Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 2 Whole Numbers Ex 2.3 Textbook Questions and Answers.
Gujarat Board Textbook Solutions Class 6 Maths Chapter 2 Whole Numbers Ex 2.3
Question 1.
Which of the following will not represent zero?
(a) 1 + 0
(b) 0 x 0
(c) \(\frac { 0 }{ 2 } \)
(d) \(\frac { 10-10 }{ 2 } \)
Solution:
Since, 0 x 0 = 0, \(\frac { 0 }{ 2 } \) = 0, \(\frac { 10-10 }{ 2 } \) = \(\frac { 0 }{ 2 } \) = 0
and 1 + 0 = 1.
(a) 1 + 0 will not represent zero.
Question 2.
If the product of two whole numbers is zero, can we say that one or both of them will be zero? Justfy through examples.
Solution:
We know that the product of any whole number and zero is always equal to zero.
0 x 0 = 0
1 x 0 = 0
2 x 0 = 0
0 x 3 = 0, etc.
Yes, if the product of two whole numbers is zero then one or both of them must 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? Jusfy through examples.
Solution:
We know that the product of any whole number and 1 is the same whole number.
i.e. 5 x 1 = 5
109 x 1 = 109
1 x 17 = 17
1 x 0 = 0
1 x 1 = 1
The product will be equal to 1, only if both the whole numbers are 1.
Question 4.
Find using distributive property:
(a) 728 x 101
(b) 5437 x 1001
(c) 824 x 25
(d) 4275 x 125
(e) 504 x 35
Solution:
(a) 728 x 101
= 728 x [100 + 1] (100 + 1 = 101)
= (728 x 100) + (728 x 1)
= 72800 + 728 = 73528
(b) 5437 x 1001 = 5437 x [1000 + 1]
= (5437 x 1000) + (5437 x 1)
= 5437000 + 5437 = 5442437
(c) 824 x 25 = 824 x (20 + 5)
= (824 x 20) + (824 x 5)
= 16480 + 4120 = 20600
(d) 4275 x 125 = 4275 x [100 + 20 + 5]
= (4275 x 100) + (4275 x 20) + (4275 x 5)
= 427500 + 85500 + 21375 = 534375
(e) 504 x 35 = (500 + 4) x 35
= (500 x 35) + (4 x 35)
= 17500 + 140 = 17640
Question 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
Solution:
Obviously the next two steps will be
123456 x 8 + 6 = 987654
and 1234567 x 8 + 7 = 9876543
The working of the pattern:
Since,
11 + 1 = 12
111 + 11 + 1 = 123
1111 + 111 + 11 + 1 = 1234
11111 + 1111 + 111 + 11 + 1 = 12345
[1] x 8 + 1 = 9 = [1] x 8 + 1
[12] x 8 + 2 = 98 = [11 + 1] x 8 + 2
[123] x 8 + 3 = 987 [111 + 11 + 1] x 8 + 3
[1234] x 8 + 4 = 9876 = [1111 + 111 + 11 + 1] x 8 + 4
[12345] x 8 + 5 = 98765 = [11111 + 1111 + 111 + 11 + 1] x 8 + 5
and the next two steps will be worked out as:
[123456] x 8 + 6 = 987654 = [111111 + 11111 + 1111 + 111 + 11 + 1] x 8 + 6
[1234567] x 8 + 7 = 9876543 = [1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1] x 8 + 7