NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers
NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers are a comprehensive study material for students preparing for Class 6 mathematics exam.
These solutions are prepared by our experts to provide a proper understanding of the basic concepts included in this chapter. It includes exercise-wise solved questions along with important formulas, shortcut tips and best methods to solve the problems
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NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers
Whole Numbers Ex 2.1
NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Exercise 2.1
1. Write the next three natural numbers after 10999.
Sol :
The next three natural numbers after 10999 are 11000, 11001 and 11002
2. Write the three whole numbers occurring just before 10001.
Sol :
The three whole numbers occurring just before 10001 are 10000, 9999 and 9998
3. Which is the smallest whole number?
Sol :
The smallest whole number is 0
4. How many whole numbers are there between 32 and 53?
Sol :
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, 52)
Hence, there are 20 whole numbers between 32 and 53
5. Write the successor of:
(a) 2440701 (b) 100199 (c) 1099999 (d) 2345670
Solutions:
The successors are :
(a) 2440701 + 1 = 2440702
(b) 100199 + 1 = 100200
(c) 1099999 + 1 = 1100000
(d) 2345670 + 1 = 2345671
6. Write the predecessor of:
(a) 94 (b) 10000 (c) 208090 (d) 7654321
Solutions:
The predecessors are :
(a) 94 – 1 = 93
(b) 10000 – 1 = 9999
(c) 208090 – 1 = 208089
(d) 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.
(a) 530, 503 (b) 370, 307 (c) 98765, 56789 (d) 9830415, 10023001
Solutions:
(a) Since, 530 > 503
Hence, 503 is on the left side of 530 on the number line
(b) Since, 370 > 307
Hence, 307 is on the left side of 370 on the number line
(c) Since, 98765 > 56789
Hence, 56789 is on the left side of 98765 on the number line
(d) Since, 9830415 < 10023001
Hence, 9830415 is on the left side 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.
Sol :
False
0 is not a natural number
(b) 400 is the predecessor of 399.
Sol :
False
The predecessor of 399 is 398 Since, (399 – 1 = 398)
(c) Zero is the smallest whole number.
Sol :
True
Zero is the smallest whole number
(d) 600 is the successor of 599.
Sol :
True
Since (599 + 1 = 600)
(e) All natural numbers are whole numbers.
Sol :
True
All natural numbers are whole numbers
(f) All whole numbers are natural numbers.
Sol :
False
0 is a whole number but is not a natural number
(g) The predecessor of a two digit number is never a single digit number.
Sol :
False
Example the predecessor of 10 is 9
(h) 1 is the smallest whole number.
Sol :
False
0 is the smallest whole number
(i) The natural number 1 has no predecessor.
Sol :
True
The predecessor of 1 is 0 but is not a natural number
(j) The whole number 1 has no predecessor.
Sol :
False
0 is the predecessor of 1 and is a whole number
(k) The whole number 13 lies between 11 and 12.
Sol :
False
13 does not lie between 11 and 12
(l) The whole number 0 has no predecessor.
Sol :
True
The predecessor of 0 is -1 and is not a whole number
(m) The successor of a two digit number is always a two digit number.
Sol :
False
As the successor of 99 is 100
Whole Numbers Ex 2.2
NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Exercise 2.2
1. Find the sum by suitable rearrangement:
(a) 837 + 208 + 363
(b) 1962 + 453 + 1538 + 647
Solutions:
(a) Given 837 + 208 + 363
= (837 + 363) + 208
= 1200 + 208
= 1408
(b) Given 1962 + 453 + 1538 + 647
= (1962 + 1538) + (453 + 647)
= 3500 + 1100
= 4600
2. Find the product by suitable rearrangement:
(a) 2 × 1768 × 50
Sol :
Given 2 × 1768 × 50
= 2 × 50 × 1768
= 100 × 1768
= 176800
(b) 4 × 166 × 25
Sol :
Given 4 × 166 × 25
= 4 × 25 × 166
= 100 × 166
= 16600
(c) 8 × 291 × 125
Sol :
Given 8 × 291 × 125
= 8 × 125 × 291
= 1000 × 291
= 291000
(d) 625 × 279 × 16
Sol :
Given 625 × 279 × 16
= 625 × 16 × 279
= 10000 × 279
= 2790000
(e) 285 × 5 × 60
Sol :
Given 285 × 5 × 60
= 285 × 300
= 85500
(f) 125 × 40 × 8 × 25
Sol :
Given 125 × 40 × 8 × 25
= 125 × 8 × 40 × 25
= 1000 × 1000
= 1000000
3. Find the value of the following:
(a) 297 × 17 + 297 × 3
Sol :
Given 297 × 17 + 297 × 3
= 297 × (17 + 3)
= 297 × 20
= 5940
(b) 54279 × 92 + 8 × 54279
Sol :
Given 54279 × 92 + 8 × 54279
= 54279 × 92 + 54279 × 8
= 54279 × (92 + 8)
= 54279 × 100
= 5427900
(c) 81265 × 169 – 81265 × 69
Sol :
Given 81265 × 169 – 81265 × 69
= 81265 × (169 – 69)
= 81265 × 100
= 8126500
(d) 3845 × 5 × 782 + 769 × 25 × 218
Sol :
Given 3845 × 5 × 782 + 769 × 25 × 218
= 3845 × 5 × 782 + 769 × 5 × 5 × 218
= 3845 × 5 × 782 + 3845 × 5 × 218
= 3845 × 5 × (782 + 218)
= 19225 × 1000
= 19225000
4. Find the product using suitable properties.
(a) 738 × 103
Sol :
Given 738 × 103
= 738 × (100 + 3)
= 738 × 100 + 738 × 3 (using distributive property)
= 73800 + 2214
= 76014
(b) 854 × 102
Sol :
Given 854 × 102
= 854 × (100 + 2)
= 854 × 100 + 854 × 2 (using distributive property)
= 85400 + 1708
= 87108
(c) 258 × 1008
Sol :
Given 258 × 1008
= 258 × (1000 + 8)
= 258 × 1000 + 258 × 8 (using distributive property)
= 258000 + 2064
= 260064
(d) 1005 × 168
Sol :
Given 1005 × 168
= (1000 + 5) × 168
= 1000 × 168 + 5 × 168 (using distributive property)
= 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?
Sol :
Petrol quantity filled on Monday = 40 litres
Petrol quantity filled on Tuesday = 50 litres
Total petrol quantity filled = (40 + 50) litre
Cost of petrol per litre = ₹ 44
Total money spent = 44 × (40 + 50)
= 44 × 90
= ₹ 3960
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?
Sol :
Milk quantity supplied in the morning = 32 litres
Milk quantity supplied in the evening = 68 litres
Cost of milk per litre = ₹ 45
Total cost of milk per day = 45 × (32 + 68)
= 45 × 100
= ₹ 4500
Hence, the money is due to the vendor per day is ₹ 4500
7. Match the following:
(i) 425 × 136 = 425 × (6 + 30 + 100) (a) Commutativity under multiplication.
(ii) 2 × 49 × 50 = 2 × 50 × 49 (b) Commutativity under addition.
(iii) 80 + 2005 + 20 = 80 + 20 + 2005 (c) Distributivity of multiplication over addition.
Solutions:
(i) 425 × 136 = 425 × (6 + 30 + 100) (c) Distributivity of multiplication over addition.
Hence (c) is the correct answer
(ii) 2 × 49 × 50 = 2 × 50 × 49 (a) Commutativity under multiplication
Hence, (a) is the correct answer
(iii) 80 + 2005 + 20 = 80 + 20 + 2005 (b) Commutativity under addition
Hence, (b) is the correct answer
Whole Numbers Ex 2.3
NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Exercise 2.3
1. Which of the following will not represent zero:
(a) 1 + 0
Sol :
1 + 0 = 1
Hence, it does not represent zero
(b) 0 × 0
Sol :
0 × 0 = 0
Hence, it represents zero
(c) 0 / 2
Sol :
0 / 2 = 0
Hence, it represents zero
(d) (10 – 10) / 2
Sol :
(10 – 10) / 2 = 0 / 2 = 0
Hence, it represents zero
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.
Sol :
If product of two whole numbers is zero, definitely one of them is zero
Example: 0 × 3 = 0 and 15 × 0 = 0
If product of two whole numbers is zero, both of them may be zero
Example: 0 × 0 = 0
Yes, if the product of two whole numbers is zero, then both of them will be zero
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.
Sol :
If the product of two whole numbers is 1, both the numbers should be equal to 1
Example: 1 × 1 = 1
But 1 × 5 = 5
Hence, it’s clear that the product of two whole numbers will be 1, only in situation when both numbers to be multiplied are 1
4. Find using distributive property:
(a) 728 × 101
Sol :
Given 728 × 101
= 728 × (100 + 1)
= 728 × 100 + 728 × 1
= 72800 + 728
= 73528
(b) 5437 × 1001
Sol :
Given 5437 × 1001
= 5437 × (1000 + 1)
= 5437 × 1000 + 5437 × 1
= 5437000 + 5437
= 5442437
(c) 824 × 25
Sol :
Given 824 × 25
= (800 + 24) × 25
= (800 + 25 – 1) × 25
= 800 × 25 + 25 × 25 – 1 × 25
= 20000 + 625 – 25
= 20000 + 600
= 20600
(d) 4275 × 125
Sol :
Given 4275 × 125
= (4000 + 200 + 100 – 25) × 125
= (4000 × 125 + 200 × 125 + 100 × 125 – 25 × 125)
= 500000 + 25000 + 12500 – 3125
= 534375
(e) 504 × 35
Sol :
Given 504 × 35
= (500 + 4) × 35
= 500 × 35 + 4 × 35
= 17500 + 140
= 17640
5. 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)
Solution :
123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543
Given 123456 = (111111 + 11111 + 1111 + 111 + 11 + 1)
123456 × 8 = (111111 + 11111 + 1111 + 111 + 11 + 1) × 8
= 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8
= 888888 + 88888 + 8888 + 888 + 88 + 8
= 987648
123456 × 8 + 6 = 987648 + 6
= 987654
Yes, here the pattern works
1234567 × 8 + 7 = 9876543
Given 1234567 = (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1)
1234567 × 8 = (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1) × 8
= 1111111 × 8 + 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8
= 8888888 + 888888 + 88888 + 8888 + 888 + 88 + 8
= 9876536
1234567 × 8 + 7 = 9876536 + 7
= 9876543
Yes, here the pattern works.
CBSE Notes for Class 6 Maths Free Download for All Chapters
CBSE Class 6 Maths Study Notes | CBSE Class 6 Maths Study Notes |
Knowing our Numbers Class 6 Notes Chapter 1 | Decimals Class 6 Notes Chapter 8 |
Whole Numbers Class 6 Notes Chapter 2 | Data Handling Class 6 Notes Chapter 9 |
Playing with Numbers Class 6 Notes Chapter 3 | Mensuration Class 6 Notes Chapter 10 |
Basic Geometrical Ideas Class 6 Notes Chapter 4 | Algebra Class 6 Notes Chapter 11 |
Understanding Elementary Shapes Class 6 Notes Chapter 5 | Ratio And Proportion Class 6 Notes Chapter 12 |
Integers Class 6 Notes Chapter 6 | Symmetry Class 6 Notes Chapter 13 |
Fractions Class 6 Notes Chapter 7 | Practical Geometry Class 6 Notes Chapter 14 |
Download PDF of NCERT Solutions for Class 6 Maths
NCERT Solutions Download Class 6 | Chapter Name | NCERT Solutions Download Class 6 | Chapter Name |
NCERT Solutions for Class 6 Maths Chapter 1 | Knowing our Numbers | NCERT Solutions for Class Maths 6 Chapter 8 | Decimals |
NCERT Solutions for Class 6 Maths Chapter 2 | Whole Numbers | NCERT Solutions for Class 6 Maths Chapter 9 | Data Handling |
NCERT Solutions for Class 6 Maths Chapter 3 | Playing with Numbers | NCERT Solutions for Class 6 Maths Chapter 10 | Mensuration |
NCERT Solutions for Class 6 Maths Chapter 4 | Basic Geometrical Ideas | NCERT Solutions for Class 6 Maths Chapter 11 | Algebra |
NCERT Solutions for Class 6 Maths Chapter 5 | Understanding Elementary Shapes | NCERT Solutions for Class 6 Maths Chapter 12 | Ratio And Proportion |
NCERT Solutions for Class 6 Maths Chapter 6 | Integers | NCERT Solutions for Class 6 Maths Chapter 13 | Symmetry |
NCERT Solutions for Class 6 Maths Chapter 7 | Fractions | NCERT Solutions for Class 6 Maths Chapter 14 | Practical Geometry |
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