# NCERT Class 6 Maths Chapter 2 ‘Whole Numbers’: Notes and Solutions (Free PDF)

In this chapter, students will understand the concept of numbers. The students will get to know that there is no limit to any number – it can be as small and as great as possible. The chapter covers topics like whole numbers, the properties of whole numbers, the number line, patterns and more. Read through for CBSE Class 6 NCERT Maths Chapter 2 Whole Numbers Notes and Important Questions.

## CBSE Class 6 NCERT Maths Chapter 2 Notes – Free PDF Download

Below we have given topic-wise notes for the CBSE Class 6 NCERT Maths Chapter 2 Notes. We have also provided a downloadable free PDF at the end of these notes so you can download and take a printout to study later when you need quick revision before going to the exam hall.

### Topic 1: Whole Numbers

The set of natural numbers along with zero are called whole numbers.

Successor: The numbers which come on adding 1 to the given number.

For eg, 16 + 1 = 17 (17 is the successor)

5 + 1 = 6 (6 is the successor)

Predecessor: The number obtained by subtracting 1 from the given number.

For eg, 16 – 1 = 15 (15 is the predecessor)

5 – 1 = 4 (4 is the predeccessor)

### Topic 2: Number Line

When you arrange a series of numbers at a unit’s distance from each other, they form a number line.

### Topic 3: Properties of the Whole Numbers

1. Closure Property: The addition and multiplication of two whole numbers result in a whole number.

For eg, 2 +1 = 3, 10 × 50 = 500, 99 + 1 = 100 and so on

1. Commutative Property: The addition and multiplication of two or more whole numbers in any order result in the same value.

For eg, 3 + 4 = 4 + 3 = 7

3 × 4 = 4 × 3 = 12

1. Associative Property: The addition and multiplication of two or more whole numbers in any manner result in the same value.

For eg, 2 + (3 + 4) = (2 + 3) + 4 = 9

2 × (3 × 4) = (2 × 3) × 4 =24

1. Distributivity of multiplication over addition: a × (b + c) = (a × b) + (a × c)

### Topic 4: Number Identity

1. 0 is the identity of the addition of whole numbers. This means that any whole number when added with 0 results in the same number in the answer.

For eg, 0 + 1 = 1, 6 + 0 = 6

1. 1 is the identity for the multiplication of whole numbers.

## Important Questions in NCERT Class 6 Maths Chapter 2: Free PDF Download

Below we have provided some important exercise questions and their solutions from Chapter 2 of CBSE NCERT Maths for Class 6.

### Exercise 2.1

Q 1. Which is the smallest whole number?

Ans. 0 is the smallest whole number.

Q 2. Write the successor of each of (a) 897, (b) 1099999 and (c) 2345670

Ans. The successor of a given number is the next successive number in the series which can obtained by adding “1” to the given number.

1. 897 + 1 = 898
2. 1099999 + 1 = 1100000
3. 2345670 + 1 = 2345671

Q 3. State whether the given statements are True (T) or False (F).

1. All whole numbers are natural numbers.
2. All natural numbers are whole numbers.
3. The whole number 1 has no predecessor.
4. The natural number 1 has no predecessor.
5. The whole number 13 lies between 11 and 12.

Ans. The answers to the above statements are given below.

1. False, unlike the natural numbers, the whole numbers also include “0”. So, all whole numbers are not natural numbers.
2. True, all natural numbers when included with zero make whole numbers. So, all natural numbers are whole numbers.
3. False, on subtracting 1 from 1, we get zero. Since whole numbers also include zero, the whole number 1 has 0 as its predecessor.
4. True, natural numbers begin with 1. So, the natural number 1 has no predecessor.
5. Fales, we know that 13 is a greater number than 11 and 12, so it comes to the right of 11 and 12 on the number line.

Also Read: Different Branches of Mathematics

### Exercise 2.2

Q 1. Find the product in each case by suitable rearrangement:

1. 2 × 1768 × 50
2. 285 × 5 × 60
3. 125 × 40 × 8 × 25

Ans. The product of each case is given below.

1. 2 × 1768 × 50

= (2 × 50) × 1768

= 100 × 1768

= 176800

1. 285 × 5 × 60

= (5 × 60) × 285

= 300 × 285

= 85500

1. 125 × 40 × 8 × 25

= (125 × 8) × (40 × 25)

= 1000 × 1000

= 1000000

Q 2. Find the value of the following:

1. 54279 × 92 + 8 × 54279
2. 81265 × 169 – 81265 × 69

Ans. This is the case of the distributive property of multiplication over addition and subtraction. The solutions are given below.

1. 54279 × 92 + 8 × 54279

Taking 54279 common: 54279 × (92 + 8) = 54279 × 100 = 5427900

1. 81265 × 169 – 81265 × 69

Taking 81265 common: 81265 × (169 – 69) = 81265 – 100 = 81165

Q 3. A taxi driver filled his car petrol tank with 40 litres of petrol on Monday. The next day,

he filled the tank with 50 litres of petrol. If the petrol costs 44 per litre, how much did

he spend in all on petrol?

Ans. On day 1, Petrol filled = 40 litres

Cost of 1 litre of Petrol = ₹ 44

So, the cost of 40 litres of Petrol = ₹ 40 × 44

Now, on day 2, Petrol filled = 50 litres

Cost of 1 litre of Petrol = ₹ 44

So, the cost of 50 litres of Petrol = ₹ 50 × 44

Hence, the total cost of petrol = ₹ 40 × 44 +  50 × 44

Now, taking 44 common: ₹ 44 × (40 + 50) = ₹ 44 × 90 = ₹ 3960

The total cost of Petrol is ₹ 3960.

Also Read: Maths Formulas for Class 10

### Exercise 2.3

Q 1. Which of the following will not represent zero:

1. 0 + 1
2. 0/2
3. (10 – 10)/2
4. 0 × 0

Ans. The answers to each of the given questions are given below.

1. 0 + 1 = 1; does not represent zero
2. 0/2 = 0; represents zero
3. (10 – 10)/2 = 0/2 = 0; represents zero
4. 0 × 0 = 0; represents zero

Q 2. If the product of two whole numbers is 1, can we say that one or both of them will be

1? Justify through examples.

Ans. The products of two whole numbers can be equal to 1 only if both the numbers are equal; to 1.

For eg, 1 × 1 = 1

But, 1 × 2 = 2, 1 × 5 = 5 and so on

Hence, the product of two whole numbers can be equal to 1 only if both numbers are equal to 1.

Q 3. Study the pattern :

1 × 8 + 1 = 9

1234 × 8 + 4 = 9876

12 × 8 + 2 = 98

12345 × 8 + 5 = 98765

123 × 8 + 3 = 987

Write the next two steps. Can you say how the pattern works?

(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).

Ans. Re-writing the given pattern:

1 × 8 + 1 = 9

12 × 8 + 2 = 98

123 × 8 + 3 = 987

1234 × 8 + 4 = 9876

12345 × 8 + 5 = 98765

So, the next two steps must be:

123456 × 8 + 6 = 987654, and

1234567 × 8 + 7 = 9876543

Now, checking for the correctness of the above two steps with the help of the given hint:

As given: 12345 = 11111 + 1111 + 111 + 11 + 1

So, 123456 = 111111 + 11111 + 1111 + 111 + 11 + 1

Hence, 123456 × 8 + 6 = (111111 + 11111 + 1111 + 111 + 11 + 1) × 8 + 6

= 888888 + 88888 + 8888 + 888 + 88 +8 + 6

= 987654

Hence, the pattern works here.

Now, again: 1234567 = 1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1

Hence, 1234567 × 8 + 6 = (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1) × 8 + 6

= 8888888 + 888888 + 88888 + 8888 + 888 + 88 +8 + 6

= 9876543

Hence, the pattern works here.

So, the pattern works on the given series.

## CBSE Class 6 NCERT Maths Chapter 2 Whole Numbers Important Questions and Answers PDF – Free Download

Look below for some important questions.

Q 1. The school canteen charges ₹ 20 for lunch and ₹ 4 for milk for each day. How much money do you spend in 5 days on these things?

Ans. Cost of lunch for 1 day = ₹ 20

So, the cost of lunch for 5 days =  ₹ 20 × 5

Similarly, the cost of milk for 1 day = ₹ 4

So, cost of milk for 5 days =  ₹ 4 × 5

Hence, the total cost of milk and lunch for 5 days = ₹ 20 × 5 + 4 × 5

Taking 5 common: 5 × (20 + 4) = 5 × 24 = ₹ 120

Q 2. Find 14 + 17 + 6 in two ways.

Ans. The question can be solved in two ways as-

1. (14 + 17) + 6

= 31 + 6

= 37

1. 14 + 17 + 6

= 14 + 6 + 17

= (14 + 6) + 17

= 20 + 17

= 37

Here, we have used a combination of associative and commutative properties.

Also See:

## FAQs

Q.1. What are whole numbers for class 6?

Ans: The set of natural numbers along with zero are called whole numbers.

Q.2. How to score a perfect 100 in Maths, Class 6?

Ans: The key to scoring a perfect 100 is regular practice. Solve all the problems given in your NCERT textbooks and pick the easiest chapter first for revision before the exam. So, you can take on the lengthy and hard chapters without any guilt later.

Q.3. Which is the smallest whole number, Class 6?

Ans: Zero is the smallest whole number.

This was all about CBSE Class 6 NCERT Maths Chapter 2 Whole Numbers Notes, Exercise and Important Questions PDF Free Download. Follow the CBSE Class 6 Maths Notes for more such chapter notes and important questions and answers for preparation for CBSE Class 6 Maths.