**Whole Numbers**

**Exercise 2.3**

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

a). 1+0 b). 0 X 0 c). 0/2 d). (10-10)/2

Answer:

a.

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.

If the product of to whole numbers is zero, then either any one of them is zero or both of them are zero.

2 X 0 = 0

0 X 5 = 0

0 X 0 = 0

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.

The product of two whole numbers is 1 only when the two whole numbers are 1.

4). Find using the distributive property.

a). 728 X 101

728 X 101 = 728 X (100+1)

= 728 X 100 + 728 X 1

= 72800 + 728

= 73528

728 X 101 = 73528

b). 5437 X 1001

5437 X 1001 = 5437 X (1000+1)

= 5437 X 1000 + 5437 X 1

= 5437000 + 5437

= 5442737

5437 X 1001 = 5442737

c). 824 X 25

824 X 25 = 824 X (20+5)

= 824 X 20 + 824 X 5

= 16480 + 4120

= 20600

824 X 25 = 20600

d). 4275 X 125

4275 X 125 = 4275 X (100+20+5)

= 427500 + 85500 + 21375

= 534375

4275 X 125 = 534375

e). 504 X 35

504 X 35 = 504 X (30+5)

= 504 X 30 + 504 X 5

= 1512 + 2520

= 4032

504 X 35 = 4032

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?

(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).

The next two steps are

123456 X 8 + 6 = 987654

1234567 X 8 + 7 = 9876543

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