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NCERT Solutions for Class 8 Maths Chapter 16 – Playing with Numbers

NCERT Solutions for Class 8 Maths Chapter 16 helps you score better in CBSE exams. Chapter 16- ‘Playing with Numbers’ is not at all a complex chapter. The NCERT Solutions includes concepts like the basics of forming any number through digits, say two-digit, three-digit, games with numbers, letters for digits and test of divisibility. 

This chapter has 2 exercises and 14 questions on divisibility by 10, 5, 9 and 3. You can access the detailed solutions to each question below. You can easily learn them stepwise through the exclusively developed NCERT Solutions for Class 8 Mathematics by Instasolv. The NCERT Solution for Class 8 Mathematics is a rather very easy compilation and also most important for the students to develop logical ability.

Chapter 16 of NCERT for Class 8 Mathematics is about how the numbers are being formed, be it a two-digit number or more than that. This chapter also describes Playing with Numbers—which means using the numbers to get the answers to some tricky questions, which are usually solved by using hit and trial methods.

NCERT Solutions for Class 8 Maths Chapter 16: Playing with Numbers- Detailed Description

The chapter tells us about the position of digits in a number formed and the divisibility of the numbers used to find the missing digits in a number. In Chapter 16 we see how a two-digit number is formed by applying a simple identity, that is 10a + b. 

For Example: Assume any two-digit number- say 28. In this number 2 is in the tens place and 8 is in the one’s place and by adding 10 to the digit 2 we get 20 and again adding 8 to it the two-digit number is 28.

Similarly, for a three-digit number, we can use 100a +10b + c to find out any three-digit number. We learn to find out numbers with the use of various techniques based on the digits itself.

This chapter further tells us the process of finding out the value of letters. So, to find out the value of letters, usually, a sum of the number is given either through addition or multiplication with any English alphabet.  

Based on this we have questions related to multiplication as well. As for example AB * 3= CAB, here we need to find out the value of ABC. The point to be kept in mind is that what should be multiplied to 3 that the result is the same number that is B. The digit can be none-other than zero, then only it will yield B as the result. Coming to find out the value of CA, again the digit multiplied to 3 is the same number that is A. 

Then the number multiplied to 3 should be 5, and the answer will be 15. The value of A, B, and C is 5, 0, 1 respectively. These are the hit and trial methods through which we can find the value of every number, be it a two-digit number or a three-digit number.

This chapter also deals with the Divisibility Test, whether a number is divisible by 2 (if the last digit is even then it will be divisible by 2), 3 (the sum of digits of a number is a multiple of 3), 6 (digits divisible by 2 and 3), 9 (sum of the digits should be multiple of 9), 5 (last digits should be 0, 5), 10 (the last digit is zero), etc.

Exercise-wise Discussion on NCERT Solution for Class 8 Mathematics Chapter 16

  1. Exercise 16.1 comprises 10 questions that test your level of understanding regarding the values of the letters. 
  2. Exercise 16.2 has 4 questions that are based on the multiplication of numbers. 
  3. Instasolv’s solutions for class 8 Maths Chapter 16 will help you to score good marks as they are designed according to the pattern of CBSE. 

Important Points to be Remembered 

  1. The variety of questions include finding the multiples of 3, 9, etc. So, it is advised to remember the rule of divisibility;
  2. To solve the questions based on puzzles, you need to apply your mind and use the hit and trial method; 
  3. The general form of representing a two-digit number is 10a + b; 
  4. Another significant point related to the chapter is that whenever a two-digit number is reversed, and then added with the number, the resulting number is divisible by 11 and the quotient is equal to the sum of digits. For example, take any two-digit number, say 28, the reverse of it 82. The sum of 28 and 82 is 110, which is divisible by 10. So, we can see that the sum is divisible by 11 and the quotient is equal to the sum of the digits of the number; 
  5. When a three-digit number is reversed and the smaller number is subtracted from the larger number, the resulting number is perfectly divisible by 99 and the quotient is equal to the difference between the first and the third digit of the selected number. 

About NCERT Solution for Class 8 Mathematics Chapter 16 by Instasolv

  1. The Chapter aims to teach you how to write a 2-digit and 3-digit number in the generalized form by solving the number of puzzles; 
  2. The NCERT Solutions for Class 8 Maths Chapter 16 brings to you the games related to numbers and thus enjoy learning the chapter; 
  3. The exercise of chapter 19 wants you to understand the concepts very minutely. To check this, the questions also ask for the reason behind a particular answer.