NCERT Solutions Class 6th Maths Chapter – 2 Whole Numbers Exercise – 2.3

Question 1. Which of the following will not represent zero:
(a) 1 + 0
(b) 0 x 0
(c) 0/2
(d) (10 − 10)/2

Solution:
(a) 1 + 0 = 1 ≠ 0, does not represent zero.
(b) 0 x 0 = 0, represents zero.
(c) 0/2 = 0, represents zero.
(d) (10 − 10)/2 = 0/2 = 0 represents zero.

A option is Correct

Question 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, Examples:
5 x 0 = 0
0 x 8 = 0
0 x 0 = 0

Question 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.

Solution: This is only true, when each of the number are 1.
1 x 1 = 1

Question 4. Find using distributive property:

(а) 728 x 101
Solution: 728 x 101
= 728 x (100 + 1)
= 728 x 100 + 728 x 1
= 72800 + 728
= 73528

(b) 5437 x 1001
Solution: 5437 x 1001
= 5437 x (1000 + 1)
= 5437 x 1000 + 5437 x 1
= 5437000 + 5437
= 5442437

(c) 824 x 25
Solution: 824 x 25
= 824 x (20 + 5)
= 824 x 20 + 824 x 5
= 16480 + 4120
= 20600

(d) 4275 x 125
Solution: 4275 x 125
= 4275 x (100 + 20 + 5)
= 4275 x 100 + 4275 x 20 + 4275 x 5
= 427500 + 85500 + 21375
= 534375

(e) 504 x 35
Solution: 504 x 35
= (500 + 4) x 35
= 500 x 35 + 4 x 35
= 17500 + 140
= 17640

Question 5. Study the pattern:
1 x 8 + 1= 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
Write the next two steps. Can you say how the pattern works?

Solution: Step I: 123456 x 8 + 6 = 987654
Step II: 1234567 x 8 + 7 = 9876543

Working pattern:
(1) x 8 + 1 = 9
(12) x 8 + 2 = (11 + 1) x 8 + 2 = 98
(123) x 8 + 3 = (111 + 11 + 1) x 8 + 3 = 987
(1234) x 8 + 4 = (1111 + 111 + 11 + 1) x 8 + 4 = 9876
(12345) x 8 + 5 = (11111 + 1111 + 111 + 11 + 1) x 8 + 5 = 98765