NCERT Exercise 2.3 Solution Class 6 Math
Question (1) Which of the following will not represent zero:
(a) 1 + 0
(b) 0 × 0
(c) 0/2
(d) 10 – 10/2
Answer (a) 1 + 0
(This option does not represent zero, because 1 + 0 = 1)
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 Yes.
If the product of two whole numbers is zero, this means one or both of them will be zero.
Example
(a) 1 × 0 = 0
(b) 2 × 0 = 0
(c) 0 × 0 = 0
(d) 2 × 2 = 4
From the examples given above, it can be said that if the product of two whole numbers is zero, this means one or both of them will be zero. As in the example (d) none of the two numbers is zero, so product is not zero. While in other examples either one or both numbers are zero, and hence product is zero.
Question (3) Find using distributive property:
(a) 728 × 101
Solution
Given, 728 × 101
Using distributive property, we can write the above expression as follow:
728 × (100 + 1)
= (728 × 100) + (728 × 1)
= 72800 + 728
= 73,528
Thus, Answer = 73,528
(b) 5437 × 1001
Solution
We can write the above expression as follow:
5437 × (1000 + 1)
= (5437 × 1000) + (5437 × 1)
= 5437000 + 5437
= 54,42,437
Thus, Answer 54,42,437
(c) 824 × 25
Solution
Given, 824 × 25
The above expression can be written as
(800 + 20 + 4) × 25
[∵ 800 + 20 + 4 = 824]
Using distributive property over addition
= (800 × 25) + (20 × 25) + (4 × 25)
= 20000 + 500 + 100
= 20000 + (500 + 100)
= 20000 + 600
= 20,600
Thus, Answer = 20,600
(d) 4275 × 125
Solution
Given, 4275 × 125
The above expression can be written as follows:
4275 × (100 + 25)
= 4275 × (100 + 20 + 5)
= (4275 × 100) + (4275 × 20) + (4275 × 5)
= 4,27,500 + 85,500 + 21,375
= 5,34,375
Thus, Answer = 5,34,375
(e) 504 × 35
Solution
Given, 504 × 35
The above expression can be written as
(500 + 4) × 35
Using distributive property, we get
= (500 × 35) + (4 × 35)
= 17,500 + 140
= 17640
Thus, Answer = 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?
Solution
The two steps are:
(i) 123456 × 8 + 6 = 987654
(ii) 1234567 × 8 + 7 = 9876543
This works as follows:
(a) 1 × 8 + 1 = 9
⇒ 1 × 8 + 1
= 8 + 1 = 9
(b) 12 × 8 + 2 = 98
= (1 + 11) × 8 + 2
= (8 × 1) + (11 × 8 ) + 2
= 8 + 88 + 2
= 96 + 2 = 98
(c) 123 × 8 + 3 = 987
= (1 + 11 + 111) × 8 + 3
= (8 × 1) + (11 × 8 ) + (111 × 8) + 3
= 8 + 88 + 888 + 3
= 984 + 3 = 987
(d) 1234 × 8 + 4 = 9876
= (1 + 11 + 111 + 1111) × 8 + 4
= (8 × 1) + (11 × 8 ) + (111 × 8) + (1111 × 8) + 4
= 8 + 88 + 888 + 8888 + 4
= 9872 + 4 = 9876
(e) 12345 × 8 + 5 = 98765
= (1 + 11 + 111 + 1111 + 11111) × 8 + 5
= (8 × 1) + (11 × 8 ) + (111 × 8) + (1111 × 8) + (11111 × 8) + 5
= 8 + 88 + 888 + 8888 + 88888 + 5
= 98760 + 5 = 98765
(f) 123456 × 8 + 6 = 987654
= (1 + 11 + 111 + 1111 + 11111 + 111111) × 8 + 6
= (8 × 1) + (11 × 8 ) + (111 × 8) + (1111 × 8) + (11111 × 8) + (111111 × 8) + 6
= 8 + 88 + 888 + 8888 + 88888 + 888888 + 6
= 987648 + 6 = 987654
And so on.