Maths Class 6 Chapter 3 Questions and Answers - Free PDF Download
Class 6 Maths Chapter 3 students explore exciting patterns and sequences through different exercises, it focuses on enhancing logical thinking by identifying and creating patterns. The chapter 3 helps students understand how patterns can be formed, recognized, and continued based on specific rules. These exercises are vital in laying the foundation for mathematical reasoning, developing a sense of logic, and preparing students for advanced mathematical concepts. Exercise 3.7 explains Clock and Calendar Numbers, which is useful in recognising time formats.
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Our Class 6 Maths NCERT Solutions PDF breaks the lesson into easy-to-understand explanations, making learning fun and interactive. Students will develop essential language skills with engaging activities and exercises. Check out the revised CBSE Class 6 Maths Syllabus and start practising the Maths Class 6 Chapter 3.
Glance on Class 6 Maths Chapter 3 Number Play Exercise 3.7
Numbers on a clock follow a cyclic pattern, where after 12 (or 24 for a 24-hour clock), the next number resets back to 1.
Understanding how to add, subtract, and perform other operations with numbers in a cyclic manner.
Days, months, and years also follow a cyclic pattern.
Calculating the number of days between two dates or determining the day of the week based on a specific date.
FAQs on NCERT Solutions For Class 6 Maths Chapter 3 Number Play Exercise 3.7 - 2025-26
1. Where can I find the correct and step-by-step NCERT Solutions for Class 6 Maths Chapter 3 for the 2025-26 session?
You can find reliable and detailed NCERT Solutions for Class 6 Maths Chapter 3, Number Play, on Vedantu. These solutions are prepared by subject experts as per the latest CBSE guidelines for the 2025-26 academic year, providing clear, step-by-step explanations for every question in the textbook exercises.
2. What are the main concepts covered in the NCERT Solutions for Class 6 Maths Chapter 3, 'Number Play'?
The solutions for Chapter 3, 'Number Play,' focus on fundamental number theory concepts. Key topics include:
- Factors and Multiples: Understanding the relationship between them.
- Prime and Composite Numbers: Identifying numbers based on their factors.
- Tests for Divisibility: Learning rules to check if a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10, and 11.
- Prime Factorisation: Breaking down numbers into their prime factors.
- HCF (Highest Common Factor) and LCM (Lowest Common Multiple): Methods to find them and their application in problems.
3. What is the basic difference between a factor and a multiple as explained in Chapter 3?
A factor of a number is an exact divisor of that number, meaning it divides the number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. A multiple is the result of multiplying a number by an integer. For example, multiples of 12 are 12, 24, 36, and so on. In short, factors are finite, while multiples are infinite.
4. How do you find the HCF of two numbers using the prime factorisation method in the NCERT solutions?
To find the Highest Common Factor (HCF) using prime factorisation, follow these steps:
- Step 1: Find the prime factors of each number. For example, for 18 and 24, the prime factorisations are 18 = 2 × 3 × 3 and 24 = 2 × 2 × 2 × 3.
- Step 2: Identify the common prime factors. In this case, the common factors are one '2' and one '3'.
- Step 3: Multiply these common prime factors together. The HCF is 2 × 3 = 6.
5. What is the correct method to find the LCM of numbers like 12, 16, and 24 as per NCERT Class 6 Maths?
The correct method to find the Lowest Common Multiple (LCM) is through the common division method, which is highly efficient. Here's how:
- Step 1: Arrange the numbers (12, 16, 24) in a row.
- Step 2: Divide them by the smallest prime number that can divide at least one of them. Write the quotients below. If a number isn't divisible, bring it down as is.
- Step 3: Repeat the process until all the quotients become 1.
- Step 4: The LCM is the product of all the prime divisors used. For 12, 16, and 24, the LCM would be 2 × 2 × 2 × 2 × 3 = 48.
6. How do the NCERT solutions explain the test for divisibility by 9?
The NCERT solutions for Chapter 3 explain that a number is divisible by 9 if the sum of its digits is divisible by 9. For example, to check if the number 729 is divisible by 9, you add its digits: 7 + 2 + 9 = 18. Since 18 is divisible by 9 (18 ÷ 9 = 2), the number 729 is also divisible by 9. This simple rule is a key part of the divisibility tests in Exercise 3.3.
7. In Chapter 3, we learn about prime and composite numbers. Why is the number 1 considered neither prime nor composite?
This is a crucial concept. A prime number must have exactly two distinct factors: 1 and itself. For example, 7 has factors 1 and 7. A composite number must have more than two factors. For example, 6 has factors 1, 2, 3, and 6. The number 1 has only one factor, which is 1 itself. Since it does not meet the criteria for either prime (needs two factors) or composite (needs more than two factors), it is classified uniquely.
8. When solving word problems in 'Number Play', how do I decide whether to use HCF or LCM?
This is a common point of confusion. Here’s a simple guide:
- Use HCF (Highest Common Factor) when you need to find the "greatest," "largest," or "maximum" number that can divide given numbers exactly. This often involves splitting things into smaller sections or arranging them into rows or groups of equal size.
- Use LCM (Lowest Common Multiple) when you need to find the "smallest," "least," or "minimum" number that is a multiple of the given numbers. This is common in problems about events happening at regular intervals, like bells ringing together. These types of questions are frequent in Exercise 3.7.
9. Is there a relationship between the HCF and LCM of two numbers?
Yes, there is a very important relationship for any two positive integers, let's call them 'a' and 'b'. The product of the two numbers is always equal to the product of their HCF and LCM. The formula is: a × b = HCF(a, b) × LCM(a, b). This formula is a useful tool for verifying your answers or finding a missing value if you know the other three. For example, if you know the numbers and their HCF, you can find the LCM without using the standard method.
10. The NCERT solutions state that a number is divisible by 3 if the sum of its digits is divisible by 3. Why does this trick work?
This rule works because of our base-10 number system. Any number can be written in an expanded form. For example, the number 432 is actually (4 × 100) + (3 × 10) + 2. This can be rewritten as:
- 4 × (99 + 1) + 3 × (9 + 1) + 2
- (4 × 99) + 4 + (3 × 9) + 3 + 2
