
CBSE Important Questions›

CBSE Previous Year Question Papers›
 CBSE Previous Year Question Papers
 CBSE Previous Year Question Papers Class 12
 CBSE Previous Year Question Papers Class 10

CBSE Revision Notes›

CBSE Syllabus›

CBSE Extra Questions›

CBSE Sample Papers›
 CBSE Sample Papers
 CBSE Sample Question Papers For Class 5
 CBSE Sample Question Papers For Class 4
 CBSE Sample Question Papers For Class 3
 CBSE Sample Question Papers For Class 2
 CBSE Sample Question Papers For Class 1
 CBSE Sample Question Papers For Class 12
 CBSE Sample Question Papers For Class 11
 CBSE Sample Question Papers For Class 10
 CBSE Sample Question Papers For Class 9
 CBSE Sample Question Papers For Class 8
 CBSE Sample Question Papers For Class 7
 CBSE Sample Question Papers For Class 6

ISC & ICSE Syllabus›

ICSE Question Paper›
 ICSE Question Paper
 ISC Class 12 Question Paper
 ICSE Class 10 Question Paper

ICSE Sample Question Papers›
 ICSE Sample Question Papers
 ISC Sample Question Papers For Class 12
 ISC Sample Question Papers For Class 11
 ICSE Sample Question Papers For Class 10
 ICSE Sample Question Papers For Class 9
 ICSE Sample Question Papers For Class 8
 ICSE Sample Question Papers For Class 7
 ICSE Sample Question Papers For Class 6

ICSE Revision Notes›
 ICSE Revision Notes
 ICSE Class 9 Revision Notes
 ICSE Class 10 Revision Notes

ICSE Important Questions›

Maharashtra board›

RajasthanBoard›
 RajasthanBoard

Andhrapradesh Board›
 Andhrapradesh Board
 AP Board Sample Question Paper
 AP Board syllabus
 AP Board Previous Year Question Paper

Telangana Board›

Tamilnadu Board›

NCERT Solutions Class 12›
 NCERT Solutions Class 12
 NCERT Solutions Class 12 Economics
 NCERT Solutions Class 12 English
 NCERT Solutions Class 12 Hindi
 NCERT Solutions Class 12 Maths
 NCERT Solutions Class 12 Physics
 NCERT Solutions Class 12 Accountancy
 NCERT Solutions Class 12 Biology
 NCERT Solutions Class 12 Chemistry
 NCERT Solutions Class 12 Commerce

NCERT Solutions Class 10›

NCERT Solutions Class 11›
 NCERT Solutions Class 11
 NCERT Solutions Class 11 Statistics
 NCERT Solutions Class 11 Accountancy
 NCERT Solutions Class 11 Biology
 NCERT Solutions Class 11 Chemistry
 NCERT Solutions Class 11 Commerce
 NCERT Solutions Class 11 English
 NCERT Solutions Class 11 Hindi
 NCERT Solutions Class 11 Maths
 NCERT Solutions Class 11 Physics

NCERT Solutions Class 9›

NCERT Solutions Class 8›

NCERT Solutions Class 7›

NCERT Solutions Class 6›

NCERT Solutions Class 5›
 NCERT Solutions Class 5
 NCERT Solutions Class 5 EVS
 NCERT Solutions Class 5 English
 NCERT Solutions Class 5 Maths

NCERT Solutions Class 4›

NCERT Solutions Class 3›

NCERT Solutions Class 2›
 NCERT Solutions Class 2
 NCERT Solutions Class 2 Hindi
 NCERT Solutions Class 2 Maths
 NCERT Solutions Class 2 English

NCERT Solutions Class 1›
 NCERT Solutions Class 1
 NCERT Solutions Class 1 English
 NCERT Solutions Class 1 Hindi
 NCERT Solutions Class 1 Maths

JEE Main Question Papers›

JEE Main Syllabus›
 JEE Main Syllabus
 JEE Main Chemistry Syllabus
 JEE Main Maths Syllabus
 JEE Main Physics Syllabus

JEE Main Questions›
 JEE Main Questions
 JEE Main Maths Questions
 JEE Main Physics Questions
 JEE Main Chemistry Questions

JEE Main Mock Test›
 JEE Main Mock Test

JEE Main Revision Notes›
 JEE Main Revision Notes

JEE Main Sample Papers›
 JEE Main Sample Papers

JEE Advanced Question Papers›

JEE Advanced Syllabus›
 JEE Advanced Syllabus

JEE Advanced Mock Test›
 JEE Advanced Mock Test

JEE Advanced Questions›
 JEE Advanced Questions
 JEE Advanced Chemistry Questions
 JEE Advanced Maths Questions
 JEE Advanced Physics Questions

JEE Advanced Sample Papers›
 JEE Advanced Sample Papers

NEET Eligibility Criteria›
 NEET Eligibility Criteria

NEET Question Papers›

NEET Sample Papers›
 NEET Sample Papers

NEET Syllabus›

NEET Mock Test›
 NEET Mock Test

NCERT Books Class 9›
 NCERT Books Class 9

NCERT Books Class 8›
 NCERT Books Class 8

NCERT Books Class 7›
 NCERT Books Class 7

NCERT Books Class 6›
 NCERT Books Class 6

NCERT Books Class 5›
 NCERT Books Class 5

NCERT Books Class 4›
 NCERT Books Class 4

NCERT Books Class 3›
 NCERT Books Class 3

NCERT Books Class 2›
 NCERT Books Class 2

NCERT Books Class 1›
 NCERT Books Class 1

NCERT Books Class 12›
 NCERT Books Class 12

NCERT Books Class 11›
 NCERT Books Class 11

NCERT Books Class 10›
 NCERT Books Class 10

Chemistry Full Forms›
 Chemistry Full Forms

Biology Full Forms›
 Biology Full Forms

Physics Full Forms›
 Physics Full Forms

Educational Full Form›
 Educational Full Form

Examination Full Forms›
 Examination Full Forms

Algebra Formulas›
 Algebra Formulas

Chemistry Formulas›
 Chemistry Formulas

Geometry Formulas›
 Geometry Formulas

Math Formulas›
 Math Formulas

Physics Formulas›
 Physics Formulas

Trigonometry Formulas›
 Trigonometry Formulas

CUET Admit Card›
 CUET Admit Card

CUET Application Form›
 CUET Application Form

CUET Counselling›
 CUET Counselling

CUET Cutoff›
 CUET Cutoff

CUET Previous Year Question Papers›
 CUET Previous Year Question Papers

CUET Results›
 CUET Results

CUET Sample Papers›
 CUET Sample Papers

CUET Syllabus›
 CUET Syllabus

CUET Eligibility Criteria›
 CUET Eligibility Criteria

CUET Exam Centers›
 CUET Exam Centers

CUET Exam Dates›
 CUET Exam Dates

CUET Exam Pattern›
 CUET Exam Pattern
CBSE Class 8 Mathematics Revision Notes Chapter 16 – Playing with Numbers
In this Class 8 Mathematics chapter 16 notes, students will learn about the fun concept of playing with numbers. In addition, in this Class 8 Chapter 16 Maths notes, students will get to know the significant details of the chapter that are important for their final examination. Along with chapter 16 Mathematics Class 8 notes, Extramarks will provide students with important questions that will help them to prepare for the exams quickly. Moreover, Class 8 Mathematics notes chapter 6 will be students’ lastminute revision guide providing all the necessary information about the chapter with essential notes that make it convenient for students to remember everything clearly during the exams. These notes are based on the CBSE syllabus.
These Class 8 chapter 16 notes playing with numbers contain various types of numbers and their uses in mathematical equations. In this chapter, you will learn that there are many types of numbers in the form of whole numbers, natural numbers, integers, rational numbers, etc. This chapter talks about the test of divisibility by exploring digits.
Access Class 8 Mathematics Chapter 16 – Playing with Numbers
Numbers in General Form
 If a number is expressed as the sum of the products of its digits with their respective place values, it can be written in a general form.
 ab is 10×a+b is the general form of a twodigit number.
 100a+10b+c is the general form of the threedigit number abc.
Games with Numbers
 Reversing Twodigit Number:
 Decide on a twodigit number.
 To create a new number, reverse the selected digit.
 Add the initial number to this amount.
 Now divide the result by 11.
 No remainder will be left.
 Reversing Threedigit Number:
 Decide on a threedigit number.
 To create a new number, reverse the selected digit.
 Take the smaller number out of the larger one.
 Divide the result by 99.
 No remainder will be left.
 Forming Threedigit Numbers with Given Threedigits:
 Decide on a threedigit number.
 Using the selected number, create two additional threedigit numbers.
 Using the selected number, create two additional threedigit numbers. Then add them.
 Next, divide the result by 37.
 No remainder will be left.
Letters for Digits
Rule to remember while solving letters for digits puzzles:
 A single digit must be used to represent each digit.
 A number’s first digit must not be zero.
Example:
Find Q in addition.
The digit in column one should be Q=8 because, from Q+3, we get 1, which is a number whose one digit is 1.
Tests of Divisibility
 Divisibility by 10
When a number’s one digit is 0, it is only a multiple of 10 and, therefore, divisible by 10. For instance, 520, 950, 630, 20, etc.
 Divisibility by 5
When a number’s one digit is either 0 or 5, then only that number is a multiple of 5. That number is divisible by 5. For instance, 50, 95, 65, 20, etc.
 Divisibility by 2
When a number’s one digit is 0, 2, 4, 6, or 8, it is divisible by 2; consequently, every even number is divisible by 2. For instance: 50, 92, 64, 26, etc.
 Divisibility by 9 and 3
When the sum of a digit of a number is 3, that number is divisible by three. For instance, the number 7263 is divisible by 3 because the sum of its digits is 18, and 18 is a multiple of 2. When the sum of digits of a number is 9, that number is divisible by 9.
For instance, the number 215847 is divisible by 9 because of the sum of its digits, 27. Therefore, 215847 is also divisible by 9.
Examples of Playing with Numbers
We must determine the values of A and B in the problem above.
Here we have A + 5 = 2 by adding the values of the one.
that means one value of the response is 2;
This means that A=7.
Hence 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
A has a value of 7, and B has a value of 6.
We can also find the values in multiplication problems in the same manner.
Think about the issue.
B A
* B 3
becomes
5 7 A
Here, we must discover the values of A and B.
A should have a value of 0 or 5 because the one’s digit in the expression A*3 is A.
As a result, we choose the other option, which will be true if A = 0 and B = 2.
20 * 23 = 460
Choose a different course of action if this is also incorrect.
if A = 5 and B = 2, then
25 * 23 = 575.
therefore, A = 5 and B = 2.
Test of Divisibility in Class 8 Revision Notes Playing With Numbers
In this part of Class 8, Chapter 14, you will learn about the divisibility of 2, 3, 5, 6, 9, and 10.
Divisibility of 2
Let’s first examine the divisibility of 2:
Let’s review the natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, and 9.
A whole number is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, …….
If a natural number’s last digit is 2, 4, 6, 8, or 0, it becomes an even number.
All even numbers are divisible by 2.
If the formula for the number ABC is 100*A + 10*B +C,
Here, 100 A and 10 B can be divided by two because their value in one’s place is zero. At the same time, the value of C determines if it can be divisible by 2.
At the same time, C’s value determines whether it can be divided by 2 or not.
If C is even, then ABC can be divided by two because 100*A, 10*B, and C can all be divided by two, which means that their sum can also be divided by 2.
2 can not divide ABC if C is odd or any other value, such as an integer or another number.
Example:
128 can be written as (100 * 1) + (10 * 2) + 8
= 100+20+8
Here, 100 can be divided by 2.
20 can be divided by 2.
8 can be divided by 2 as well.
Therefore, 128 can be divided by 2 as well.
Divisibility of 3
According to the mathematical principle, a number is divisible by three if the sum of its digits is a multiple of three. Example:
Let’s look at 1254 to see if it can be divided into smaller amounts.
1 + 2 + 5 + 4 = 12. 12 is a multiple of 3 here. It can therefore be divided by 3.
Divisibility of 9
The rule of mathematics that applies in this situation is that if a number’s digit sum is a multiple of 3, the number itself is divisible by 9.
Take the number 3582 into consideration. Its digit sum of 3 + 5 + 8 + 2 is 18, which can be divided by 9. 3582 is therefore also divisible by 9.
Divisibility of 5
If the last digit is either 5 or 0, then the number is divisible by 5, according to the mathematical rule in this situation.
Divisibility of 10
Here, the rule of mathematics is “if the last digit is 0, the number is divisible by 10.”
Test of Divisibility Example
Find the value of y if 21y5 is a multiple of 9 and y is a digit.
Solution:
A number’s digit sum will also be divisible by 9 if the number is divisible by 9. so 2 + 1 + y + 5 = 8 + y.
Thus, y could be 1, 10, etc.
Y = 1 because y is a single digit.
The result is 2115.
The method learned above can be used to solve puzzles.
Why choose Extramarks?
These notes contain all the topics in the NCERT books concisely. Download the Class 8 Revision Notes for Mathematics Chapter 7 on this page to improve your exam results. Once you go through these notes, you can easily solve CBSE sample papers to further improve your mathematical ability to solve questions. These notes also contain CBSE extra questions that will help students to test their level of preparedness for the exam. .
These CBSE revision notes are made according to the CBSE syllabus. The questions in these notes are based on CBSE’s past years’ question papers. These notes contain Important questions and Formulas to help students achieve high grades in their examinations.
FAQs (Frequently Asked Questions)
1. How can we represent numbers in a general form?
A number with 2 digits can be expressed in the form
10a + b=ab
2. What do you mean by a twodigit number?
A twodigit number is a number with a ones and tens place value.
3. What is the principle for divisibility of 5?
The principle states that if the last of a given number is either 5 or 0, then it will be divisible by 5.
4. What is the principle for divisibility of 10?
The principle states that if the last digit of a given number is 0, then it will be divisible by 10.