# NCERT Solutions Class 6 Maths

## Chapter - 2: Whole Numbers

### Exercise 2.1

1. Write the next three natural numbers after 10999.

Explanation: Natural numbers are the positive numbers starting from 1, 2, 3, .. and so on.

10999 +1 = 11000

11000 + 1 = 11001

11001 + 1 = 11002

Thus, the next three natural numbers are 11000, 11001, and 11002.

2. Write the three whole numbers occurring just before 10001.

Explanation: The natural numbers along with zero form the collection of whole

numbers. 0, 1, 2, 3, .. and so on are the whole numbers.

The three whole numbers occuring just before 10001 are:

10001 - 1 = 10000

10000 - 1 = 9999

9999 - 1 = 9998

3. Which is the smallest whole number?

Explanation: 0 is the smallest whole number because whole numbers starts from 0, 1, 2, 3, .. and so on.

4. How many whole numbers are there between 32 and 53?

Explanation: Whole numbers are the natural numbers starting from 0.

The whole numbers between 32 and 53 are:

33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, and 52.

These are the total 20 numbers counting from 33 to 52.

5. Write the successor of :

Explanation: When 1 is added to a number, it is called as a successor of that number.

For example,

2 is the successor of 1

(a) 2440701

2440701+ 1 = 2440702

(b) 100199

100199 + 1 = 100200

(c) 1099999

1099999 + 1 = 1100000

(d) 2345670

2345670 + 1 =2345671

6. Write the predecessor of:

Explanation: When 1 is subtracted from a number, it is called as a predecessor of that number.

For example,

3 is the predecessor of 2

(a) 94

94 - 1 = 93

(b) 10000

10000 - 1 = 9999

(c) 208090

208090 - 1 = 208089

(d) 7654321

7654321 - 1 = 7654320

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.

Explanation: The smaller number is on the left of the other on the number line.

(a) 530, 503

503 is less than 530

Hence, 503 is on the left of 530 on the number line.

(b) 370, 307

307 is less than 370

Hence, 307 is on the left of 370 on the number line.

(c) 98765, 56789

56789 is less than 98765

Hence, 56789 is on the left of 98765 on the number line.

(d) 9830415, 10023001

9830415 is less than 10023001

Hence, 9830415 is on the left of 10023001 on the number line.

8. Which of the following statements are true (T) and which are false (F) ?

(a) Zero is the smallest natural number.

Explanation: 0 is not a natural number. Natural numbers are the positive numbers starting from 1, 2, 3, .. and so on.

(b) 400 is the predecessor of 399.

Explanation: When 1 is subtracted from a number, it is called predecessor. The predecessor of 399 is 398.

(c) Zero is the smallest whole number.

Explanation: Zero is the smallest whole number because whole numbers starts from 0, 1, 2, 3, .. and so on.

(d) 600 is the successor of 599.

Explanation: When 1 is added to a number, it is called successor. The successor of 599 is 600.

(e) All natural numbers are whole numbers.

Explanation: All natural numbers like 1, 2, 3, .. and so on are also the whole numbers.

(f) All whole numbers are natural numbers.

Explanation: 0 is a whole number, but not a natural number.

(g) The predecessor of a two digit number is never a single digit number.

Explanation: The predecessor of a two digit number can also be a single number.

For example,

Predecessor of 10 is 9.

10 - 1 = 9

(h) 1 is the smallest whole number.

Explanation: The natural numbers along with zero form the collection of whole numbers. 0, 1, 2, 3, .. and so on are the whole numbers.

Hence, 0 is the smallest whole number.

(i) The natural number 1 has no predecessor.

Explanation: 1 is the smallest natural number. Hence, it has no predecessor.

(j) The whole number 1 has no predecessor.

Explanation: 0 is the predecessor of 1.

1 - 1 = 0

0 is also a whole number.

(k) The whole number 13 lies between 11 and 12.

Explanation: There is no whole number between 11 and 12.

(l) The whole number 0 has no predecessor.

Explanation: 0 is the smallest whole number and has no predecessor.

(m) The successor of a two digit number is always a two digit number.

Explanation: The successor of a two digit number can also be a three digit number.

For example,

Successor of 99 is 100.

100 is a three digit number.

99 + 1 = 100

### 1. Find the sum by suitable rearrangement:

(a) 837 + 208 + 363

= (837 + 363) + 208

= 1200 + 208

= 1408

(b) 1962 + 453 + 1538 + 647

= (1962 + 1538) + (453 + 647)

= 3500 + 1100

= 4600

### 2. Find the product by suitable rearrangement:

(a) 2 × 1768 × 50

= 1768 × (2 × 50)

= 1768 × 100

= 176800

(b) 4 × 166 × 25

= 166 × (4 × 25)

= 166 × 100

= 16600

(c) 8 × 291 × 125

= 291 × (8 × 125)

= 291 × (1000)

= 291000

(d) 625 × 279 × 16

= 279 × (625 × 16)

= 279 × 10000

= 2790000

(e) 285 × 5 × 60

= 285 × (5 × 60)

= 285 × 300

= 85500

(f) 125 × 40 × 8 × 25

= (125 × 8) × (40 × 25)

= 1000 × 1000

= 1000000

### 3. Find the value of the following:

(a) 297 × 17 + 297 × 3

= 297 × (17 + 3)

= 297 × 20

= 5940

(b) 54279 × 92 + 8 × 54279

= 54279 × (92 + 8)

= 54279 × 100

= 5427900

(c) 81265 × 169 - 81265 × 69

= 81265 × (169 - 69)

= 81265 × 100

= 8126500

(d) 3845 × 5 × 782 + 769 × 25 × 218

(3845 × 5) × 782 + (769 × 25) × 218

= 19225 × 782 + 19225 × 218

= 19225 × (782 + 218)

= 19225 × 1000

= 19225000

### 4. Find the product using suitable properties.

(a) 738 × 103

= 738 × (100 + 3)

= 738 × 100 + 738 × 3

= 73800 + 2214

= 76014

(b) 854 × 102

854 × (100 + 2)

= 854 × 100 + 854 × 2

= 85400 + 1708

= 87108

(c) 258 × 1008

= 258 × (1000 + 8)

= 258 × 1000 + 258 × 8

= 258000 + 2064

= 260064

(d) 1005 × 168

168 × (1000 + 5)

= 168 × 1000 + 168 × 5

= 168000 + 840

= 168840

5. A taxidriver 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?

Solution: Petrol filled on Monday = 40 litres

Petrol filled on the next day = 50 litres

Total petrol filled on both the days = 40 + 50 = 90 litres

Cost of petrol per litre = 44

Total cost of petrol for 90 litres = 44 × 90

= 3960

Thus, he spend rupees 3960 to fill the petrol in the petrol tank.

6. A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres of milk in the evening. If the milk costs ` 45 per litre, how much money is due to the vendor per day?

Solution: Milk supplied in the morning = 32 litres

Milk supplied in the evening = 68 litres

Total milk supplied on the same day = 32 + 68 = 100 litres

Cost of milk per litre = 45

Cost of 100 litres of milk = 45 × 100

= 4500

Thus, rupees 4500 is due to the vendor per day.

7. Match the following:

(i) 425 × 136 = 425 × (6 + 30 +100) - (c) Distributivity of multiplication

(ii) 2 × 49 × 50 = 2 × 50 × 49 - (a) Commutativity under multiplication.

(iii) 80 + 2005 + 20 = 80 + 20 + 2005 - (b) Commutativity under addition.

### Exercise 2.3

1. Which of the following will not represent zero:

(a) 1 + 0

Answer: It does not represent 0.

1 + 0 = 1

(b) 0 × 0

0 × 0 = 0

(c) 0/2

0/2 = 0

(d) 10 - 10/2

(10 -10) = 0

0/2 = 0

Thus, only option (a) does not represent 0.

2. If the product of two whole numbers is zero, can we say that one or both of them will be zero? Justify through examples.

Answer: If the product of two whole numbers is zero, one or both of them will be zero.

For example,

0 × 1 = 0

2 × 0 = 0

5 × 0 = 0

0 × 6 = 0

Thus, if any one number is 0, the product will always be 0.

0 × 0 = 0

Thus, if both numbers are 0, the product will always be 0.

3. If the product of two whole numbers is 1, can we say that one or both of them will be 1? Justify through examples.

Answer: If the product of two whole numbers is one, both of them will be one.

For example,

1 × 1 = 1

Thus, if both numbers are 1, the product will always be 1.

2 × 1 = 2

5 × 1 = 5

1 × 3 = 3

Thus, if any one number is 1, the product will not be 1.

4. Find using distributive property:

(a) 728 × 101

= 728 × (100 + 1)

= 728 × 100 + 728 × 1

= 72800 + 728

= 73528

(b) 5437 × 1001

= 5437 × (1000 + 1)

= 5437 × 1000 + 5437 × 1

= 5437000 + 5437

= 5442437

(c) 824 × 25

= 824 × (20 + 5)

= 824 × 20 + 824 × 5

= 16480 + 4120

= 20600

(d) 4275 × 125

= 4275 × (100 + 20 + 5)

= 4275 × 100 + 4275 × 20 + 4275 × 5

= 427500 + 85500 + 21375

= 534375

(e) 504 × 35

= 504 × (30 + 5)

= 504 × 30 + 504 × 5

= 15120 + 2520

= 17640

5. Study the pattern :

1 × 8 + 1 = 9

12 × 8 + 2 = 98

123 × 8 + 3 = 987

1234 × 8 + 4 = 9876

12345 × 8 + 5 = 98765

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

Answer: The next two steps in the pattern are:

123456 × 8 + 6 = 987654

1234567 × 8 + 7 = 9876543

Explanation: The pattern works in the following way:

1 × 8 + 1 = 9

(11 + 1) × 8 + (1 + 1) = 98

(111 + 11 + 1) × 8 + (1 + 1 + 1) = 987

(1111 + 111 + 11 + 1) × 8 + (1 + 1 + 1 + 1) = 9876

(11111 + 1111 + 111 + 11 + 1) × 8 + (1 + 1 + 1 + 1 + 1) = 98765

(111111 + 11111 + 1111 + 111 + 11 + 1) × 8 + (1 + 1 + 1 + 1 + 1 + 1) = 987654

(1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1) × 8 + (1 + 1 + 1 + 1 + 1 + 1 + 1) = 9876543

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