1). Which of the following will not represent zero:

1. 1 + 0             b) 0 x 0              c) 0 ÷ 2            d) 10 – 10 ÷ 2
Ans.
a) 1 + 0 = 1,hence it does not represent zero.
b) 0 x 0 = 0, hence it represents
c) 0 ÷ 2 = 0, hence it represents
d) 10 – 10 ÷ 2 = 0 ÷ 2 = 0, hence it represents

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.
Ans.
Yes, we can say that
Examples (1) 2 x 0 = 0 ,    12 x 0 = 0
Therefore, if the product is 0 , then one of them may be zero
(2) 0 x 0 = 0
Therefore, If the product of two whole numbers is zero 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.
Ans. If the product of two whole numbers is 1, both of the numbers should be equal to 1.
Example:   1 x 1 = 1
But             1 x 8 = 8 ≠ 1

4). Find by distributive method
a) 728 x 101
Ans. = 728 x (100 + 1)
= 728 x 100 + 728 x 1
= 72800 + 728
= 73,528

b) 5437 x 1001
Ans. = 5437 x (1000 + 1)
= 5437 x 1000 + 5437 x 1
= 5437000 + 5437
= 54,42,437

c) 824 x 25
Ans. = 824 x (30 – 5 )
= 824 x 30 – 824 x 5
= 24,720 – 4120
= 20,600

d) 4275 x 125
Ans = 4275 x (130 – 5)
= 4275 x 130 – 4275 x 5
= 5,55,750 – 21,375
= 5,34,375
e)  504 x 35
Ans.= 504 x (40 – 5)
= 504 x 40 – 504 x 5
= 20,160 – 2,520
= 17,640

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?

Ans. 123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
123456 x 8      = (111111 + 11111 + 1111 + 111 + 11 + 1) x 8
=  888888 + 88888 + 8888 + 888 + 88 + 8
=  987648
123456 x 8 + 6
= 987648 x 6
= 987654
Hence, this is how the pattern works.