NCERT solutions for Class 8 Mathematics Chapter Algebra Play – complete answers & explanations

Algebra Play in Class 8 Mathematics introduces students to fun and engaging ways of understanding algebraic concepts through puzzles, tricks, grids, and number patterns. This chapter focuses on developing logical thinking and problem-solving skills using creative mathematical approaches. It helps students explore how numbers behave in patterns, pyramids, and algebraic expressions, making learning more interactive and enjoyable. With clear and reliable NCERT solutions, students can confidently practice and understand each concept step by step. These solutions help in building a strong foundation in algebra and improve accuracy in solving problems. Download the worksheet and practice alongside solutions for better clarity. Book a free trial now to get expert guidance.

What this NCERT chapter covers?

1. Understanding number tricks and how algebra works behind them.
2. Learning to apply logical reasoning in “think of a number” problems.
3. Exploring number pyramids and identifying patterns in them.
4. Understanding relationships between numbers in pyramid structures.
5. Working with algebraic grids and solving for unknown values.
6. Learning about Fibonacci patterns in number arrangements.
7. Applying algebra in fun and interactive activities.
8. Understanding divisibility tricks and number properties.
9. Solving real-life problems using algebraic thinking.
10. Developing analytical and reasoning skills through puzzles.

How to use these NCERT solutions?

1. Begin by reading each question carefully before solving.
2. Try solving all problems independently to test your understanding.
3. Use the solutions to verify your answers after attempting them.
4. Compare your steps with the given answers for better clarity.
5. Focus on understanding patterns and logic used in solutions.
6. Follow the exact order of questions as given in the worksheet.
7. Parents and teachers can guide students through discussions.
8. Revisit tricky questions and practice them again.
9. Pay special attention to explanation-based answers.
10. Practice regularly to strengthen algebraic concepts.

Important tips & tricks for students

1. Always look for patterns when solving algebra-based puzzles.
2. Break down complex problems into smaller steps.
3. Carefully follow instructions in number tricks.
4. Double-check calculations in pyramids and grids.
5. Practice recognizing relationships between numbers.
6. Avoid guessing answers without proper reasoning.
7. For activity-based questions, focus on understanding the process.
8. Keep practicing different types of algebra problems.
9. Revise key concepts like patterns and divisibility rules.
10. Stay consistent and patient while solving challenging questions.

NCERT solutions – complete answer key

6.2 Think of a Number Tricks

1 Modify the trick to get final answer 3 / 5
To get 3: Add 6 instead of 4
To get 5: Add 10 instead of 4

2 Date Trick
Final answers:
(i) 1269 → 12 September (12/09)
(ii) 394 → 2 February (02/02)
(iii) 296 → 1 January (01/01)

6.3 Number Pyramids

Basic pyramid filling

Pyramid 2: Top = 14
Middle = 7, 7
Bottom = 3, 4, 3

Pyramid 1: Top = 8
Bottom = 6, 2

Pyramid 3: Top = 32,
Bottom = 5, 4, 5, 0
Second = 9, 9, 5,
Third = 18, 14,

Solved Pyramid (Algebra)

Final values:
c = 20, a = 32, b = 28

Fill the following pyramids:

Pyramid 1: Bottom = 4, 9, 6, 1
Second = 13, 15, 7
Third = 28, 22
Top = 50

Pyramid 2: Bottom = 5, 14, 7, 2
Second = 19, 21, 9
Third = 40, 30
Top = 70

Figure it Out (6.3 Number Pyramids)

Pyramid 3: Bottom = 3, 5, 5, 2
Second = 8, 10, 7
Third = 18, 17
Top = 35

Key Relationship
→ Top = a + 2b + c
Top number = sum of bottom row with Pascal-type coefficients
For 3 rows:

Answers

1 38, 32, 63

2 a + 3b + 3c + d

3 141, 124, 56

4 Grid numbers: 1, 2, 3, 5, 8, 13
Top number: 8
Yes, all are Fibonacci numbers

5
(i) All numbers are Fibonacci numbers; top is also Fibonacci
(ii) Same observation holds

6 In an n-row pyramid with Fibonacci base:
All numbers in pyramid are Fibonacci numbers
Top is Fibonacci number

6.4 Fun with Grids

Answers

Calendar Magic = 5, 6, 12, 13

Algebra Grids:
First Grid = Blue square = 9,
Red circle = 5

Other Grids = All values correctly filled to satisfy row sums

6.5 The Largest Product

Answer: Largest product using 2, 3, 5:
→ 32 × 5

Figure it Out (6.5)

Answers

1 Using 1, 3, 7 → 31 × 7

2 Using 3, 5, 9 → 53 × 9

6.6 Decoding Divisibility Tricks

Answers

If digits reversed and subtracted:
Result = 9(a − b) or 9(b − a
Always divisible by 9

Figure it Out (6.6)

Answers

1 Quotient = difference of digits

2 Yes, always divisible by 11

3 Sum is divisible by 37 and also divisible by 3

4 Result after division by 7, 11, 13 →
→ Original number

5 Let initial flowers = x, Correct solution:
Initial flowers = 7, Flowers in each shrine = 8

6 Heads = 55, Legs = 150, Solution: Hens = 35, Horses = 20

7 Daughter’s age = 3 years

8 Gauri = 9 cows, Naina = 18 cows

9
(i) Selling price = ₹70
(ii) Required sales = 150 dosas

10 All values = 1

11
(i) 7 coins
(ii) Cost per round should be less than 8 coins
(iii) Cost = 8 coins (to take all money)

Why NCERT solutions help students?

NCERT solutions support students in building a strong understanding of algebraic concepts and improve their ability to solve problems accurately. They help in exam preparation, provide clarity in concepts, and guide students toward the correct approach to answering questions, boosting confidence and performance.

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