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## Chapter 2 Whole Numbers Exercise 2.3

Question 1: Which of the following will not represent zero:
a) 1 + 0
b) 0 × 0
c) 0/2
d) 10 - 10/2

a) 1 + 0 = 1
Therefore, it does not represent zero
b) 0 × 0 = 0
Therefore, it represents zero
c) 0/2 = 0
Therefore, it represents zero
d) 10 - 10/2 = 0/2 = 0
Therefore, it 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.
If product of two whole numbers is zero, definitely one of them is zero. Example: 0 × 5 = 0 and 1560 × 0 = 0. If product of two whole numbers is zero, both of them may be zero. Example: 0 × 0 = 0. Yes, if the product of two whole numbers is zero, then both of them will be zero

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.
If the product of two whole numbers is 1, both the numbers should be equal to 1.  Example: 1 × 1 = 1 but 1 × 15048 = 15048. Therefore, it’s clear that the product of two whole numbers will be 1, only in situation when both numbers to be multiplied are 1.

Question 4: Find using distributive property:
a) 728 × 101
b) 5437 × 1001
c) 824 × 25
d) 4275 × 125
e) 504 × 35

a)
= 728 × 101
= 728 × (100 + 1)
= 728 × 100 + 728 × 1
= 72800 + 728
= 73528

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

c)
= 824 × 25
= (800 + 24) × 25
= (800 + 25 - 1) × 25
= 800 × 25 + 25 × 25 - 1 × 25
= 20000 + 625 - 25
= 20000 + 600
= 20600

d)
= 4275 × 125
= (4000 + 200 + 100 - 25) × 125
= (4000 × 125 + 200 × 125 + 100 × 125 - 25 × 125)
= 500000 + 25000 + 12500 – 3125
= 534375

e)
= 504 × 35
= (500 + 4) × 35
= 500 × 35 + 4 × 35
= 17500 + 140
= 17640

Question 5: Study the pattern:
1 × 8 + 1 = 9
12 × 8 + 2 = 98
123 × 8 + 3 = 987
1234 × 8 + 4 = 9876
12345 × 8 + 5 = 98765
Write the next two steps. Can you say how the pattern works? (Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).

123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543
123456 = (111111 + 11111 + 1111 + 111 + 11 + 1)
123456 × 8 = (111111 + 11111 + 1111 + 111 + 11 + 1) × 8
= 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8
= 888888 + 88888 + 8888 + 888 + 88 + 8
= 987648
123456 × 8 + 6 = 987648 + 6
= 987654
Yes, here the pattern works.

1234567 × 8 + 7 = 9876543
Given 1234567 = (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1)
1234567 × 8 = (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1) × 8
= 1111111 × 8 + 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8
= 8888888 + 888888 + 88888 + 8888 + 888 + 88 + 8
= 9876536
1234567 × 8 + 7 = 9876536 + 7
= 9876543
Yes, here the pattern works.