Chapter 4 of 14
⬅️ Ch 3: How Many Squares? Ch 5: Does it Look the Same? ➡️
NCERT Class 5 Mathematics • Classic CBSE Track

Chapter 4: Parts and Wholes

हिस्से और पूरे (राष्ट्रीय ध्वज, चॉकलेट बंटवारा एवं रामू का खेत) | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts
  • Fractions in everyday life: tricolour flags, chocolate bars, and garden plots.
  • Fraction of a collection: e.g., 1/4 of 16 balls = 4 balls.
  • Equivalent fractions: visual representations using fraction strips and circles.
  • Money fractions: 50 paise = 1/2 rupee, 25 paise = 1/4 rupee, 20 paise = 1/5 rupee, 10 paise = 1/10 rupee.
  • Total equal parts: 9.
  • Total pieces of chocolate: 12.
  • Raji's share: $\frac{1}{4} \times 12 = \mathbf{3\text{ pieces}}$.
  • Sugatha's share: $\frac{1}{3} \times 12 = \mathbf{4\text{ pieces}}$.
  • Sheela's share: $\frac{1}{6} \times 12 = \mathbf{2\text{ pieces}}$.
  • Total pieces given away: $3 + 4 + 2 = 9\text{ pieces}$.
  • Pieces left for Manju: $12 - 9 = \mathbf{3\text{ pieces}}$.
  • Fraction left for Manju: $\frac{3}{12} = \mathbf{\frac{1}{4}}$.
PARTS AND WHOLES: FRACTION STRIP MODEL 1 WHOLE (1) ½ ½ ¼ ¼ ¼ ¼ Equivalent Fractions: 1 = ²⁄₂ = ⁴⁄₄ = ⁸⁄₈

All Textbook Exercises & In-Text Tasks (24 Questions)

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Q1 Textbook Exercise • Indian Flag & Fractions
Our national flag has three horizontal stripes: saffron at the top, white in the middle, and green at the bottom. (a) What fraction of the flag is saffron? (b) Is the white portion more than 1/3 or less than 1/3 of the flag? Explain why. (c) What fraction of the flag is green?
[3 Marks]
✅ Step-by-Step Solution & Working
Flag Fractions:
• (a) Saffron fraction: The flag is divided into 3 equal stripes, so saffron is 1/3.
• (b) White portion: The white stripe contains the navy blue Ashoka Chakra in its center. Because the Chakra takes up space inside the white band, the pure white area is a little less than 1/3 of the flag.
• (c) Green fraction: Green occupies exactly one of the three equal bands, which is 1/3.
CBSE Step-by-Step Marking Scheme
Part (a): 1/3 saffron 1 M
Part (b): Less than 1/3 due to Ashoka Chakra 1 M
Part (c): 1/3 green 1 M
Q2 Textbook Exercise • Chocolate Bar Distribution
Manju had a chocolate bar with 12 equal pieces. She gave: 1/4 of it to Raji; 1/3 of it to Sugatha; 1/6 of it to Sheela. She ate the remaining pieces. (a) How many pieces did Raji get? (b) How many pieces did Sugatha get? (c) How many pieces did Sheela get? (d) How many pieces did Manju eat?
[4 Marks]
✅ Step-by-Step Solution & Working
Piece Distribution (Total = 12 pieces):
• (a) Raji: 1/4 of 12 = 12 ÷ 4 = 3 pieces.
• (b) Sugatha: 1/3 of 12 = 12 ÷ 3 = 4 pieces.
• (c) Sheela: 1/6 of 12 = 12 ÷ 6 = 2 pieces.
• (d) Manju: Total given away = 3 + 4 + 2 = 9 pieces. Manju ate: 12 - 9 = 3 pieces.
CBSE Step-by-Step Marking Scheme
Raji: 3 pieces 1 M
Sugatha: 4 pieces 1 M
Sheela: 2 pieces 1 M
Manju: 3 pieces 1 M
Q3 Textbook Exercise • Ramu's Vegetable Field
Ramu's vegetable field has 9 equal parts. In these parts he grows: chillies in 1 part, potatoes in 2 parts, brinjals in 2 parts, tomatoes in 3 parts, and spinach in 1 part.
(a) Which vegetable grows in the biggest part of his field? What fraction is it?
(b) On what fraction of the field does he grow potatoes?
(c) What fraction is used for growing spinach?
[3 Marks]
✅ Step-by-Step Solution & Working
Field Fractions (Total = 9 equal parts):
• (a) Biggest part: Tomatoes grow in 3 parts. Fraction = 3/9 = 1/3 of the field.
• (b) Potatoes fraction: Potatoes occupy 2 parts out of 9 = 2/9 of the field.
• (c) Spinach fraction: Spinach occupies 1 part out of 9 = 1/9 of the field.
CBSE Step-by-Step Marking Scheme
Part (a): Tomatoes (3/9 or 1/3) 1 M
Part (b): Potatoes (2/9) 1 M
Part (c): Spinach (1/9) 1 M
Q4 Textbook Exercise • Sleeping Time Fractions
A day has 24 hours. (a) A child sleeps for 1/3 of a day. How many hours does the child sleep? (b) A person studies for 1/4 of a day. How many hours does the person study? (c) A cat sleeps for 1/2 of a day. How many hours does the cat sleep?
[3 Marks]
✅ Step-by-Step Solution & Working
Daily Hour Calculations (Total = 24 hours):
• (a) Sleeping time: 1/3 of 24 = 24 ÷ 3 = 8 hours.
• (b) Study time: 1/4 of 24 = 24 ÷ 4 = 6 hours.
• (c) Cat sleeping time: 1/2 of 24 = 24 ÷ 2 = 12 hours.
CBSE Step-by-Step Marking Scheme
Part (a): 8 hours 1 M
Part (b): 6 hours 1 M
Part (c): 12 hours 1 M
Q5 Textbook Exercise • Fractions of a Rupee
Answer the following based on Indian coins:
(a) How many 50-paise coins make one rupee? What fraction of a rupee is 50 paise?
(b) How many 25-paise coins make one rupee? What fraction of a rupee is 25 paise?
(c) What fraction of a rupee is 20 paise?
[3 Marks]
✅ Step-by-Step Solution & Working
Rupee Conversions (1 Rupee = 100 paise):
• (a) 50-paise coins: 100 ÷ 50 = 2 coins. Fraction = 50/100 = 1/2 of a rupee.
• (b) 25-paise coins: 100 ÷ 25 = 4 coins. Fraction = 25/100 = 1/4 of a rupee.
• (c) 20-paise coins: 100 ÷ 20 = 5 coins. Fraction = 20/100 = 1/5 of a rupee.
CBSE Step-by-Step Marking Scheme
Part (a): 2 coins, 1/2 1 M
Part (b): 4 coins, 1/4 1 M
Part (c): 1/5 fraction 1 M
Q6 Textbook Exercise • Equivalent Fractions
Complete the equivalent fraction chains:
(a) 1/2 = 2/4 = ___/6 = 4/___ = ___/10
(b) 3/5 = ___/10 = 9/___ = ___/20
(c) Show why 2/3 is equal to 8/12.
[3 Marks]
✅ Step-by-Step Solution & Working
Equivalent Fractions:
• (a) 1/2 = 2/4 = 3/6 = 4/8 = 5/10.
• (b) 3/5 = 6/10 = 9/15 = 12/20.
• (c) Verification: Multiply numerator and denominator of 2/3 by 4: (2 × 4) / (3 × 4) = 8/12. Hence, they are equal.
CBSE Step-by-Step Marking Scheme
Chain (a) filled correctly 1 M
Chain (b) filled correctly 1 M
Verification in (c) 1 M
Q7 Textbook Exercise • Shopping List & Price Fractions
At a vegetable shop: Tomato costs ₹12/kg, Potato costs ₹10/kg, Onion costs ₹16/kg, Carrot costs ₹18/kg, and Pumpkin costs ₹8/kg. Find the cost of:
(a) 2½ kg of tomatoes
(b) 3¼ kg of potatoes
(c) 1½ kg of pumpkin
[3 Marks]
✅ Step-by-Step Solution & Working
Cost Calculations:
• (a) 2½ kg tomatoes: 2.5 × ₹12 = ₹30 (or 2 × 12 + 1/2 × 12 = 24 + 6 = ₹30).
• (b) 3¼ kg potatoes: 3 × 10 = 30; 1/4 × 10 = 2.50. Total = 30 + 2.50 = ₹32.50.
• (c) 1½ kg pumpkin: 1.5 × ₹8 = ₹12 (or 8 + 4 = ₹12).
CBSE Step-by-Step Marking Scheme
Tomatoes: ₹30 1 M
Potatoes: ₹32.50 1 M
Pumpkin: ₹12 1 M
Q8 Textbook Exercise • Fractions on a Grid (Coloring)
A grid rectangle has 16 small equal squares. (a) How many squares must you color blue to color 1/2 of the grid? (b) How many squares must you color red to color 1/4 of the grid? (c) How many squares remain uncolored?
[3 Marks]
✅ Step-by-Step Solution & Working
Grid Square Calculations (Total = 16 squares):
• (a) Blue squares (1/2): 1/2 of 16 = 16 ÷ 2 = 8 squares.
• (b) Red squares (1/4): 1/4 of 16 = 16 ÷ 4 = 4 squares.
• (c) Uncolored squares: 16 - (8 + 4) = 16 - 12 = 4 squares (which is 4/16 or 1/4 of the grid).
CBSE Step-by-Step Marking Scheme
Blue: 8 squares 1 M
Red: 4 squares 1 M
Uncolored: 4 squares 1 M
Q9 Textbook Exercise • Train Journey Delay
A passenger train is running late by 1/4 of an hour. The scheduled arrival time was 6:45 PM. (a) How many minutes is the train delayed? (b) At what time will the train actually arrive?
[2 Marks]
✅ Step-by-Step Solution & Working
Time Calculations:
• (a) Minutes of delay: 1 hour = 60 minutes. Delay = 1/4 of 60 = 60 ÷ 4 = 15 minutes.
• (b) Actual arrival time: Scheduled time (6:45 PM) + 15 minutes = 7:00 PM.
CBSE Step-by-Step Marking Scheme
Delay: 15 minutes 1 M
Actual arrival: 7:00 PM 1 M
Q10 Textbook Exercise • Comparing Fractions
Insert >, < or = between the pairs of fractions:
(a) 3/7 and 5/7
(b) 2/3 and 2/5
(c) 3/4 and 6/8
[3 Marks]
✅ Step-by-Step Solution & Working
Comparisons:
• (a) 3/7 & 5/7: Same denominator; 3 < 5. Therefore, 3/7 < 5/7.
• (b) 2/3 & 2/5: Same numerator; smaller denominator means larger parts (3 < 5). Therefore, 2/3 > 2/5.
• (c) 3/4 & 6/8: Multiply 3/4 by 2/2 = 6/8. Therefore, 3/4 = 6/8.
CBSE Step-by-Step Marking Scheme
Part (a): < 1 M
Part (b): > 1 M
Part (c): = 1 M
Q11 Textbook Exercise • Cooking Recipe Fractions
To make a cake, a recipe requires: 1/2 kg flour, 1/4 kg sugar, 1/8 kg butter. What is the total weight of these three ingredients in grams?
[3 Marks]
✅ Step-by-Step Solution & Working
Grams Conversion (1 kg = 1,000 g):
• Flour: 1/2 of 1,000 g = 500 g.
• Sugar: 1/4 of 1,000 g = 250 g.
• Butter: 1/8 of 1,000 g = 125 g.
• Total weight: 500 + 250 + 125 = 875 grams.
CBSE Step-by-Step Marking Scheme
Flour: 500 g, Sugar: 250 g, Butter: 125 g 1.5 M
Total: 875 g 1.5 M
Q12 Textbook Exercise • Fractions of a Group
In a class of 40 students: 1/5 like Cricket, 2/5 like Football, and the rest like Badminton. (a) How many students like Cricket? (b) How many students like Football? (c) What fraction of students like Badminton?
[3 Marks]
✅ Step-by-Step Solution & Working
Group Analysis (Total = 40 students):
• (a) Cricket: 1/5 of 40 = 40 ÷ 5 = 8 students.
• (b) Football: 2/5 of 40 = (40 ÷ 5) × 2 = 8 × 2 = 16 students.
• (c) Badminton: Remaining students = 40 - (8 + 16) = 40 - 24 = 16 students. Fraction = 16/40 = 2/5.
CBSE Step-by-Step Marking Scheme
Cricket: 8 students 1 M
Football: 16 students 1 M
Badminton: 16 students (2/5) 1 M
Q13 Textbook Exercise • Milk Bottle Sharing
A 1-litre bottle of milk is shared equally among 4 children. (a) How many millilitres of milk does each child get? (b) What fraction of a litre does each child get?
[2 Marks]
✅ Step-by-Step Solution & Working
Sharing Calculations (1 litre = 1,000 mL):
• (a) Millilitres per child: 1,000 mL ÷ 4 = 250 mL.
• (b) Fraction of a litre: 250/1,000 = 1/4 of a litre.
CBSE Step-by-Step Marking Scheme
250 mL 1 M
1/4 litre 1 M
Q14 Textbook Exercise • Mixed Numbers to Improper Fractions
Convert the following mixed fractions into improper fractions: (a) 2 1/3 (b) 3 3/4 (c) 5 1/2.
[3 Marks]
✅ Step-by-Step Solution & Working
Conversions (Improper Fraction = (Whole × Denominator + Numerator) / Denominator):
• (a) 2 1/3 = (2 × 3 + 1) / 3 = 7/3.
• (b) 3 3/4 = (3 × 4 + 3) / 4 = 15/4.
• (c) 5 1/2 = (5 × 2 + 1) / 2 = 11/2.
CBSE Step-by-Step Marking Scheme
Part (a): 7/3 1 M
Part (b): 15/4 1 M
Part (c): 11/2 1 M
Q15 Textbook Exercise • Fraction Addition
Solve: (a) 2/7 + 3/7 (b) 1/4 + 1/2 (c) 1 - 3/8.
[3 Marks]
✅ Step-by-Step Solution & Working
Fraction Arithmetic:
• (a) 2/7 + 3/7 = (2 + 3) / 7 = 5/7.
• (b) 1/4 + 1/2 = 1/4 + 2/4 = 3/4.
• (c) 1 - 3/8 = 8/8 - 3/8 = 5/8.
CBSE Step-by-Step Marking Scheme
Part (a): 5/7 1 M
Part (b): 3/4 1 M
Part (c): 5/8 1 M
Q16 Textbook Exercise • Ribbon Cutting Problem
A ribbon is 6 metres long. How many pieces of 3/4 metre length can be cut from it?
[2 Marks]
✅ Step-by-Step Solution & Working
Division of Whole Number by Fraction:
• Number of pieces = Total length ÷ Length of one piece.
• 6 ÷ (3/4) = 6 × (4/3) = (6 × 4) ÷ 3 = 24 ÷ 3 = 8 pieces.
CBSE Step-by-Step Marking Scheme
Reciprocal multiplication: 6 × 4/3 1 M
Final answer: 8 pieces 1 M
Q17 Textbook Exercise • Fraction of an Hour
Find how many minutes are there in: (a) 1/2 of an hour (b) 2/3 of an hour (c) 3/4 of an hour.
[3 Marks]
✅ Step-by-Step Solution & Working
Conversions (1 hour = 60 minutes):
• (a) 1/2 × 60 = 30 minutes.
• (b) 2/3 × 60 = 2 × 20 = 40 minutes.
• (c) 3/4 × 60 = 3 × 15 = 45 minutes.
CBSE Step-by-Step Marking Scheme
Part (a): 30 mins 1 M
Part (b): 40 mins 1 M
Part (c): 45 mins 1 M
Q18 Textbook Exercise • Fraction Simplification
Reduce each fraction to its simplest form (lowest terms): (a) 12/16 (b) 15/25 (c) 18/24.
[3 Marks]
✅ Step-by-Step Solution & Working
Simplification by dividing HCF:
• (a) 12/16: Divide numerator and denominator by 4: (12÷4)/(16÷4) = 3/4.
• (b) 15/25: Divide by 5: (15÷5)/(25÷5) = 3/5.
• (c) 18/24: Divide by 6: (18÷6)/(24÷6) = 3/4.
CBSE Step-by-Step Marking Scheme
Part (a): 3/4 1 M
Part (b): 3/5 1 M
Part (c): 3/4 1 M
Q19 Textbook Exercise • Fraction of a Year
(a) What fraction of a year is 3 months? (b) What fraction of a year is 6 months? (c) What fraction of a leap year is 73 days?
[3 Marks]
✅ Step-by-Step Solution & Working
Calculations (1 year = 12 months; normal year = 365 days):
• (a) 3 months: 3/12 = 1/4 of a year.
• (b) 6 months: 6/12 = 1/2 of a year.
• (c) 73 days of 365 days: 73/365 = 1/5 of a year (since 73 × 5 = 365).
CBSE Step-by-Step Marking Scheme
Part (a): 1/4 1 M
Part (b): 1/2 1 M
Part (c): 1/5 1 M
Q20 Textbook Exercise • Finding the Whole from a Part
If 1/3 of a number is 15: (a) What is the whole number? (b) What is 2/5 of that number?
[2 Marks]
✅ Step-by-Step Solution & Working
Calculations:
• (a) Whole number: If 1/3 = 15, then Whole = 15 × 3 = 45.
• (b) 2/5 of the number: 2/5 of 45 = (45 ÷ 5) × 2 = 9 × 2 = 18.
CBSE Step-by-Step Marking Scheme
Whole number: 45 1 M
2/5 calculation: 18 1 M
Q21 Textbook Exercise • Distance Covered as Fraction
A bus has to cover a total journey of 120 km. It covers 3/4 of the distance in the morning. (a) How many kilometres did it cover in the morning? (b) How many kilometres are left to travel?
[2 Marks]
✅ Step-by-Step Solution & Working
Distance Calculations:
• (a) Morning distance: 3/4 of 120 = (120 ÷ 4) × 3 = 30 × 3 = 90 km.
• (b) Distance remaining: 120 - 90 = 30 km (or 1/4 of 120 = 30 km).
CBSE Step-by-Step Marking Scheme
Morning distance: 90 km 1 M
Remaining distance: 30 km 1 M
Q22 Textbook Exercise • Fraction Subtraction Problem
Anita had ₹500. She spent 2/5 of it on books and 1/10 of it on stationery. (a) How much money did she spend in total? (b) How much money does she have left?
[3 Marks]
✅ Step-by-Step Solution & Working
Expense Calculation:
• On books: 2/5 of 500 = (500 ÷ 5) × 2 = ₹200.
• On stationery: 1/10 of 500 = ₹50.
• (a) Total spent: 200 + 50 = ₹250.
• (b) Money left: 500 - 250 = ₹250.
CBSE Step-by-Step Marking Scheme
Books: ₹200, Stationery: ₹50 1 M
Total spent: ₹250 1 M
Money left: ₹250 1 M
Q23 Textbook Exercise • Equal Fraction Division Puzzle
Divide 5 apples equally among 4 children. How much apple will each child get? Express as a mixed number and as an improper fraction.
[2 Marks]
✅ Step-by-Step Solution & Working
Sharing Solution:
• Each child gets 5 ÷ 4 apples.
• Improper fraction: 5/4 apples.
• Mixed number: 5 ÷ 4 = 1 1/4 apples (1 whole apple and 1 quarter of an apple).
CBSE Step-by-Step Marking Scheme
5/4 improper fraction 1 M
1 1/4 mixed fraction 1 M
Q24 Textbook Exercise • Fraction Comparison in Real Life
Sunil studies for 3/4 of an hour, while Rohit studies for 2/3 of an hour. Who studies for a longer time, and by how many minutes?
[2 Marks]
✅ Step-by-Step Solution & Working
Comparison in Minutes:
• Sunil: 3/4 of 60 minutes = 45 minutes.
• Rohit: 2/3 of 60 minutes = 40 minutes.
• Sunil studies longer by 45 - 40 = 5 minutes.
CBSE Step-by-Step Marking Scheme
Calculations of 45 mins and 40 mins 1 M
Conclusion: Sunil by 5 mins 1 M
🌟 NEP 2020 Competency-Based Case Study

NEP 2020 Competency Case: Parts and Wholes

A practical scenario involving Parts and Wholes in everyday life and community contexts.

Analytical Task: Analyze the quantitative relationships and state the conclusion.
Evaluation & Model Answer:
Apply the step-by-step formulas and concepts mastered in this chapter.
Rubric: 1M formula + 1M working + 1M answer
⬅️ Ch 3: How Many Squares? Ch 5: Does it Look the Same? ➡️