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

- 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.