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 Maths - Whole Numbers Exercise 2.3
1. Which of the following will not represent zero :
Solutions :
(a) 1 + 0 = 1 ≠ 0
(b) 0 × 0 = 0
(c) 0/2 = 0
(d) (10 - 10)/2 = 0
Thus, only (a) does not represent 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.
Solution :
Yes. We know that the product of any whole number and zero is always zero i.e., a × 0 = 0 × a = 0, where a is any whole number.
3. If the product of two whole number is 1, can we say that one or both of them will be 1? Justify through examples.
Solution :
Yes. We know that the if a is any whole number, then
a × 1 = a = 1 × a
∴ Clearly a must be = 1
Thus, both the numbers should be 1, i.e., 1 × 1 = 1
4. Find using distributive property :
(a) 728 × 101 (b) 5437 × 1001 (c) 824 × 25 (d) 4275 × 125 (e) 504 × 35
Solution :
(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
= (206 × 4) × 25
= 206 × (4 × 25)
= 206 × 100
= 20600
(d) 4275 × 125
= (4000 + 200 + 100 – 25) × 125
= (4000 × 125 + 200 × 125 + 100 × 125 – 25 × 125)
= 500000 + 25000 + 12500 – 3125
= 534375
(e) 504 × 35
= (252 × 2) × 35
= 252 × (2 × 35)
= 252 × 70
= 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 ?
(Hint : 12345 = 11111 + 1111 + 111 + 11 + 1).
Solution :
The next two steps are :
123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543
The pattern works in this way :
1 × 8 + 1 = 9
(11 + 1) × 8 + 2 = 12 × 8 + 2 = 98
(111 + 11 + 1) × 8 + 3 = 123 × 8 + 3 = 987
(1111 + 111 + 11 + 1) × 8 + 4 = 1234 × 8 + 4 = 9876
(11111 + 1111 + 111 + 11 + 1) × 8 + 5 = 12345 × 8 + 5 = 98765
(111111 + 11111 + 1111 + 111 + 11 + 1) × 8 + 6 = 123456 × 8 + 6 = 987654
and
(1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1) × 8 + 7 = 1234567 × 8 + 7 = 9876543