Playing With Numbers Class 8 Notes CBSE Maths Chapter 16 (Free PDF Download)

Numbers in General Form

1. A number can be written in a general form if it is expressed as the sum of the products of its digits with their respective place values.

2. General form of two-digit number $ab$ is $10\times a+b$  

3. General form of three-digit number $abc$ is $100\times a+10\times b+c$ 

Games with Numbers

1. Reversing Two-digit Number: 

a. Choose a two-digit number 

b. Reverse the chosen digit to get a new number

c. Add this to the number you started with

d. Now divide the answer by $11$ 

e. There won’t be any remainder

2. Reversing Three-digit Number:

a. Choose a three-digit number

b. Reverse the chosen digit to get a new number 

c. Subtract smaller number from larger one

d. Now divide the answer by $99$ 

e. There won’t be any remainder

3. Forming Three-digit Numbers with Given Three-digits:

a. Choose a three-digit number

b. Form two more three-digit numbers from the chosen number

c. Add them

d. Now divide the answer by $37$ 

e. There won’t be any remainder

Letters for Digits 

Rule to follow while solving letters for digits puzzles:

a. Each digit must be represented by only one digit

b. The first digit of a number must be non-zero.

Example: 

Find $Q$  in the addition

$\quad1Q$

$\:+Q3$

$\quad\overline{101}$

In column one: from $Q+3$, we get $1$ , that is, a number whose ones digit is $1$  therefore the digit should be $Q=8$ 

Tests of Divisibility 

1. Divisibility by $10$ 

A number is divisible by $10$ when its ones digit is $0$ then only it is the multiple of $10$ 

For example: $520,950,630,20$ etc.

2. Divisibility by $5$ 

A number is divisible by $5$  when its ones digit is either $0$ or $5$  then only it is the multiple of $5$ 

For example: $50,95,65,20$ etc.

3. Divisibility by $2$ 

A number is divisible by $2$  when its ones digit is $0,2,4,6$ or $8$  i.e., every even number is divisible by $2$ 

For example: $50,92,64,26,68$ etc.

4. Divisibility by $9$ and $3$ 

A number is divisible by $3$ when sum of its digit is divisible by $3$

For example: $7263$, the sum of digits of $7263$ is $18$ and $18$ is divisible by $3$ therefore $7263$ is also divisible by $3$ 

A number is divisible by $9$ when sum of its digit is divisible by $9$ 

For example:$215847$, the sum of digits of $215847$ is $27$ and $27$ is divisible by $9$ therefore $215847$ is also divisible by $9$

Examples of Playing with Numbers

1.    3   A

    +  2   5

-  - - - - - - - - -

        B    2

- - - - - - - - - - -

In the above problem we need to find the value of  A and B..

Here  adding ones values we have A + 5 = 2

Which means one value of the answer is 2 ,

Which in turn means A = 7,

So that 7 + 5 = 12. One place's value of 12 is 2.

By applying that

    3   A

+  2   5

becomes

   B    2

   3    7

+ 2   5

becomes

   6   2

So the value of A is 7, and  B is 6.

In the same way we can find the values in multiplication problems also.

Consider the problem

      B A

   * B 3

becomes

5   7  A

Here we need to find values of A and B.

Since the ones digit  of A* 3 is A the value of A should be  0 or either 5.

Hence we go for other option i.e if A = 0  and B = 2 which will be

20 * 23 = 460

If this is also wrong, then go for another option?

A = 5 and B = 2 which will be

25 * 23 = 575.

Hence A = 5 and B = 2.

Test of Divisibility in Class 8 Revision Notes Playing With Numbers

In this category of playing with numbers class 8 notes, you will learn about divisibility of 2 , 3 ,5 , 6 , 9,10.

A. Divisibility of 2:

First let us check about the divisibility of 2 :

Let us recall natural numbers  which are 1 , 2 ,3 , 4 , 5 , 6, 7, 8, 9 …..

A whole number is 0,1, 2, 3, 4, 5, 6, 7, 8, 9 …..

A natural number becomes an even number if its last digit is 2, 4 ,6, 8, 0.

All even numbers are always divisible by 2.

If a number ABC can be expressed as  100*A + 10* B +C

Here 100 A  and  10B are divisible by 2 as its value in one’s place is 0.

Whereas the value of C determines if it can be divisible by 2 .

If C is even, then ABC is divisible by 2 as 100*A, 10* B, C are all divisible by 2 which means their sum is also divisive by 2.

If C is odd or any other value like integer, etc. then,  ABC cannot be divisible by 2.

Example:

128 can be expressed as (100 * 1) +( 10* 2)+ 8

                                 = 100+20+8

Here 100 is divisible by 2

20 is divisible by 2

8 is also divisible by 2.

Which means 128 is also divisible by 2.

B. Divisibility of 3:

The rule over here is “if the sum of the digits in the number is multiple of three then the number itself is divisible by 3”.

Example :

Take the number 1254,to check the divisibility let us sum the numbers

1 + 2 + 5 + 4 = 12. Here 12 is a multiple of 3. Hence it is divisible by 3.

C. Divisibility of 5:

The mathematical principle applied here is “if the last digit is either 5 or 0 then the number is divisible by 5”.

D. Divisibility of 9:

The mathematical principle applied here is “if the sum of the digits in the number is multiple of three then the number itself is divisible by 9”.

Consider the number 3582 here the sum of the digit 3 + 5 + 8 + 2 is 18 which is divisible by 9. Hence 3582 is also divisible by 9.

E. Divisibility of 10:

The mathematical principle applied here is “if the last digit is 0 then the number is divisible by 10”.

Test of Divisibility Example:

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

Solution:

If a number is divisible by 9 then its sum of the digits is also divisible by 9. so 2 + 1 + y + 5 = 8 + y.

So y can be 1 , 10 etc.

As  y is single digit y = 1.

So the number is 2115.

Note: The above learning can also be used in solving puzzles.

Importance of CBSE Class 8 Maths Chapter 16 Playing With Numbers Notes

The concepts related to numbers are crucial to the Class 8 Maths syllabus. This is an arithmetic chapter that explains how numbers are interrelated. This chapter will explain various theorems and formulas developed by the top mathematicians along with the formulas. Maths Class 8 playing with numbers notes includes various types of numbers and their use in mathematical equations. In this chapter, you will learn that there are varieties of numbers in the form of whole numbers, natural numbers, integers, rational numbers etc. This chapter further deals with the test of divisibility by exploring digits.

Students must refer to the notes designed by the subject experts to make this chapter easier to study. These notes enable students to study the concepts with examples. They will also be able to revise this chapter faster by using these notes. Hence, these notes are an integral part of the study material for this chapter to use.

Advantages of Class 8 Maths Chapter 16 Playing With Numbers Notes

• The notes can be used to reduce your study and revision time for this chapter.

• Resolve doubts related to the concepts of this chapter and prepare it faster.

• Use the simpler version of the concepts explained in these notes to study and recall faster during an exam.

• Formulate precise answers to the fundamental questions by using what you have studied in these notes and score more in the exams.

Download CBSE Class 8 Maths Chapter 16 Playing with Numbers Notes Free PDF

Add the free PDF version of these notes to the study material for this chapter. Focus on how the experts have explained these topics in a simpler version and understand them well. Learn how to use these notes precisely to formulate accurate answers too. Revise the whole chapter in no time and progress with an exam syllabus more efficiently.