NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Ex 2.3

Exercise 2.3

Question 1.
Which of the following will not represent zero:
(a) 1 + 0
(b) 0 x 0
(c)
(d)
Solution:
(a) 1 + 0 = 1 ≠ 0, does not represent zero.
(b) 0 x 0 = 0, represents zero
(c) = 0, represents zero.
(d) = = 0 represents zero.

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
(b) 5437 x 1001
(c) 824 x 25
(d) 4275 x 125
(e) 504 x 35
Solution:
(a) 728 x 101 = 728 x (100 + 1)
= 728 x 100 + 728 x 1
= 72800 + 728
= 73528

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

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

(d) 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 = (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