Gujarat BoardĀ 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