# RS Aggarwal Class 8 Chapter 5 Solutions (Playing With Numbers)

RS Aggarwal Class 8 Maths Solutions for Chapter 5 ‘Playing With Numbers’ are here to help you with all the important concepts related to this chapter. Till now, you have studied about whole numbers, integers, rational numbers and natural numbers. This chapter of RS Aggarwal Class 8 Maths Solutions includes advanced topics such as the general form of numbers, tricks for divisibility by 2,3,4,5,6,7,8,9,10,11, and representing alphabets as numbers.

RS Aggarwal Class 8 Maths Chapter 5 has 4 exercises and 44 questions based on the above-stated concepts of the chapter. The exercises will give you a thorough revision of the chapter so that you can prepare well for your exams. Also, there are typical questions included in the exercises to help you prepare for olympiads and competitions as well.

Our subject matter experts have solved all the problems given in Chapter 5 of RS Aggarwal Class 8 Maths book in a step-by-step manner. This way, if you have any doubts in the chapter you will easily understand how to solve the questions correctly. Our subject matter experts are thorough with the latest CBSE guidelines and syllabus for Class 8 Maths and create the solutions accordingly. Below you will find some important topics related to the chapter and a quick discussion of the exercises.

## Important Topics for RS Aggarwal Class 8 Maths Solutions Chapter 5: Playing With Numbers

**General Form of 2-Digit and 3-Digit Numbers**

We can write any two digit number ‘wx’ in the form: wx = 10w + x

For example, 65 = 10 x 6 + 5, 46 = 10 x 4 + 6

Similarly, we can write any three digit number ‘wxy’ in the form: wxy = 100w + 10x + y = 100w + 10y + x

For example: 782 = 100 x 7 + 10 x 8 + 2, 561 = 100 x 5 + 10 x 6 + 1

**Some Interesting Results**

- A two-digit number ‘uv’ can be written as ‘10u + v’ and its reverse ‘vu’ can be written as ‘10v + u’.

If we add the 2-digit number with its reverse, we would get ‘11(u + v)’

This means, every 2-digit number when added with its reverse is a multiple of 11. Also, the quotient so obtained by dividing the sum by 11 would be the sum of the digits of the two-digit number.

**For example:** Let us take the number 56 and add it with its reverse 65. The answer would be 56+65 = 121 and 121 divided by 11 gives 0 as remainder and 11 as quotient.

- A three-digit number ‘def’ can be written as ‘100d + 10e + f’ and its reverse ‘fed’ can be written as ‘100f + 10e + d’.

If we subtract the reverse of a three-digit number from the number then, we get, (100d + 10e + f) – (100f + 10e + d) = 99(d – f). This means that the resulting number will always be divisible by 99.

**For example: **Let us take the number 756 and its reverse 657.

756 – 657 = 99 which is divisible by 99.

Now let us take the number 255 and its reverse 552. The reverse is greater than the original number so here,

552 – 255 = 297

297 / 99 = 3

This means, even if it is (d-f) or (f-d), the resulting number will always be divisible by 99.

**Test of Divisibility **

- Any number is divisible by 2 if it ends with an even digit. For example, 46, 78, 124432 all are divisible by 2 because they have an even digit at their units-place.
- Any number is divisible by 3 if the sum of its digits is divisible by 3. For example, 63 is divisible by 3 because 6+3 = 9 and 9 is divisible by 3.
- Any number is divisible by 5 if it ends with a ‘0’ or a ‘5’. For example, 100, 345, 2786865, all are divisible by 5.
- Any number is divisible by 10 if it ends with a ‘0’. For example, 10000, 45656780, 20 all are divisible by 10.

### Exercise Discussion for RS Aggarwal Class 8 Maths Solutions Chapter 5: Playing With Numbers

- Exercise 5A of RS Aggarwal Class 8 Maths Chapter 5 ‘Playing with Numbers’ has only 6-word problems where you need to find the number when the sum or difference of its digits is given to you.
- Exercise 5B is based on the test of divisibility of numbers and has 15 questions. This is an important exercise.
- Exercise 5C has 14 questions and is based on the concept of representing letters as numbers. For example, you are given 5A + 87 = CB3 and you have to find the values of A, B and C.
- Exercise 5D has 9 questions based on the same concept of Exercise 5C but it involves division rather than addition or subtraction. For example, you are given a number 8xy7 which is exactly divisible by 3. Then, you have to find the least value of (x + y).

### Why Use RS Aggarwal Class 8 Maths Solutions Chapter 5: Playing With Numbers by Instasolv?

- We have the best Maths subject matter experts who understand what problems you might face in solving the exercises of Chapter 5 ‘Playing With Numbers’ of RS Aggarwal Class 8 book.
- Our subject matter experts ensure that all those problems are tackled in the solutions and you can understand the problem-solving process easily.

Our RS Aggarwal Solutions are based on the CBSE exam pattern and syllabus for Class 8 Maths so practising them would surely prepare you for your CBSE Maths exam.