Chapter 2 Whole Numbers Ex 2.3 Solutions
Question - 1 : - Which of the following will not represent zero?
(a) 1 + 0 (b) 0 × 0
(c) 
(d) 
Answer - 1 : -
(a) 1 + 0 = 1
It does not represent zero.
(b) 0 × 0 = 0
It represents zero.
(c) 
It represents zero.
(d) 
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.
Answer - 2 : -
If the product of 2 whole numbers is zero, then one of them is definitely zero.
For example, 0 × 2 = 0 and 17 × 0 = 0
If the product of 2 whole numbers is zero, then both of them may be zero.
0 × 0 = 0
However, 2 × 3 = 6
(Since numbers to be multiplied are not equal to zero, the result of the product will also be non-zero.)
Question - 3 : - If the product of two whole numbers is 1, can we say that one of both of them will be 1? Justify through examples.
Answer - 3 : -
If the product of 2 numbers is 1, then both the numbers have to be equal to 1.
For example, 1 × 1 = 1
However, 1 × 6 = 6
Clearly, the product of two whole numbers will be 1 in the 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
Answer - 4 : -
(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 1234 × 8 + 4 = 9876
12 × 8 + 2 = 98 12345 × 8 + 5 = 98765
123 × 8 + 3 = 987
Write the next two steps. Can you say how the pattern works?
(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).
Answer - 5 : -
123456 × 8 + 6 = 987648 + 6 = 987654
1234567 × 8 + 7 = 9876536 + 7 = 9876543
Yes, the pattern works.
As 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