal parts and shading

✅ AnswerCircle only the squares whose parts are all the same size. Then count: shaded parts over total parts. For the children’s claims, draw extra lines to make equal parts, then count again. The claim is correct only if the shaded part matches that many equal parts. To shade ⅔, divide into 3 equal parts and shade 2. For 4/6: 6 parts, shade 4. For ¼: 4 parts, shade 1. For ¾: 4 parts, shade 3. For ⅛: 8 parts, shade 1.

👨‍👩‍👧 Tips for Parents

  • Cut fruits and rotis into halves and quarters, and name the fractions.
  • Share 12 grapes among family members and talk about ½, ⅓, and ¼ of 12.
  • Fold paper strips together to discover ½ = 2/4.
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