NCERT Solutions for Class 8 Maths Chapter 16, Playing with Numbers is available for students to understand the concepts included in this chapter in an easy way. These NCERT Class 8 Solutions help students to frame a better understanding of the topic with the help of solved questions. When students need help with their homework, or while preparing for exams and while learning, NCERT solutions are an invaluable aid to students. Download NCERT Solutions to excel in their Class 8 examination.
NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Exercise 16.2
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Exercise 16.1 Solutions : 10 Questions (Short answer type)
Access Answers to NCERT Class 8 Maths Chapter 16 Playing with Numbers Exercise 16.2 Page number 260
1. If 21y5 is a multiple of 9, where y is a digit, what is the value of y?
Solution:
Suppose 21y5 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.
That is, 2+1+y+5 = 8+y
Therefore, 8+y is a factor of 9.
This is possible when 8+y is any one of these numbers 0, 9, 18, 27, and so on
However, since y is a single-digit number, this sum can be only 9.
Therefore, the value of y should be 1 only, i.e. 8+y = 8+1 = 9.
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?
Solution:
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
Therefore, 9+z is a multiple of 9
This is only possible when 9+z is any one of these numbers: 0, 9, 18, 27, and so on.
This implies, 9+0 = 9 and 9+9 = 18
Hence 0 and 9 are two possible answers.
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.)
Solution:
Let’s say 24x is a multiple of 3.
Then, according to the divisibility rule of 3, the sum of all the digits should be a multiple of 3.
2+4+x = 6+x
So, 6+x is a multiple of 3, and 6+x is one of these numbers: 0, 3, 6, 9, 12, 15, 18 and so on.
Since x is a digit, the value of x will be either 0 or 3 or 6 or 9, and the sum of the digits can be 6 or 9 or 12 or 15, respectively.
Thus, x can have any of the four different values: 0 or 3 or 6 or 9.
4. If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?
Solution:
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.
That is, 3+1+z+5 = 9+z
Therefore, 9+z is a multiple of 3.
This is possible when the value of 9+z is any of the values: 0, 3, 6, 9, 12, 15, and so on.
At z = 0, 9+z = 9+0 = 9
At z = 3, 9+z = 9+3 = 12
At z = 6, 9+z = 9+6 = 15
At z = 9, 9+z = 9+9 = 18
The value of 9+z can be 9 or 12 or 15 or 18.
Hence 0, 3, 6 or 9 are four possible answers for z.
NCERT Class 8 Maths Chapter 16 Playing with Numbers Exercise 16.2, based on the topic, Tests of Divisibility: Divisibility by 10, Divisibility by 5, Divisibility by 2 and Divisibility by 9 and 3. You can also give the reasons for the divisibility of numbers by 10, 5, 2, 9, or 3 when numbers are written in a general form.
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