What is the main objective of NCERT Class 7 Maths Chapter 6: Number Play?

The main objective of this chapter is to develop students' logical reasoning, analytical skills, and understanding of number properties through engaging activities, puzzles, and divisibility rules, rather than just rote memorization of arithmetic.

How are two-digit and three-digit numbers represented in general form in this chapter?

A two-digit number with tens digit 'a' and units digit 'b' is represented as 10a+b. A three-digit number with hundreds digit 'a', tens digit 'b', and units digit 'c' is represented as 100a+10b+c. These general forms are used to prove various number properties.

What are "letter puzzles" in this chapter?

"Letter puzzles" (also known as cryptarithms) are arithmetic problems where letters are used in place of digits. The goal is to figure out which digit each letter represents, with the rule that each letter stands for a unique digit from 0 to 9, and no leading digit can be 0. They require logical deduction and trial-and-error.

Can you give an example of a divisibility rule explained in this chapter?

One key rule is divisibility by 3 and 9. A number is divisible by 3 if the sum of its digits is divisible by 3. Similarly, a number is divisible by 9 if the sum of its digits is divisible by 9. For example, 342 is divisible by 3 (since 3+4+2=9, which is divisible by 3) and also by 9 (since 9 is divisible by 9).

How does this chapter help in building a foundation for higher mathematics?

By exploring numbers in a generalized way (e.g., general forms, properties based on sum/difference of digits), the chapter subtly introduces algebraic thinking. The logical deduction required for puzzles and the systematic application of divisibility rules enhance problem-solving skills that are fundamental to more advanced mathematical concepts.

NCERT Solutions

Class 7

Maths

Chapter 6 Number Play

NCERT Solutions Class 7 Maths Chapter 6 Number Play

NCERT Solutions Class 7 Maths Chapter 6 Number Play introduces students to interesting patterns and tricks with numbers. In this chapter, students explore concepts like divisibility rules, prime and composite numbers, and various number puzzles that make learning maths enjoyable.

These NCERT Solutions follow the official NCERT guidelines and provide clear, step-by-step answers for each question. The solutions are explained in a way that is easy to understand and helps students solve the problems without confusion. Practicing from NCERT Solutions for this chapter builds strong number sense and improves a student’s ability to work with different types of numbers confidently.

1.0NCERT Solutions Class 7 Maths Chapter 6 Number Play – Download PDF

This ALLEN‑prepared PDF features easy-to-follow answers to every question of NCERT Solutions Class 7 Maths Chapter 6 , aligned with the updated syllabus and optimized for clarity, exam readiness, and revision.

NCERT Solutions for Class 7 Maths Chapter 6: Number Play

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2.0Key Concepts in Chapter 6: Number Play

1. Factors and Multiples

A factor divides a number evenly; e.g., 6 is a factor of 18.
A multiple of a number is obtained by multiplying it by an integer; e.g., 18 is a multiple of 6.
Students learn to list factors, multiples, and understand their significance in solving problems.

2. Common Factors and Common Multiples

Common factors are numbers dividing two or more numbers without a remainder.
Common multiples are numbers divisible by each of a set.
Learning about common factors/multiples prepares students for GCD and LCM concepts and their applications.

3. Highest Common Factor (HCF) & Lowest Common Multiple (LCM)

HCF (or GCD) is the greatest number that divides two given numbers.
LCM is the smallest number that is a multiple of both.
NCERT introduces prime factorization, a fundamental method to compute HCF and LCM.
Practical examples: synchronizing schedules or comparing fractions with different denominators.

4. Prime and Composite Numbers

A prime number has exactly two factors: 1 and itself.
A composite number has more than two factors.
Recognizing primes helps in factorization and understanding number structure.

5. Tests of Divisibility

Divisibility rules (for 2, 3, 4, 5, 6, 9, 10) allow quick mental testing of numbers.
These rules are explained with logic to help in fast problem solving and number pattern detection.

6. Relationships between HCF and LCM

NCERT emphasizes the product rule: HCF × LCM = product of two numbers, given they share only those factors.
This powerful property simplifies many computational tasks.

7. Playing with Numbers – Magic Squares & Patterns

The chapter includes puzzles like magic squares, where rows, columns, and diagonals sum to the same value.
Such exercises develop logical reasoning, pattern recognition, and creativity.

8. Word Problems Involving Numbers

Real-life scenarios are framed as word problems that require HCF/LCM, divisibility, or arranging numbers in patterns.
Through guided practice, students learn to model such problems mathematically.

3.0Key Features of NCERT Solutions Class 7 Maths Chapter 6 : Number Play

Clear Explanation of General Forms: The solutions provide thorough explanations of how to represent two-digit and three-digit numbers in their general forms (10a+b, 100a+10b+c), which is crucial for proving divisibility rules and solving advanced number problems.
Comprehensive Divisibility Rule Coverage: All divisibility rules (for 2, 3, 4, 5, 6, 8, 9, 10) are explained with illustrative examples, helping students master these essential shortcuts.
Logical Reasoning Development: Solutions to letter puzzles emphasize the logical deduction process, guiding students through the thought process required to solve such problems, thereby enhancing their critical thinking skills.
Adherence to NCERT Syllabus: The content strictly follows the updated NCERT Ganita Prakash curriculum for Class 7, ensuring that students are well-prepared for their examinations and aligned with academic standards.
Downloadable PDF Format: Conveniently available as a PDF, these NCERT Solutions allow for easy access and offline study, enabling flexible and effective learning for all students.