Chapter 9 of 14
Chapter 9: Halves and Quarters
Fractions: 1/2, 1/4, 3/4, Fraction Walls, Splitting Objects & Metric Fractions | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Concept of a fraction: equal parts of a whole.
- Half (1/2), One-quarter (1/4), and Three-quarters (3/4).
- Two quarters make one half: 1/4 + 1/4 = 2/4 = 1/2.
- Four quarters make one whole: 4/4 = 1.
- Fractions of collections (e.g., half of 20 apples = 10; quarter of ₹100 = ₹25).
All Textbook Exercises & In-Text Tasks (15 Questions)
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Q1
Fraction of Amounts & Metric Conversions
Calculate: (a) 1/2 of ₹100, (b) 1/4 of a metre (in cm), (c) 3/4 of a kilogram (in grams), (d) 1/2 of a litre (in ml).
[4 Marks]
✅ Step-by-Step Solution & Working
(a) 1/2 of ₹100:
• ₹100 ÷ 2 = ₹50.
(b) 1/4 of a metre:
• 1 m = 100 cm.
• 100 cm ÷ 4 = 25 cm.
(c) 3/4 of a kilogram:
• 1 kg = 1,000 g.
• 1/4 of 1,000 g = 250 g.
• 3/4 = 3 × 250 g = 750 grams.
(d) 1/2 of a litre:
• 1 l = 1,000 ml.
• 1,000 ml ÷ 2 = 500 ml.
• ₹100 ÷ 2 = ₹50.
(b) 1/4 of a metre:
• 1 m = 100 cm.
• 100 cm ÷ 4 = 25 cm.
(c) 3/4 of a kilogram:
• 1 kg = 1,000 g.
• 1/4 of 1,000 g = 250 g.
• 3/4 = 3 × 250 g = 750 grams.
(d) 1/2 of a litre:
• 1 l = 1,000 ml.
• 1,000 ml ÷ 2 = 500 ml.
CBSE Step-by-Step Marking Scheme
Correct values for (a) and (b)
2.0 M
Correct values for (c) and (d)
2.0 M
Q2
Word Problem on Splitting Food
Rani had a chocolate bar with 12 equal pieces. She gave 1/4 of it to Reena, 1/3 of it to Sugatha, and ate the rest herself. How many pieces did each girl get?
[3 Marks]
✅ Step-by-Step Solution & Working
Total pieces in chocolate bar = 12.
• Reena's share: 1/4 of 12 = 12 ÷ 4 = 3 pieces.
• Sugatha's share: 1/3 of 12 = 12 ÷ 3 = 4 pieces.
• Pieces given away: 3 + 4 = 7 pieces.
• Rani's share: 12 - 7 = 5 pieces.
Check: 3 + 4 + 5 = 12 pieces. Correct!
• Reena's share: 1/4 of 12 = 12 ÷ 4 = 3 pieces.
• Sugatha's share: 1/3 of 12 = 12 ÷ 3 = 4 pieces.
• Pieces given away: 3 + 4 = 7 pieces.
• Rani's share: 12 - 7 = 5 pieces.
Check: 3 + 4 + 5 = 12 pieces. Correct!
CBSE Step-by-Step Marking Scheme
Reena = 3 pieces; Sugatha = 4 pieces
2.0 M
Rani = 5 pieces with verification
1.0 M
Q3
Fractional Pricing • Vegetable Market
Look at the vegetable price list:
• Tomato: ₹16 per kg
• Potato: ₹20 per kg
• Carrot: ₹32 per kg
Calculate the total cost of 1/2 kg tomatoes, 3/4 kg potatoes, and 1 1/4 kg carrots.
[3 Marks]
• Tomato: ₹16 per kg
• Potato: ₹20 per kg
• Carrot: ₹32 per kg
Calculate the total cost of 1/2 kg tomatoes, 3/4 kg potatoes, and 1 1/4 kg carrots.
✅ Step-by-Step Solution & Working
Step-by-Step Pricing:
1. Cost of 1/2 kg Tomatoes: 1/2 × ₹16 = ₹8.
2. Cost of 3/4 kg Potatoes: 3/4 × ₹20 = 3 × (20 ÷ 4) = 3 × ₹5 = ₹15.
3. Cost of 1 1/4 kg Carrots:
• 1 kg = ₹32
• 1/4 kg = ₹32 ÷ 4 = ₹8
• Total = ₹32 + ₹8 = ₹40.
Grand Total Bill:
₹8 + ₹15 + ₹40 = ₹63.
1. Cost of 1/2 kg Tomatoes: 1/2 × ₹16 = ₹8.
2. Cost of 3/4 kg Potatoes: 3/4 × ₹20 = 3 × (20 ÷ 4) = 3 × ₹5 = ₹15.
3. Cost of 1 1/4 kg Carrots:
• 1 kg = ₹32
• 1/4 kg = ₹32 ÷ 4 = ₹8
• Total = ₹32 + ₹8 = ₹40.
Grand Total Bill:
₹8 + ₹15 + ₹40 = ₹63.
CBSE Step-by-Step Marking Scheme
Tomatoes (₹8) and Potatoes (₹15)
1.0 M
Carrots (₹40)
1.0 M
Total bill = ₹63
1.0 M
Q4
Fraction Arithmetic • Cutting Shapes
A square sheet of paper is folded in half diagonally, and then folded in half again. (a) What fraction of the original sheet is each small triangle? (b) How many such small triangles make three-quarters (3/4) of the sheet?
[2 Marks]
✅ Step-by-Step Solution & Working
Fractional Folding:
1. First diagonal fold divides the square into 2 equal halves (1/2 each).
2. Second fold divides the halves into 4 equal triangles (1/4 each).
• (a) Fraction of each small triangle: 1/4 of the original square sheet.
• (b) To make 3/4: Exactly 3 small triangles make 3/4 of the sheet (3 × 1/4 = 3/4).
1. First diagonal fold divides the square into 2 equal halves (1/2 each).
2. Second fold divides the halves into 4 equal triangles (1/4 each).
• (a) Fraction of each small triangle: 1/4 of the original square sheet.
• (b) To make 3/4: Exactly 3 small triangles make 3/4 of the sheet (3 × 1/4 = 3/4).
CBSE Step-by-Step Marking Scheme
Part (a): 1/4 fraction
1.0 M
Part (b): 3 small triangles
1.0 M
Q5
Building with Bricks • Brick Geometry & Measurement
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long?
[3 Marks]
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long?
✅ Step-by-Step Solution & Working
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
A Trip to Bhopal • Diesel Fuel Budget
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay?
[3 Marks]
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay?
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
Long and Short • Height Comparisons
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)?
[2 Marks]
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)?
✅ Step-by-Step Solution & Working
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
Tick-Tick-Tick • Expiry Dates on Food
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
[2 Marks]
✅ Step-by-Step Solution & Working
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
The Junk Seller • Loan and Interest
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank?
[3 Marks]
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank?
✅ Step-by-Step Solution & Working
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
Jugs and Mugs • Measuring Medicine Dose
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last?
[3 Marks]
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last?
✅ Step-by-Step Solution & Working
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
Carts and Wheels • Circle Geometry
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle?
[2 Marks]
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle?
✅ Step-by-Step Solution & Working
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Halves and Quarters • Fraction Sharing
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left?
[3 Marks]
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left?
✅ Step-by-Step Solution & Working
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
Play with Patterns • Secret Message Cipher
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell?
[2 Marks]
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell?
✅ Step-by-Step Solution & Working
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
Tables and Shares • Division with Remainder
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over?
[2 Marks]
(a) How many complete bouquets can she make?
(b) How many roses will be left over?
✅ Step-by-Step Solution & Working
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
Review Questions • True or False
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time.
[3 Marks]
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time.
✅ Step-by-Step Solution & Working
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study
Vegetable Price List Fraction Math
At the sabzi mandi: Tomato costs ₹16 per kg, Potato costs ₹20 per kg, and Onion costs ₹24 per kg. Mrs. Sharma buys 1/2 kg tomatoes, 3/4 kg potatoes, and 1/4 kg onions.
Analytical Task: How much total money does Mrs. Sharma spend?
Evaluation & Model Answer:
Cost breakdown:
• Tomatoes: 1/2 × ₹16 = ₹8.
• Potatoes: 3/4 × ₹20 = 3 × ₹5 = ₹15.
• Onions: 1/4 × ₹24 = ₹6.
• Total spent = ₹8 + ₹15 + ₹6 = ₹29.
• Tomatoes: 1/2 × ₹16 = ₹8.
• Potatoes: 3/4 × ₹20 = 3 × ₹5 = ₹15.
• Onions: 1/4 × ₹24 = ₹6.
• Total spent = ₹8 + ₹15 + ₹6 = ₹29.
Rubric: 1.5 Marks for itemized fractions; 1.5 Marks for total ₹29.