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

NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers are prepared by subject experts keeping in mind the studentโs requirements of CBSE Class 8. These solutions do not confuse students but help them in reaching a conclusion using the ideal method. Solving NCERT questions will give students the advantage of preparing themselves better before the final CBSE exams. the advansity aims at bringing out the very best in students through additional skill-building exercises that are tailored to their grade levels, abilities and interests. Class 8ย NCERT Solutionsย are a valuable help to students in their exams.

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## Exercise 16.1 Page No: 255

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

**1.**

**Solution:**

Say, A = 7 and we get,

7+5 = 12

In which oneโs place is 2.

Therefore, A = 7

And putting 2 and carry over 1, we get

B = 6

Hence **A = 7 and B = 6**

**2.**

**Solution:**

If A = 5 and we get,

8+5 = 13 in which ones place is 3.

Therefore, A = 5 and carry over 1 then

B = 4 and C = 1

Hence, **A = 5, B = 4 and C = 1**

**3**.

**Solution:**

On putting A = 1, 2, 3, 4, 5, 6, 7 and so on and we get,

AxA = 6ร6 = 36 in which ones place is 6.

Therefore, **A = 6**

**4.**

**Solution:**

Here, we observe that B = 5 so that 7+5 =12

Putting 2 at ones place and carry over 1 and A = 2, we get

2+3+1 =6

Hence **A = 2 and B =5**

**5.**

**Solution:**

Here on putting B = 0, we get 0x3 = 0.

And A = 5, then 5ร3 =15

A = 5 and C=1

Hence **A = 5, B = 0 and C = 1**

**6.**

**Solution:**

On putting B = 0, we get 0x5 = 0 and A = 5, then 5ร5 =25

A = 5, C = 2

Hence **A = 5, B = 0 and C =2**

**7.**

**Solution**:

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

6ร1 = 6, 6ร2 = 12, 6ร3 = 18, 6ร4 =24

On putting B = 4, we get the ones digit 4 and remaining two Bโs value should be44.

Therefore, for 6ร7 = 42+2 =44

Hence **A = 7 and B = 4**

**8.**

**Solution:**

On putting B = 9, we get 9+1 = 10

Putting 0 at ones place and carry over 1, we get for A = 7

7+1+1 =9

Hence, **A = 7 and B = 9**

**9.**

**Solution:**

On putting B = 7, we get 7+1 =8

Now A = 4, then 4+7 =11

Putting 1 at tens place and carry over 1, we get

2+4+1 =7

Hence, **A = 4 and B = 7**

**10.**

**Solution:**

Putting A = 8 and B = 1, we get

8+1 =9

Now, again we add2 + 8 =10

Tens place digit is โ0โ and carry over 1. Now 1+6+1 = 8 =A

Hence **A = 8 and B =1**

## Exercise 16.2 Page No: 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 9 only.

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, โฆ . 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:**

Letโs 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.

Also Access |

CBSE Notes for Class 8 Maths Chapter 16 |

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

Class 8 NCERT exercise wise questions and answers are very important for students in order to develop logical and mental ability. Some of the important topics introduced in Solutions of Class 8 NCERT Maths are Numbers in General Form, Games with Numbers, Letters for Digits and Tests of Divisibility. In previous classes, students have studied various types of numbers, their properties and relationships among them. In this section, numbers are explored in more detail.

**NCERT Solutions for Class 8 Maths Chapter 16 Exercises:**

Get a detailed solution for all the questions listed under the below exercises:

Exercise 16.1 Solutions : 10 Questions (Short answer type)

Exercise 16.2 Solutions : 4 Questions (Short answer type)

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

NCERT Class 8 Maths Chapter 16-Playing with Numbers, introduce Numbers in General Form, Games with Numbers and Divisibility test by some numbers: by 2, 3, 5, and 10.

**The main topics covered in this chapter include:**

Exercise | Topic |

16.1 | Introduction |

16.2 | Numbers in General Form |

16.3 | Games with Numbers |

16.4 | Letters for Digits |

16.5 | Tests of Divisibility |

## Key Features of NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers

- These NCERT exercises are meticulously solved by subject experts.
- Simple and easy language is used.
- All questions are solved using a step-by-step approach.
- Practise all the solved examples given and get exam ready.
- These NCERT solutions are a valuable help to students in their assignments and competitive exams.

## Frequently Asked Questions on NCERT Solutions for Class 8 Maths Chapter 16

### Write the key benefits of NCERT Solutions for Class 8 Maths Chapter 16.

1. The solutions provided in NCERT Solutions for Class 8 Maths Chapter 16 are offered in a step by step approach for a comfortable and better understanding of concepts.

2. It also provides explanatory diagrams and tables for comparative study, which creates an interest in learning.

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4. It also helps students in retaining and quickly retrieving the concepts.

### How are NCERT Solutions for Class 8 Maths Chapter 16 helpful for Class 8 students?

The NCERT Solutions for Class 8 Maths Chapter 16 can help the students to clear their doubts and prepare themselves for the exam in a better way. The NCERT questions not only help for board exam preparation but also for different competitive exams.

### How to score high marks using NCERT Solutions for Class 8 Maths Chapter 16 in board exams?

Students are advised to follow the NCERT Solutions for Class 8 Chapter 16 on a regular basis to get in-depth knowledge about all the concepts covered in the syllabus. These NCERT Solutions for Class 8 are prepared by our BYJUโS expert team, focusing completely on accuracy. Using these solutions regularly helps you score high marks in board exams.