Class 6 Exam  >  Class 6 Notes  >  Maths Olympiad Class 6  >  Chapter Notes: Whole Numbers

Whole Numbers Chapter Notes | Maths Olympiad Class 6 PDF Download

Introduction

  • Numbers play an important role in our life. 
  • We use numbers in our day to day life to count things. 
  • While counting we use numbers to represent any quantity, to measure any distance or length.                                              

Whole Numbers Chapter Notes | Maths Olympiad Class 6

                        3 apples and 3 pepper                                  Discount                          City distance                                             Length of the table 

  • The counting numbers starting from 1, 2, 3, 4, 5, ……… are termed as  natural numbers. 
  • The set of counting numbers and zero are known as whole numbers.
  •  Whole numbers are 0, 1, 2, 3, 4, 5, 6, 7,…….. and so on.Whole Numbers Chapter Notes | Maths Olympiad Class 6

Example: Write the next three natural numbers after 10999. 
Solution: 10999 + 1 = 11000
11000 + 1= 11001
11001 + 2 = 11002.
Thus, 11000, 11001, 11002 are the next three natural numbers after 10999.

Whole numbers on a number line 

Number Line 

A pictorial representations of numbers evenly marked on a straight line is known as a number line. 

  • To mark whole numbers on a number line draw a horizontal line and mark a point on it as 0.
  •  Extend this line towards right direction. 
  • Starting from 0, mark points 1, 2, 3, 4, 5, 6, 7, 8, 9….on a line at equal distance towards right side.
    Whole Numbers Chapter Notes | Maths Olympiad Class 6
  • There is no whole number on the left of zero. Therefore zero is the smallest whole number.

Comparison using Number Line

The number line also helps us to compare two whole numbers. i.e., to decide which of the two given whole numbers is greater or smaller.

  • A whole number is greater than all the whole numbers which lie to the left of it on the number line. 
  • A whole number is less than all the whole numbers which lie to the right of it on the number line
    Example:  We can say that 5 is less than 9 and write 5 < 9.
    We can also say that 5 is greater than 4 and write 5 > 4.Whole Numbers Chapter Notes | Maths Olympiad Class 6

Example: Identify which whole number comes first on the number line in each pair and write the appropriate sign (> or <) between them:
(a) 507 and 503
(b) 338 and 342

Sol:  (a) 503 is on the left side of 507 on the number line. So, 507 > 503.

Whole Numbers Chapter Notes | Maths Olympiad Class 6(b) 338 is on the left side of 342 on the number line. So, 342 > 338.Whole Numbers Chapter Notes | Maths Olympiad Class 6

Operations on a number line

Addition 

For eg: Add 2 and 5. i.e 2 + 5.

  • Start from 0, 2 jumps towards right. You reach at 2. 
  • Start from 2, 5 jumps towards right. You reach at 7. 
  • Therefore, 2 + 5 = 7.Whole Numbers Chapter Notes | Maths Olympiad Class 6

Subtraction 

For eg: Subtract 4 from 7.  i.e 7 - 4.

  • Start from 0, jump directly to 7. 
  • Start from 7,  4 jumps towards left. You reach at 3.
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Multiplication 

For eg:  Multiply 3 and 2 i.e. 3 x 2 

  • Multiplication means repeated addition. Thereofore 3 x 2 means 3 added twice.
  • Start from 0. Make 2 jumps (each jump of 3 units).You reach at 6.
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Division

For eg: 6 ÷ 3 = 2. 

  • Start from 6 and subtract 3 for a number of times till 0 is reached. 
  • The number of times 3 is subtracted gives the quotient.Whole Numbers Chapter Notes | Maths Olympiad Class 6

Ques: Using the number line, determine the following products:
(a) 3 x 3
(b) 4 x 2

Sol: (a)

  • Start from 0. Make 1 jump of 3 steps towards right. You reach at 3.     
  • Start from 3.  Make 1 jump of 3 steps towards right. You reach at 6.     
  • Start from 6. Make 1 jump of 3 steps towards right. You reach at 9.
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Therefore, 3 x 3 = 9

(b) 

  • Start from 0.  Make 1 jump of 4 steps towards right. You reach at 4.      
  • Start from 4.  Make 1 jump of 4 steps towards right. You reach at 8.
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Therefore, 4 x 2 = 8.

Predecessor and Successor

Predecessor

  • The number which comes right before a given number is called its predecessor.
  • The predecessor of a whole number found by subtracting 1 from it.

Number - 1 = Predecessor

Whole Numbers Chapter Notes | Maths Olympiad Class 6

Successor

  • The number which comes right after a given number is called its successor.
  • The successor of a whole number found by adding 1 to it.

Number + 1 = Successor.

Whole Numbers Chapter Notes | Maths Olympiad Class 6


Properties of addition 

Closure property 

  • For any two whole numbers a and b, their sum  a + b is always a whole number.
  • For eg:  12 + 45 = 57. Here, 12, 45 and 57 all are whole numbers.
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Commutative property

  • For any two whole numbers a and b, a +b = b + a. 
  • We can add any two whole numbers in any order.
     For eg:  12 + 45 = 45 + 12
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Associative property

  • For any three whole numbers a, b and c, (a + b) + c = a + (b + c). 
  • This means the sum is regardless of how grouping is done.
    For eg:  31 + (24 + 38) = (31 + 24) + 38
    Whole Numbers Chapter Notes | Maths Olympiad Class 6 

 Additive identity property

  • For every whole number a, a + 0 = a.
  • Therefore ‘0’ is called the Additive identity.
    E.g. 19 + 0 = 19
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Example: Find the sum of 435, 216 and 165
Sol: 435 + 216 + 165
Now, 5 + 5 = 10. So, we add 435 + 165 first.
= (435 + 165) + 216
= 600 + 216 = 816

Example: Find the sum by suitable arrangement:
(a) 837 + 208 + 363            
(b) 1962 + 453 + 1538 + 647      

Sol: (a) 837 + 208 + 363
Now, 7 + 3 = 10.
So, we add 837 + 363 first.
= (837 + 363) + 208
= 1200 + 208 = 1408

(b) 1962 + 453 + 1538 + 647
Now, 2 + 8 = 10 .So, we make one group of (1962 + 1538)
3 + 7 = 10.  Next we make another group of (453 + 647)
= (1962 + 1538) + (453 + 647)
=3500 + 1100 = 4600

Properties of subtraction 

Closure property

  • For any two whole numbers, a and b, if a  > b then a – b is a whole number.
  • If a < b then a – b is never a whole number.
  •  Closure property is not always applicable to subtraction.
    E.g. 150 – 100 = 50, is a whole number but 100 – 150 = -50 is not a whole number.
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Commutative property

  • For any two whole numbers a and b, a – b ≠  b – a . 
  • Hence subtraction of whole number is not commutative.
    E.g  16 – 7 = 9 but  7 – 16 ≠ 9
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Associative property

  • For any three whole numbers a, b and c, (a – b) – c ≠ a – (b – c). 
  • Hence  subtraction of whole numbers is not associative.
    E.g.  25 – (10 – 4) = 25 – 6 = 19  
    Also,  (25 – 10) – 4 = 15 – 4 = 11. This means that 25 – (10 – 4) ≠ (25 – 10) – 4
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

(iv) If 𝒂 is any whole number other than zero, then 𝒂 – 𝟎 = 𝒂 but 𝟎 − 𝒂 is not defined.

For eg: 
(i) 18 – 5 = 13 but 5 – 18 is not defined in whole numbers. 
(ii) 30 – 12 = 18 but 12 – 30 is not defined in whole numbers 

(v) If 𝒂, 𝒃 and 𝒄 are whole numbers such that 𝒂 – 𝒃 = 𝒄, then 𝒃 + 𝒄 = 𝒂Whole Numbers Chapter Notes | Maths Olympiad Class 6

For eg:
(i) If 25 – 16 = 9 then 25 = 9 + 16,
(ii) If 46 – 8 = 38 then 46 = 38 + 8 

Example: Solve the following:

(i) 367 – 99
= 367 + (– 100 + 1)
= 367 – 100 + 1
= (367 + 1) – 100
= 368 – 100
= 268

(ii) 5689 – 99
= 5689 + (- 100 +1)
= 5689 – 100 + 1
= (5689 + 1) – 100
= 5690 – 100
= 5590

Properties of multiplication

Closure property

  • For any two whole numbers a and b,their product  a x b is always a whole number. 
  • E.g. 12 x 7 =  84. Here,  12, 7 and 84 all are whole numbers.
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Commutative property

  • For any two whole numbers a and b, a x b = b x a.
  • Order of multiplication is not important.
    E.g  11 x 6 =  66 and   6 x 11 = 66 Therefore, 11 x 6 = 6 x 11.
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Associative property

  • For any three whole numbers a, b and c, (a x b) x c = a x (b x c). 
  • This means the product is regardless of how grouping is done.
     E.g   8 x (4 x 5) = 8 x 20 = 160;   (8 x 4) x 5 = 32 x 5 = 160 Therefore,  8 x (4 x 5) = (8 x 4) x 5
    Whole Numbers Chapter Notes | Maths Olympiad Class 6
  • We can explain the associative property with the help of following example 
  • Count the number of dots in figure (a) and figure (b)
    Whole Numbers Chapter Notes | Maths Olympiad Class 6
  •  In figure (a), there are 2 rows and 2 columns which means 2 x 2 dots in each box. So the total number of dots are (2 x 2) x 3 = 12 
  • In figure (b), there are 3 rows and 2 columns which means 3 x 2 dots in each box. So the total number of dots are 2 x (3 x 2) = 12
  • This explain the associative property of multiplication.

Multiplicative identity

  • For any whole number a, a x 1 = a.
  • Since any number multiplied by 1 doesn’t change its identity 
  • Hence 1 is called as multiplicative identity of a whole number.
    E.g. 21 x 1 = 21
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Multiplication by zero

  • For any whole number a, a x 0 = 0,
  •  E.g 25 x 0 = 0
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Distributive property of multiplication over Addition

  • This property is used when we have to multiply a number by the sum.
  • If 𝒂, 𝒃&𝒄 are any three whole numbers, then 𝒂 × (𝒃 + 𝒄) = 𝒂 × 𝒃 + 𝒂 × 𝒄.

Example: Find the product by suitable rearrangement:
(i) 4 × 1768 × 25
(ii) 2 × 166 × 50
(iii) 285 × 4 × 75
(iv) 625 × 279 × 16

Sol: 
(i) 4 × 1768 × 25= (4 × 25) × 1768 (by commutative property)
= 100 × 1768 = 176800
(ii) 2 × 166 × 50= (2 × 50) × 166 (by commutative property)
= 100 × 166 = 16600
(iii) 285 × 4 × 75= 285 × (4 × 75) (by commutative property)
= 285 × 300 = 85500
(iv) 625 × 279 × 16= (625 × 16) × 279 (by commutative property)
= 10000 × 279 = 2790000

Properties of division 


Closure property

  • For any two whole numbers a and b, a ÷ b is not always a whole number. 
  • Hence closure property is not applicable to division. 
    For eg:  68 and 5 are whole numbers but 68 ÷ 5 is not a whole number.

    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Commutative property

  • For any two whole numbers a and b, a ÷ b ≠ b ÷ a. 
  • This means division of whole number is not commutative. 
    For eg: 16 ÷ 4 ≠ 4 ÷ 16  
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Associative property

  • For any 3 whole numbers a, b and c,(a ÷ b)  ÷ c ≠ a ÷ (b ÷ c)  
  •  For eg: consider (80 ÷ 10) ÷ 2 = 8 ÷ 2 = 4 80 ÷ (10 ÷2) = 80 ÷ 5 = 16 (80 ÷ 10) ÷ 2 ≠80 ÷ (10 ÷2) 
  • Hence division does not follow associative property. 
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Division by 1

  • For any whole number a, a ÷ 1 = a.
  • This means any whole number divided by 1 gives the quotient as the number itself. 
    For eg: 14 ÷ 1 = 14;                 
     26 ÷ 1 = 26  
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Division of 0 by any whole number

  • For any whole number, a ≠ 0, 0 ÷ a = 0, 
  • This shows zero divided by any whole number (other than zero) gives the quotient as zero.
      For eg: (i) 0 ÷ 1 = 0;                    
    (ii) 0 ÷ 25 = 0;         
    Whole Numbers Chapter Notes | Maths Olympiad Class 6
                  

Division by 0


  • To divide any number, say 7 by 0, we first have to find  out a whole number which when multiplied by 0 gives us 7. This is not possible. 
  • Therefore, division by 0 is not defined.
    Whole Numbers Chapter Notes | Maths Olympiad Class 6

Example: Solve the following
(i) 636 ÷ 1

(ii) 0 ÷ 253
(iii) 246 – (121 ÷ 121)
(iv) (45÷ 5) – (9÷ 3)
Sol: (i) 636 ÷ 1 = 636 (∵ a ÷1 = a )
(ii) 0 ÷ 253 = 0 (∵ 0 ÷ a = 0)
(iii) 246 – (121 ÷ 121)
= 246 – (1)
= 246 – 1
= 245
(iv) (45÷ 5) – (9 ÷ 3)
= 9 – 3 = 6

The document Whole Numbers Chapter Notes | Maths Olympiad Class 6 is a part of the Class 6 Course Maths Olympiad Class 6.
All you need of Class 6 at this link: Class 6
9 videos|114 docs|49 tests

Up next

FAQs on Whole Numbers Chapter Notes - Maths Olympiad Class 6

1. How are whole numbers represented on a number line?
Ans. Whole numbers are represented on a number line by marking points at equal intervals starting from zero in the positive direction. Each point represents a whole number.
2. What are the basic operations that can be performed on a number line with whole numbers?
Ans. The basic operations that can be performed on a number line with whole numbers include addition, subtraction, multiplication, and division.
3. What is the predecessor of a whole number on a number line?
Ans. The predecessor of a whole number on a number line is the whole number that comes before it when moving to the left on the number line.
4. How can we find the successor of a whole number on a number line?
Ans. The successor of a whole number on a number line can be found by moving to the right on the number line and identifying the next whole number.
5. How do whole numbers play a role in everyday life applications?
Ans. Whole numbers are used in everyday life applications such as counting objects, measuring quantities, and representing scores in games and sports.
9 videos|114 docs|49 tests
Download as PDF

Up next

Explore Courses for Class 6 exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Previous Year Questions with Solutions

,

pdf

,

Free

,

Semester Notes

,

Important questions

,

Whole Numbers Chapter Notes | Maths Olympiad Class 6

,

shortcuts and tricks

,

Exam

,

ppt

,

Whole Numbers Chapter Notes | Maths Olympiad Class 6

,

study material

,

mock tests for examination

,

video lectures

,

MCQs

,

Extra Questions

,

Objective type Questions

,

past year papers

,

Sample Paper

,

Whole Numbers Chapter Notes | Maths Olympiad Class 6

,

Viva Questions

,

Summary

,

practice quizzes

;