MP Board Class 6th Maths Solutions Chapter 2 Whole Numbers Ex 2.3

Question 1.
Which of the following will not represent zero:
(a) 1 + 0
(b) 0 × 0
(c) \(\frac{0}{2}\)
(d) \(\frac{10-10}{2}\)
Solution:
(a) 1 + 0 = 1
(b) 0 × 0 = 0
(c) \(\frac{0}{2}\) = 0
(d) \(\frac{10-10}{2}\) = \(\frac{0}{2}\) = 0
Thus, (a) does 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? Justify through examples.
Solution:
Yes, if we multiply any number with zero, then the product will be zero.
i. e., 2 × 0 = 0, 5 × 0 = 0, 9 × 0 = 0
If both numbers are zero, then the product will also be zero, i.e., 0 × 0 = 0

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.
Solution:
No, if only one number be 1, then the product cannot be 1.
i.e., 5 × 1 = 5, 4 × 1 = 4, 8 × 1 = 8
If both numbers are 1, then the product is 1
i.e., 1 × 1 = 1

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

(d) 4275 × 125
= 4275 × (100 + 20 + 5)
= 4275 × 100 + 4275 × 20 + 4275 × 5
= 427500 + 85500 + 21375
= 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).
Solution:
The next two steps are :
123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543
Pattern works like this :
1 × 8 + 1 = 9
12 × 8 + 2 = 98
123 × 8 + 3 = 987
1234 × 8 + 4 = 9876
12345 × 8 + 5 = 98765
123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543