NCERT Solutions For Class 6 Maths Chapter 2 Whole Numbers Exercise 2.3 deals with the answers to the questions related to the topic Patterns in Whole Numbers. We know that whole numbers can be arranged in elementary shapes with the help of dots. The solutions for Exercise 2.3 are prepared by our faculty to make students clear about how the questions should be answered. Solving these NCERT Solutions will help the students develop and practise the answers from an examination point of view.
NCERT Solutions for Class 6 Chapter 2: Whole Numbers Exercise 2.3
Access NCERT Solutions for Class 6 Chapter 2: Whole Numbers Exercise 2.3
1. Which of the following will not represent zero?
(a) 1 + 0
(b) 0 × 0
(c) 0 / 2
(d) (10 – 10) / 2
Solutions:
(a) 1 + 0 = 1
Hence, it does not represent zero
(b) 0 × 0 = 0
Hence, it represents zero
(c) 0 / 2 = 0
Hence, it represents zero
(d) (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.
Solutions:
If the product of two whole numbers is zero, definitely one of them is zero
Example: 0 × 3 = 0 and 15 × 0 = 0
If the 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.
Solutions:
If the product of two whole numbers is 1, both numbers should be equal to 1
Example: 1 × 1 = 1
But 1 × 5 = 5
Hence, it is clear that the product of two whole numbers will be 1, only in situations when both numbers to be multiplied are 1.
4. Find using distributive property:
(a) 728 × 101
(b) 5437 × 1001
(c) 824 × 25
(d) 4275 × 125
(e) 504 × 35
Solutions:
(a) Given 728 × 101
= 728 × (100 + 1)
= 728 × 100 + 728 × 1
= 72800 + 728
= 73528
(b) Given 5437 × 1001
= 5437 × (1000 + 1)
= 5437 × 1000 + 5437 × 1
= 5437000 + 5437
= 5442437
(c) Given 824 × 25
= (800 + 24) × 25
= (800 + 25 – 1) × 25
= 800 × 25 + 25 × 25 – 1 × 25
= 20000 + 625 – 25
= 20000 + 600
= 20600
(d) Given 4275 × 125
= (4000 + 200 + 100 – 25) × 125
= (4000 × 125 + 200 × 125 + 100 × 125 – 25 × 125)
= 500000 + 25000 + 12500 – 3125
= 534375
(e) 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)
Solutions:
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
Access Other Exercise Solutions of Class 6 Maths Chapter 2: Whole Numbers
Exercise 2.1 Solutions
Exercise 2.2 Solutions
Also, explore –
NCERT Solutions for Class 6 Maths Chapter 2
NCERT Solutions for Class 6 Maths
NCERT Solutions for Class 6
