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Playing with Numbers NCERT Solutions - Class 8 PDF Download

Exercise 16.1 

Question 1: 

Find the values of the letters in the following and give reasons for the steps involved. 

Playing with Numbers NCERT Solutions - Class 8

Answer 1: 

Playing with Numbers NCERT Solutions - Class 8

Question 2:

Find the values of the letters in the following and give reasons for the steps involved. 

Playing with Numbers NCERT Solutions - Class 8

Answer 2: 

Playing with Numbers NCERT Solutions - Class 8

Question 3: 

Find the values of the letters in the following and give reasons for the steps involved. 

Playing with Numbers NCERT Solutions - Class 8

Answer 3: 

Playing with Numbers NCERT Solutions - Class 8

Question 4: 

Find the values of the letters in the following and give reasons for the steps involved. 

Playing with Numbers NCERT Solutions - Class 8

Answer 4: 

Playing with Numbers NCERT Solutions - Class 8

Question 5: 

Find the values of the letters in the following and give reasons for the steps involved.

Playing with Numbers NCERT Solutions - Class 8

Answer 5: 

Playing with Numbers NCERT Solutions - Class 8

Question 6: 

Find the values of the letters in the following and give reasons for the steps involved. 

Playing with Numbers NCERT Solutions - Class 8

Answer 6: 

Playing with Numbers NCERT Solutions - Class 8

Question 7: 

Find the values of the letters in the following and give reasons for the steps involved. 

Playing with Numbers NCERT Solutions - Class 8

Answer 7:

Here product of B and 6 must be same as ones place digit as B.

6x1 = 6, 6x2 = 12,6x3 = 18, 6x4 = 24

On putting B = 4, we get the ones digit 4 and remaining two B's value should he 44,

∴ For 6x7 = 42+ 2= 44

Hence, A = 7 and B = 4

Question 8: 

Find the values of the letters in the following and give reasons for the steps involved.

Playing with Numbers NCERT Solutions - Class 8

Answer 8: 

Playing with Numbers NCERT Solutions - Class 8

 

Question 9: 

Find the values of the letters in the following and give reasons for the steps involved. 

Playing with Numbers NCERT Solutions - Class 8

Answer 9: 

Playing with Numbers NCERT Solutions - Class 8

Question 10: 

Find the values of the letters in the following and give reasons for the steps involved. 

Playing with Numbers NCERT Solutions - Class 8

Answer 10: 

Playing with Numbers NCERT Solutions - Class 8

Exercise 16.2 

Question 1: 

If 21y5 is a multiple of 9, where y is a digit, what is the value of y? 

Answer 1: 

Since 2ly5 is a multiple of 9.

Therefore according to the divisibility rule of 9, the sum of all the digits should be a multiple of 9.

2+1+y+5=&+y  => 8 + y

=> 8 + y = 9  

=>  y = 1

Question 2:

If 31z5 is a multiple of 9, where z is a digit, what is the value of z? You will find that there are two answers for the last problem. Why is this so? 

Answer 2:

Since 31z5 is a multiple of 9.

Therefore according to the divisibility rule of 9, the sum of all the digits should be a multiple of 9.

3 +1 + z+ 5 = 9 + z

=>   9+z = 9

=>  z = 0

If 3+1+z+5 = 9+z

=>  9+z= 18

=>   z = 9

Hence, 0 and 9 are two possible answers.

Question 3: 

If 24x is a multiple of 3, where x is a digit, what is the value of x? 

(Since 24x is a multiple of 3, its sum of digits 6 + x is a multiple of 3; so 6 + x is one of these numbers: 0, 3, 6, 9, 12, 15, 18 ... But since x is a digit, it can only be that 6 + x = 6 or 9 or 12 or 15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values.) 

Answer 3: 

Since 24x is a multiple of 3.

Therefore according to the divisibility rule of 3, the sum of all the digits should be a multiple of 3.

∴ 2 + 4 + x = 6+x

Since x is a digit.

=>  6 + x = 6  => x = 0

=>  6+X = 9   => x = 3

=> 6 + x = 12 => x = 6

=>  6 + x -15  => x = 9

Thus, x can have any of four different values.

Question 4:

If 31z5 is a multiple of 3, where z is a digit, what might be the values of z? 

Answer 4: 

Since 31z5 is a multiple of 3.

Therefore according to the divisibility rule of 3, the sum of all the digits should be a multiple of 3.

Since r is a digit,

3 + 1 + z + 5 = 9+z

=> 9 + z = 9  => z= 0

If   3+1+z+5 = 9+z

=> 9 + z = 12   =>  = 3

If  3 + l + z + 5 = 9 + z

=>  9+r = 15  => z = 6

If 3 + l+ z + 5 = 9 + z

=>9+r = 18  => z = 9

Hence, 0, 3,6 and 9 are four possible answers.

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FAQs on Playing with Numbers NCERT Solutions - Class 8

1. What is Playing with Numbers in Class 8?
Ans. Playing with Numbers is a chapter in the Class 8 Mathematics textbook that deals with various mathematical operations, including factors and multiples, prime and composite numbers, and divisibility rules. The chapter aims to help students understand the properties of numbers and their manipulations.
2. What are the important topics covered in the Playing with Numbers chapter in Class 8?
Ans. The Playing with Numbers chapter in Class 8 Mathematics covers various topics, including prime and composite numbers, factors and multiples, divisibility rules for 2, 3, 5, 9, and 10, tests of divisibility, and common factors and multiples.
3. How can I score well in the Playing with Numbers chapter in Class 8 Mathematics?
Ans. To score well in the Playing with Numbers chapter in Class 8 Mathematics, students should practice the various problems given in the textbook and solve sample papers and previous year question papers. They should also try to understand the underlying concepts and properties of numbers and their manipulations.
4. What are the real-life applications of the concepts covered in the Playing with Numbers chapter in Class 8?
Ans. The concepts covered in the Playing with Numbers chapter in Class 8 Mathematics have various real-life applications, including in banking, accounting, cryptography, and computer science. For example, the concept of prime numbers is used in cryptography, while the concept of divisibility is used in accounting and banking.
5. Is the Playing with Numbers chapter in Class 8 Mathematics important for competitive exams?
Ans. Yes, the Playing with Numbers chapter in Class 8 Mathematics is essential for various competitive exams, including the National Talent Search Examination (NTSE), Olympiad exams, and other scholarship exams. The chapter covers fundamental concepts and properties of numbers that are crucial for solving mathematical problems in these exams.
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