Whole Numbers

Whole Numbers

Exercise 2.3

Ex 2.3 Question 1.

Which of the following will not represent zero:
(a) 1 + 0
(b) 0 x 0
(c) 0/2
(d) 10 – 10/2
Solution:
(a) 1 + 0 = 1 ≠ 0, (Does not represent zero.)
(b) 0 x 0 = 0, (Represents zero)
(c) 0/2= 0, (Represents zero.)
(d) 10 – 10 / 2 = 0/2= 0 (Represents zero.)

Ex 2.3 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 the resultant product will be zero.

Examples-
8x 0 = 0
0 x 5= 0

If both numbers are zero, then the result also be zero.

Example-

0 x 0 = 0

Ex 2.3  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:
This is only true when each of the numbers is 1.
Example- 1 x 1 = 1

If there is only one number is 1 then the product cannot be 1

Examples- 5 x 1 = 5 , 6 x 1 = 6

Ex 2.3  Question 4.

Find using distributive property:
(а) 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)
= 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

Ex 2.3 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?
Solution:
Step I: 123456 x 8 + 6 = 987654
Step II: 1234567 x 8 + 7 = 9876543

Working pattern:
(1) x 8 + 1 = 9
(12) x 8 + 2 = (11 + 1) x 8 + 2 = 98
(123) x 8 + 3 = (111 + 11 + 1) x 8 + 3 = 987
(1234) x 8 + 4 = (1111 + 111 + 11 + 1) x 8 + 4 = 9876
(12345) x 8 + 5 = (11111 + 1111 + 111 + 11 + 1) x 8 + 5 = 98765