Lets now have a look at the last chapter of Ganita Prakash, Part – I. Here we are presenting the worksheet for Class 7 Mathematics Chapter 8 Worksheet, Working with Fractions. Let’s practise multiplication, division, reciprocals, and some real-life fraction situations.
Class 7 Mathematics – Working with Fractions | Practice Set: Challenging
A. Quick Concept Check (1 mark each)
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MCQ: The reciprocal of 3/7 is:
(a) 7/3 (b) 3/7 (c) 7/10 (d) 10/7 - Find: 3/5 × 10/9. Write your answer in the simplest form.
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MCQ: Without calculating fully, choose the correct statement:
7/9 × 5/6 is
(a) greater than 7/9 (b) less than 7/9 (c) equal to 7/9 (d) cannot be decided - True/False: If you multiply a positive number by a fraction between 0 and 1, the product becomes smaller than the original number.
- Simplify using cancellation first (if possible): 18/35 × 7/12
- Compute: 2 1/3 ÷ 7/9
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MCQ: For which divisor will the quotient be greater than the dividend?
6 ÷ (choose one)
(a) 3/2 (b) 5 (c) 1/4 (d) 2 -
Fill in the blank:
a/b ÷ c/d = a/b × ______ - Evaluate: 1 ÷ 2/3
- Convert to a mixed fraction: 35/12
B. Skill Builder (2 marks each)
- Find: 5/6 of 3/4 litre (Write the answer in simplest form.)
- Compute: 2/5 ÷ 3/10
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Without multiplying completely, decide and write one line reason:
11/12 × 5/6 is less than or greater than 11/12. - Solve: (3/7 × 14/15) ÷ (2/5)
- Find x such that: x ÷ 3/4 = 2/3
C. Word Problems (3 marks each)
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A cook uses 1/4 kg of flour to make 12 rotis.
How much flour is needed to make 18 rotis? -
A train takes 5 1/6 hours for a trip. A plane takes 1/2 hour.
How many hours does the plane save? -
A novel has 400 pages. Mira read 1/5 of the pages yesterday and 3/10 of the pages today.
How many pages are still left to finish the novel?
D. Higher Order Thinking (5 marks)
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Evaluate and spot the pattern:
(1 − 1/2)
(1 − 1/2) × (1 − 1/3)
(1 − 1/2) × (1 − 1/3) × (1 − 1/4)
(1 − 1/2) × (1 − 1/3) × (1 − 1/4) × … × (1 − 1/10)Make a general statement for:
(1 − 1/2)(1 − 1/3)…(1 − 1/n), and explain in 2–3 lines.
(Hint: This is a “domino-cancellation” type product—like cancelling your homework excuses one by one.)
E. Case Study Based (4 marks)
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Case Study 1: Ants and Equal Splits
A group of ants starts together and keeps splitting into two equal groups at each junction.Split Map:
Start → splits into Left and Right
Left → splits into L1 and L2
Right → splits into R1 and R2
R1 → splits into Mango Tree and Sugarcane FieldAnswer:
(a) What fraction of the original group reached the Mango Tree?
(b) What fraction reached the Sugarcane Field?
(c) What fraction reached neither of these two food sources (i.e., ended up at L1, L2, or R2)?
(d) If the original group had 480 ants, how many reached the Mango Tree? -
Case Study 2: Petrol and Distance
A car runs 16 km using 1 litre of petrol.Answer:
(a) How far will it go using 2 3/4 litres of petrol?
(b) If it has 11 1/2 litres in the tank, what is the maximum distance it can travel?
(c) How many litres are needed to travel 88 km?
(d) True/False (with one line reason): If petrol is less than 1 litre, the distance covered is less than 16 km.
Answer Key with Hints (Do not peek too early—your future self will judge you)
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Answer: (a) 7/3
Hint: Reciprocal means swap numerator and denominator. -
Answer: 2/3
Hint: Multiply and simplify: (3×10)/(5×9) = 30/45 = 2/3. -
Answer: (b) less than 7/9
Hint: 5/6 is between 0 and 1, so multiplying makes it smaller. -
Answer: True
Hint: Multiplying by a fraction less than 1 “shrinks” the number. -
Answer: 3/10
Hint: Cancel first: 18/35 × 7/12 → (18÷6)/(35) × (7)/(12÷6) = 3/35 × 7/2 = 21/70 = 3/10. -
Answer: 3
Hint: 2 1/3 = 7/3. Then 7/3 ÷ 7/9 = 7/3 × 9/7 = 9/3 = 3. -
Answer: (c) 1/4
Hint: Dividing by a number between 0 and 1 increases the result. -
Answer: d/c
Hint: Division by a fraction = multiply by its reciprocal. -
Answer: 3/2
Hint: 1 ÷ (2/3) = 1 × (3/2) = 3/2. -
Answer: 2 11/12
Hint: 35/12 = 24/12 + 11/12 = 2 11/12. -
Answer: 5/8 litre
Hint: “of” means multiply: (5/6)×(3/4) = 15/24 = 5/8. -
Answer: 4/3
Hint: 2/5 ÷ 3/10 = 2/5 × 10/3 = 20/15 = 4/3. -
Answer: Less than 11/12
Hint: 5/6 is less than 1, so multiplying reduces the number. -
Answer: 5/2
Hint: 3/7 × 14/15 = (3×14)/(7×15) = 6/15 = 2/5. Then (2/5) ÷ (2/5) = 1.
Teacher note: If you got 1, you’re correct—this one is a “trap” only for overconfidence. -
Answer: 1/2
Hint: x ÷ 3/4 = 2/3 ⇒ x = 2/3 × 3/4 = 6/12 = 1/2. -
Answer: 3/8 kg
Hint: Flour per roti = (1/4)/12 = 1/48 kg. For 18 rotis: 18×(1/48) = 18/48 = 3/8. -
Answer: 4 2/3 hours
Hint: 5 1/6 − 1/2 = 31/6 − 3/6 = 28/6 = 14/3 = 4 2/3. -
Answer: 200 pages
Hint: Read fraction = 1/5 + 3/10 = 2/10 + 3/10 = 5/10 = 1/2. Half of 400 = 200 read, so 200 left. -
Answer:
1 − 1/2 = 1/2
(1 − 1/2)(1 − 1/3) = (1/2)(2/3) = 1/3
(1 − 1/2)(1 − 1/3)(1 − 1/4) = (1/3)(3/4) = 1/4
Up to (1 − 1/10) gives = 1/10General statement: (1 − 1/2)(1 − 1/3)…(1 − 1/n) = 1/n
Hint: Write (1 − 1/k) as (k−1)/k. Everything cancels like magic: (1/2)(2/3)(3/4)…((n−1)/n) = 1/n. -
Answer:
(a) Mango Tree = 1/8
(b) Sugarcane Field = 1/8
(c) Neither = 1 − (1/8 + 1/8) = 3/4
(d) 480 × 1/8 = 60 ants
Hint: Each split halves the group. Count how many splits happen before reaching the food source. -
Answer:
(a) 16 × 2 3/4 = 16 × 11/4 = 44 km
(b) 16 × 11 1/2 = 16 × 23/2 = 184 km
(c) Litres = 88 ÷ 16 = 11/2 = 5 1/2 litres
(d) True
Hint: Distance = 16 × litres. If litres < 1, distance must be < 16.
Other Class 7 Maths worksheet
- Class 7 Maths Chapter 1 Worksheet: Large Numbers Around Us
- Class 7 Maths Chapter 2 Worksheet: Arithmetic Expressions
- Class 7 Maths Chapter 3 Worksheet: A Peek Beyond the Point
- Class 7 Maths Chapter 4 Worksheet: Another Peek Beyond the Point
- Class 7 Maths Chapter 6 Worksheet: Number Play
- Class 7 Chapter 7 Maths Worksheet: Finding the Unknown
