NCERT Textbook - Whole Numbers Class 6 Notes | EduRev

Mathematics (Maths) Class 6

Created by: Praveen Kumar

Class 6 : NCERT Textbook - Whole Numbers Class 6 Notes | EduRev

 Page 1


As we know, we use 1, 2, 3, 4,... when we begin to count. They come naturally
when we start counting. Hence, mathematicians call the counting numbers as
Natural numbers.
Predecessor and successor
Given any natural number, you can add 1 to
that number and get the next number i.e. you
get its successor.
The successor of 16 is 16 + 1 = 17,
that of 19 is 19 +1 = 20 and so on.
The number 16 comes before 17, we
say that the predecessor of 17 is 17–1=16,
the predecessor of 20 is 20 – 1 = 19, and
so on.
The number 3 has a predecessor and a
successor. What about 2? The successor is
3 and the predecessor is 1. Does 1 have both
a successor and a predecessor?
We can count the number of children in our school; we
can also count the number of people in a city; we can count
the number of people in India. The number of people in the
whole world can also be counted. We may not be able to
count the number of stars in the sky or the number of hair
on our heads but if we are able, there would be a number for
them also. We can then add one more to such a number and
2.1 Introduction
Chapter 2
W W Wh h ho o ol l le e e
N N Nu u um m mb b be e er r rs s s
1. Write the predecessor
and successor of
19; 1997; 12000;
49; 100000.
2. Is there any natural
number that has no
predecessor?
3. Is there any natural
number which has no
successor? Is there a
last natural number?
Page 2


As we know, we use 1, 2, 3, 4,... when we begin to count. They come naturally
when we start counting. Hence, mathematicians call the counting numbers as
Natural numbers.
Predecessor and successor
Given any natural number, you can add 1 to
that number and get the next number i.e. you
get its successor.
The successor of 16 is 16 + 1 = 17,
that of 19 is 19 +1 = 20 and so on.
The number 16 comes before 17, we
say that the predecessor of 17 is 17–1=16,
the predecessor of 20 is 20 – 1 = 19, and
so on.
The number 3 has a predecessor and a
successor. What about 2? The successor is
3 and the predecessor is 1. Does 1 have both
a successor and a predecessor?
We can count the number of children in our school; we
can also count the number of people in a city; we can count
the number of people in India. The number of people in the
whole world can also be counted. We may not be able to
count the number of stars in the sky or the number of hair
on our heads but if we are able, there would be a number for
them also. We can then add one more to such a number and
2.1 Introduction
Chapter 2
W W Wh h ho o ol l le e e
N N Nu u um m mb b be e er r rs s s
1. Write the predecessor
and successor of
19; 1997; 12000;
49; 100000.
2. Is there any natural
number that has no
predecessor?
3. Is there any natural
number which has no
successor? Is there a
last natural number?
WHOLE NUMBERS
29
get a larger number. In that case we can even write the number of hair on two
heads taken together.
It is now perhaps obvious that there is no largest number. Apart from these
questions shared above, there are many others that can come to our mind
when we work with natural numbers. You can think of a few such questions
and discuss them with your friends. You may not clearly know the answers to
many of them !
2.2 Whole Numbers
We have seen that the number 1 has no predecessor in natural numbers. To the
collection of natural numbers we add zero as the predecessor for 1.
The natural numbers along with zero form the collection of whole
numbers.
In your previous classes you have learnt to
perform all the basic operations like addition,
subtraction, multiplication and division on
numbers. Y ou also know how to apply them to
problems. Let us try them on a number line.
Before we proceed, let us find out what a
number line is!
2.3 The Number Line
Draw a line. Mark a point on it. Label it 0. Mark a second point to the right of
0. Label it 1.
The distance between these points labelled as 0 and 1 is called unit distance.
On this line, mark a point to the right of 1 and at unit distance from 1 and
label it 2. In this way go on labelling points at unit distances as 3, 4, 5,... on
the line. You can go to any whole number on the right in this manner.
This is a number line for the whole numbers.
What is the distance between the points 2 and 4? Certainly, it is 2 units.
Can you tell the distance between the points 2 and 6, between 2 and 7?
On the number line you will see that the number 7 is on the right of 4.
This number 7 is greater than 4, i.e. 7 > 4. The number 8 lies on the right of 6
1. Are all natural numbers
also whole numbers?
2. Are all whole numbers
also natural numbers?
3. Which is the greatest
whole number?
Page 3


As we know, we use 1, 2, 3, 4,... when we begin to count. They come naturally
when we start counting. Hence, mathematicians call the counting numbers as
Natural numbers.
Predecessor and successor
Given any natural number, you can add 1 to
that number and get the next number i.e. you
get its successor.
The successor of 16 is 16 + 1 = 17,
that of 19 is 19 +1 = 20 and so on.
The number 16 comes before 17, we
say that the predecessor of 17 is 17–1=16,
the predecessor of 20 is 20 – 1 = 19, and
so on.
The number 3 has a predecessor and a
successor. What about 2? The successor is
3 and the predecessor is 1. Does 1 have both
a successor and a predecessor?
We can count the number of children in our school; we
can also count the number of people in a city; we can count
the number of people in India. The number of people in the
whole world can also be counted. We may not be able to
count the number of stars in the sky or the number of hair
on our heads but if we are able, there would be a number for
them also. We can then add one more to such a number and
2.1 Introduction
Chapter 2
W W Wh h ho o ol l le e e
N N Nu u um m mb b be e er r rs s s
1. Write the predecessor
and successor of
19; 1997; 12000;
49; 100000.
2. Is there any natural
number that has no
predecessor?
3. Is there any natural
number which has no
successor? Is there a
last natural number?
WHOLE NUMBERS
29
get a larger number. In that case we can even write the number of hair on two
heads taken together.
It is now perhaps obvious that there is no largest number. Apart from these
questions shared above, there are many others that can come to our mind
when we work with natural numbers. You can think of a few such questions
and discuss them with your friends. You may not clearly know the answers to
many of them !
2.2 Whole Numbers
We have seen that the number 1 has no predecessor in natural numbers. To the
collection of natural numbers we add zero as the predecessor for 1.
The natural numbers along with zero form the collection of whole
numbers.
In your previous classes you have learnt to
perform all the basic operations like addition,
subtraction, multiplication and division on
numbers. Y ou also know how to apply them to
problems. Let us try them on a number line.
Before we proceed, let us find out what a
number line is!
2.3 The Number Line
Draw a line. Mark a point on it. Label it 0. Mark a second point to the right of
0. Label it 1.
The distance between these points labelled as 0 and 1 is called unit distance.
On this line, mark a point to the right of 1 and at unit distance from 1 and
label it 2. In this way go on labelling points at unit distances as 3, 4, 5,... on
the line. You can go to any whole number on the right in this manner.
This is a number line for the whole numbers.
What is the distance between the points 2 and 4? Certainly, it is 2 units.
Can you tell the distance between the points 2 and 6, between 2 and 7?
On the number line you will see that the number 7 is on the right of 4.
This number 7 is greater than 4, i.e. 7 > 4. The number 8 lies on the right of 6
1. Are all natural numbers
also whole numbers?
2. Are all whole numbers
also natural numbers?
3. Which is the greatest
whole number?
MATHEMATICS
30
and 8 > 6. These observations help us to say that, out of any two whole
numbers, the number on the right of the other number is the greater number.
We can also say that whole number on left is the smaller number.
For example, 4 < 9; 4 is on the left of 9. Similarly, 12 > 5; 12 is to the
right of 5.
What can you say about 10 and 20?
Mark 30, 12, 18 on the number line. Which number is at the farthest left?
Can you say from 1005 and 9756, which number would be on the right
relative to the other number.
    Place the successor of 12 and the predecessor of 7 on the number line.
Addition on the number line
Addition of whole numbers can be shown on the number line. Let us see the
addition of 3 and 4.
Start from 3. Since we add 4 to this number so we
make 4 jumps to the right; from 3 to 4, 4 to 5, 5 to 6 and 6
to 7 as shown above. The tip of the last arrow in the fourth
jump is at 7.
The sum of 3 and 4 is 7, i.e. 3 + 4 = 7.
Subtraction on the number line
The subtraction of two whole numbers can also be shown on the number line.
Let us find 7 – 5.
Start from 7. Since 5 is being subtracted, so move
towards left with 1 jump of 1 unit. Make 5 such jumps. We
reach the point 2. We get 7 – 5 = 2.
Multiplication on the number line
We now see the multiplication of whole numbers on the
number line.
Let us find 4 × 3.
Find 4 + 5;
2 + 6; 3 + 5
and 1+6
using the
number line.
Find 8 – 3;
6 – 2; 9 – 6
using the
number line.
Page 4


As we know, we use 1, 2, 3, 4,... when we begin to count. They come naturally
when we start counting. Hence, mathematicians call the counting numbers as
Natural numbers.
Predecessor and successor
Given any natural number, you can add 1 to
that number and get the next number i.e. you
get its successor.
The successor of 16 is 16 + 1 = 17,
that of 19 is 19 +1 = 20 and so on.
The number 16 comes before 17, we
say that the predecessor of 17 is 17–1=16,
the predecessor of 20 is 20 – 1 = 19, and
so on.
The number 3 has a predecessor and a
successor. What about 2? The successor is
3 and the predecessor is 1. Does 1 have both
a successor and a predecessor?
We can count the number of children in our school; we
can also count the number of people in a city; we can count
the number of people in India. The number of people in the
whole world can also be counted. We may not be able to
count the number of stars in the sky or the number of hair
on our heads but if we are able, there would be a number for
them also. We can then add one more to such a number and
2.1 Introduction
Chapter 2
W W Wh h ho o ol l le e e
N N Nu u um m mb b be e er r rs s s
1. Write the predecessor
and successor of
19; 1997; 12000;
49; 100000.
2. Is there any natural
number that has no
predecessor?
3. Is there any natural
number which has no
successor? Is there a
last natural number?
WHOLE NUMBERS
29
get a larger number. In that case we can even write the number of hair on two
heads taken together.
It is now perhaps obvious that there is no largest number. Apart from these
questions shared above, there are many others that can come to our mind
when we work with natural numbers. You can think of a few such questions
and discuss them with your friends. You may not clearly know the answers to
many of them !
2.2 Whole Numbers
We have seen that the number 1 has no predecessor in natural numbers. To the
collection of natural numbers we add zero as the predecessor for 1.
The natural numbers along with zero form the collection of whole
numbers.
In your previous classes you have learnt to
perform all the basic operations like addition,
subtraction, multiplication and division on
numbers. Y ou also know how to apply them to
problems. Let us try them on a number line.
Before we proceed, let us find out what a
number line is!
2.3 The Number Line
Draw a line. Mark a point on it. Label it 0. Mark a second point to the right of
0. Label it 1.
The distance between these points labelled as 0 and 1 is called unit distance.
On this line, mark a point to the right of 1 and at unit distance from 1 and
label it 2. In this way go on labelling points at unit distances as 3, 4, 5,... on
the line. You can go to any whole number on the right in this manner.
This is a number line for the whole numbers.
What is the distance between the points 2 and 4? Certainly, it is 2 units.
Can you tell the distance between the points 2 and 6, between 2 and 7?
On the number line you will see that the number 7 is on the right of 4.
This number 7 is greater than 4, i.e. 7 > 4. The number 8 lies on the right of 6
1. Are all natural numbers
also whole numbers?
2. Are all whole numbers
also natural numbers?
3. Which is the greatest
whole number?
MATHEMATICS
30
and 8 > 6. These observations help us to say that, out of any two whole
numbers, the number on the right of the other number is the greater number.
We can also say that whole number on left is the smaller number.
For example, 4 < 9; 4 is on the left of 9. Similarly, 12 > 5; 12 is to the
right of 5.
What can you say about 10 and 20?
Mark 30, 12, 18 on the number line. Which number is at the farthest left?
Can you say from 1005 and 9756, which number would be on the right
relative to the other number.
    Place the successor of 12 and the predecessor of 7 on the number line.
Addition on the number line
Addition of whole numbers can be shown on the number line. Let us see the
addition of 3 and 4.
Start from 3. Since we add 4 to this number so we
make 4 jumps to the right; from 3 to 4, 4 to 5, 5 to 6 and 6
to 7 as shown above. The tip of the last arrow in the fourth
jump is at 7.
The sum of 3 and 4 is 7, i.e. 3 + 4 = 7.
Subtraction on the number line
The subtraction of two whole numbers can also be shown on the number line.
Let us find 7 – 5.
Start from 7. Since 5 is being subtracted, so move
towards left with 1 jump of 1 unit. Make 5 such jumps. We
reach the point 2. We get 7 – 5 = 2.
Multiplication on the number line
We now see the multiplication of whole numbers on the
number line.
Let us find 4 × 3.
Find 4 + 5;
2 + 6; 3 + 5
and 1+6
using the
number line.
Find 8 – 3;
6 – 2; 9 – 6
using the
number line.
WHOLE NUMBERS
31
Start from 0, move 3 units at a time to the right, make
such 4 moves. Where do you reach? You will reach 12.
So, we say, 3 × 4 = 12.
EXERCISE 2.1
1. Write the next three natural numbers after 10999.
2. Write the three whole numbers occurring just before 10001.
3. Which is the smallest whole number?
4. How many whole numbers are there between 32 and 53?
5. Write the successor of :
(a) 2440701 (b) 100199 (c) 1099999 (d) 2345670
6. Write the predecessor of :
(a) 94 (b) 10000 (c) 208090 (d) 7654321
7. In each of the following pairs of numbers, state which whole number is on the left of
the other number on the number line. Also write them with the appropriate sign (>, <)
between them.
(a) 530, 503 (b) 370, 307 (c) 98765, 56789 (d) 9830415, 10023001
8. Which of the following statements are true (T) and which are false (F) ?
(a) Zero is the smallest natural number. (b) 400 is the predecessor of 399.
(c) Zero is the smallest whole number. (d) 600 is the successor of 599.
(e) All natural numbers are whole numbers.
(f ) All whole numbers are natural numbers.
(g) The predecessor of a two digit number is never a single digit number.
(h) 1 is the smallest whole number.
(i) The natural number 1 has no predecessor.
(j) The whole number 1 has no predecessor.
(k) The whole number 13 lies between 11 and 12.
(l) The whole number 0 has no predecessor.
(m) The successor of a two digit number is always a two digit number.
2.4 Properties of Whole Numbers
When we look into various operations on numbers closely, we notice several
properties of whole numbers. These properties help us to understand the
numbers better. Moreover, they make calculations under  certain operations
very simple.
Find 2 × 6;
3 × 3; 4 × 2
using the
number line.
Page 5


As we know, we use 1, 2, 3, 4,... when we begin to count. They come naturally
when we start counting. Hence, mathematicians call the counting numbers as
Natural numbers.
Predecessor and successor
Given any natural number, you can add 1 to
that number and get the next number i.e. you
get its successor.
The successor of 16 is 16 + 1 = 17,
that of 19 is 19 +1 = 20 and so on.
The number 16 comes before 17, we
say that the predecessor of 17 is 17–1=16,
the predecessor of 20 is 20 – 1 = 19, and
so on.
The number 3 has a predecessor and a
successor. What about 2? The successor is
3 and the predecessor is 1. Does 1 have both
a successor and a predecessor?
We can count the number of children in our school; we
can also count the number of people in a city; we can count
the number of people in India. The number of people in the
whole world can also be counted. We may not be able to
count the number of stars in the sky or the number of hair
on our heads but if we are able, there would be a number for
them also. We can then add one more to such a number and
2.1 Introduction
Chapter 2
W W Wh h ho o ol l le e e
N N Nu u um m mb b be e er r rs s s
1. Write the predecessor
and successor of
19; 1997; 12000;
49; 100000.
2. Is there any natural
number that has no
predecessor?
3. Is there any natural
number which has no
successor? Is there a
last natural number?
WHOLE NUMBERS
29
get a larger number. In that case we can even write the number of hair on two
heads taken together.
It is now perhaps obvious that there is no largest number. Apart from these
questions shared above, there are many others that can come to our mind
when we work with natural numbers. You can think of a few such questions
and discuss them with your friends. You may not clearly know the answers to
many of them !
2.2 Whole Numbers
We have seen that the number 1 has no predecessor in natural numbers. To the
collection of natural numbers we add zero as the predecessor for 1.
The natural numbers along with zero form the collection of whole
numbers.
In your previous classes you have learnt to
perform all the basic operations like addition,
subtraction, multiplication and division on
numbers. Y ou also know how to apply them to
problems. Let us try them on a number line.
Before we proceed, let us find out what a
number line is!
2.3 The Number Line
Draw a line. Mark a point on it. Label it 0. Mark a second point to the right of
0. Label it 1.
The distance between these points labelled as 0 and 1 is called unit distance.
On this line, mark a point to the right of 1 and at unit distance from 1 and
label it 2. In this way go on labelling points at unit distances as 3, 4, 5,... on
the line. You can go to any whole number on the right in this manner.
This is a number line for the whole numbers.
What is the distance between the points 2 and 4? Certainly, it is 2 units.
Can you tell the distance between the points 2 and 6, between 2 and 7?
On the number line you will see that the number 7 is on the right of 4.
This number 7 is greater than 4, i.e. 7 > 4. The number 8 lies on the right of 6
1. Are all natural numbers
also whole numbers?
2. Are all whole numbers
also natural numbers?
3. Which is the greatest
whole number?
MATHEMATICS
30
and 8 > 6. These observations help us to say that, out of any two whole
numbers, the number on the right of the other number is the greater number.
We can also say that whole number on left is the smaller number.
For example, 4 < 9; 4 is on the left of 9. Similarly, 12 > 5; 12 is to the
right of 5.
What can you say about 10 and 20?
Mark 30, 12, 18 on the number line. Which number is at the farthest left?
Can you say from 1005 and 9756, which number would be on the right
relative to the other number.
    Place the successor of 12 and the predecessor of 7 on the number line.
Addition on the number line
Addition of whole numbers can be shown on the number line. Let us see the
addition of 3 and 4.
Start from 3. Since we add 4 to this number so we
make 4 jumps to the right; from 3 to 4, 4 to 5, 5 to 6 and 6
to 7 as shown above. The tip of the last arrow in the fourth
jump is at 7.
The sum of 3 and 4 is 7, i.e. 3 + 4 = 7.
Subtraction on the number line
The subtraction of two whole numbers can also be shown on the number line.
Let us find 7 – 5.
Start from 7. Since 5 is being subtracted, so move
towards left with 1 jump of 1 unit. Make 5 such jumps. We
reach the point 2. We get 7 – 5 = 2.
Multiplication on the number line
We now see the multiplication of whole numbers on the
number line.
Let us find 4 × 3.
Find 4 + 5;
2 + 6; 3 + 5
and 1+6
using the
number line.
Find 8 – 3;
6 – 2; 9 – 6
using the
number line.
WHOLE NUMBERS
31
Start from 0, move 3 units at a time to the right, make
such 4 moves. Where do you reach? You will reach 12.
So, we say, 3 × 4 = 12.
EXERCISE 2.1
1. Write the next three natural numbers after 10999.
2. Write the three whole numbers occurring just before 10001.
3. Which is the smallest whole number?
4. How many whole numbers are there between 32 and 53?
5. Write the successor of :
(a) 2440701 (b) 100199 (c) 1099999 (d) 2345670
6. Write the predecessor of :
(a) 94 (b) 10000 (c) 208090 (d) 7654321
7. In each of the following pairs of numbers, state which whole number is on the left of
the other number on the number line. Also write them with the appropriate sign (>, <)
between them.
(a) 530, 503 (b) 370, 307 (c) 98765, 56789 (d) 9830415, 10023001
8. Which of the following statements are true (T) and which are false (F) ?
(a) Zero is the smallest natural number. (b) 400 is the predecessor of 399.
(c) Zero is the smallest whole number. (d) 600 is the successor of 599.
(e) All natural numbers are whole numbers.
(f ) All whole numbers are natural numbers.
(g) The predecessor of a two digit number is never a single digit number.
(h) 1 is the smallest whole number.
(i) The natural number 1 has no predecessor.
(j) The whole number 1 has no predecessor.
(k) The whole number 13 lies between 11 and 12.
(l) The whole number 0 has no predecessor.
(m) The successor of a two digit number is always a two digit number.
2.4 Properties of Whole Numbers
When we look into various operations on numbers closely, we notice several
properties of whole numbers. These properties help us to understand the
numbers better. Moreover, they make calculations under  certain operations
very simple.
Find 2 × 6;
3 × 3; 4 × 2
using the
number line.
MATHEMATICS
32
Let each one of you in the class take any two whole numbers and add them.
Is the result always a whole number?
Y our additions may be like this:
Try with five other pairs of numbers. Is the sum always a whole number?
Did you find a pair of whole numbers whose sum is not a whole number?
Hence, we say that sum of any two whole numbers is a whole number i.e. the
collection of whole numbers is closed under addition. This property is known
as the closure property for addition of whole numbers.
Are the whole numbers closed under multiplication too? How will you
check it?
Your multiplications may be like this :
The multiplication of two whole numbers is also found to be a whole
number again. We say that the system of whole numbers is closed under
multiplication.
Closure property : Whole numbers are closed under addition and also
under multiplication.
Think, discuss and write
1. The whole numbers
are not closed under
subtraction. Why?
Your subtractions may
be like this :
Take a few examples of your own and confirm.
7 × 8 = 56, a whole number
5 × 5 = 25, a whole number
0 × 15 = 0, a whole number
. × . = …
. × . = …
Do This
7 + 8 = 15, a whole number
5 + 5 = 10, a whole number
0 + 15 = 15, a whole number
. + . = …
. + . = …
6 – 2 = 4, a whole number
7 – 8 = ?, not a whole number
5 – 4 = 1, a whole number
3 – 9 = ?, not a whole number
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