NCERT Solutions Class 6 Maths Chapter 3 Number Play Exercise 3.8

Exercise 3.8 of Class 6 Maths Chapter 3 – Playing with Numbers presents you with the opportunity to learn how to determine if one number is divisible by another by using the rules of divisibility. This skill will help you check your answers quickly instead of just working it out with long division.You will learn some of the divisibility rules for numbers and these are also useful not only for exams but also in higher classes.

By completing these questions, you will understand units of numbers more robustly and you will be able to solve questions faster in CBSE school tests. This exercise is part of the latest NCERT syllabus and is part of the important topics in Class 6 Maths.

We have shared the NCERT Solutions for exercise 3.8 in free PDF format to help you learn even better. The Solutions are prepared in simple steps for clear understading. You can use the solutions to study, revise and practice.

1.0Download NCERT Solutions Class 6 Maths Chapter 3 Number Play Exercise 3.8: Free PDF

Exercise 3.8 helps you learn how to identify the rules of divisibility of different numbers in a simple way. The NCERT Solutions for Class 6 Maths Chapter 3 include simple and clear steps for each question. Download the free PDF now to practice and do well in your exams.

2.0NCERT Solutions Class 6 Chapter 3 Number Play: All Exercises

Find the NCERT solutions for other exercises from chapter 3 Maths here.

3.0NCERT Class 6 Maths Chapter 3 Number Play Exercise 3.8: Detailed Solutions

1. Write an example for each of the below scenarios whenever possible.

Could you find examples for all the cases? If not, think and discuss what could be the reason. Make other such questions and challenge your classmates.

Sol.

Let's go through the scenarios presented and provided examples for each:

5-digit + 5-digit to give a 5-digit sum more than 90,250:

Example: 60,000+35,000=95,000

5-digit + 3-digit to give a 6-digit sum:

Example: 99,250+750=1,00,000

4-digit + 4-digit to give a 6-digit sum:

This seems impossible because two 4-digit numbers added together can't give a 6-digit number.

While adding two largest 4 -digit number, the result is a 5 -digit number (9999+9999=19998) so we can say 6-digit number sum is not possible.

5-digit + 5-digit to give a 6-digit sum:

Example: 70,000+45,000=1,15,000

5-digit + 5-digit to give 18,500:

While adding two smallest 5 -digit number (i.e., 10000), the result is a 20000 i.e., greater than 18500,

So, we can say 18500 is not possible.

5-digit-5-digit to give a difference less than 56,503:

Example: 90,000−40,000=50,000

5-digit-3-digit to give a 4-digit difference:

Example: 10,000−600=9,400

5-digit - 4-digit to give a 4-digit difference:

Example: 15,000−8,000=7,000

5-digit - 5 -digit to give a 3 -digit difference:

Example: 11700-11000=700

5-digit - 5-digit to give 91,500:

Example: 99999-10000=89999 i.e., not equal to 91500

While difference of greatest 5-digit number and smallest 5-digit number is 89999 so, we can say required difference 91500 is not possible

Conclusion

• We found examples for all the cases, except for
• Adding two 4-digit numbers to get a 6-digit sum, which is impossible. the largest sum is still a 5-digit number.
• Adding two 5-digit numbers to give 18500 as sum.
• Subtracting 5-digit number from another 5-digit number to give 91500 as sum.

Always, Sometimes, Never?

2. Below are some statements. Think, explore and find out if each of the statement is 'Always true', 'Only sometimes true' or 'Never true'. Why do you think so? Write your reasoning; discuss this with the class.

a. 5-digit number + 5-digit number gives a 5-digit number

b. 4-digit number +2 -digit number gives a 4 -digit number

c. 4-digit number +2 -digit number gives a 6 -digit number

d. 5-digit number-5-digit number gives a 5-digit number

e. 5-digit number-2-digit number gives a 3-digit number

Sol.

Checking Whether Always, Sometimes, Or Never:

a. 5-digit number + 5-digit number gives a 5-digit number

Sometimes true

If both numbers are small, like 20,000+10,000=30,000,

The result is a 5 -digit number.

But with large numbers, like 95,000+95,000=190,000, it becomes a 6 -digit number.

b. 4-digit number +2 -digit number gives a 4-digit number

Sometimes true

a small 4 -digit number, like 2,000+70=2070, gives a 4 -digit result. but if the 4 -digit number is large, like 9,999+99=10,098, the result is a 5 - digit number.

c. 4-digit number +2 -digit number gives a 6 -digit number

Never true

Even the largest 4-digit number (9,999) and the largest 2-digit number (99) only give a 5 -digit result (10,098), not 6 digits.

So, 6 digit number is not possible.

d. 5-digit number-5-digit number gives a 5-digit number

Sometimes true

If they're far apart, like 99999−10,000=89999, the result is a 5 -digit number.

but if they're close, like 20,000−11000=9000, the result is a 4 -digit number.

e. 5-digit number-2-digit number gives a 3 -digit number

Never true

If we take the smallest 5 -digit number: 10,000 and the largest 2 -digit number: 99 Then the difference =10,000−99=9,901 (a 4-digit number).

4.0Key Features and benefits for Class 6 Maths Chapter 3 Exercise 3.8

• The exercise shows divisibility rules for 2, 3, 5, 9, and ten.
• All of the questions are aligned with the latest Class 6 NCERT syllabus and examination structure.
• Practising NCERT solutions helps students to solve questions correctly, once in the examinations in a much quicker way and without confusion.
• NCERT solutions also supports the preparation for maths Olympiad and other competitions at school level.
• Regular practice of these solutions builds confidence and improves logical thinking, adding to problem-solving.