NCERT Solutions For Class 6 Maths Chapter 2 Exercise 2.3

NCERT Solutions for Class 6 Maths Chapter 2: NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Exercise 2.3

NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Exercise 2.3

1. Which of the following will not represent zero?

Solution:

Hence, option (A) do not represent zero.

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:

If the product of two numbers is zero, then either one of them or both ought to be zero.
This is because zero multiplied with any other number gives zero.
Example: 2×0=0,5×0=0,9×0=0
If both numbers are zero, then the result is zero.
0×0=0.

3. If the product of two whole number is 1, can we say that one or both of them will be 1? Justify through examples.

Solution:

1 being the multiplicative identity of whole numbers, the number remains unchanged when multiplied by 1.
Hence, a product of 1 can be obtained only when both the whole numbers multiplied are ones.
If only one number be 1 then the product cannot be 1.
Examples: 5×1=5,4×1=4,8×1=8
If both numbers are 1, then the product is 1 1×1=1

4. Find using distributive property:
(A) 728×101
(B) 5437×1001
(C) 824×25
(D) 4275×125
(E) 504×35

Solution:

(A) Given, 728×101
=728×(100+1)
=72800+728
=73528
Hence, the required answer is 73528

(B) Given, 5437×1001
=5437×(1000+1)
=5437×1000+5437×1
=5437000+5437
=5442437
Hence, the required answer is 5442437

(D) Given, 4275×125
=4275×(100+20+5)
=4275×100+4275×20+4275×5
=427500+85500+21375
=534375
Hence, the required answer is 534375

(E) Given, 504×35
=(500+4)×35
=500×35×4×35
=17500+140
=17640
Hence, the required answer is 17640

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:

From the given data, the next two steps can be written as follows:
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

The explanation to the pattern is as follows:
1 × 8 + 1 = 9
12 × 8 + 2 = 98
=(11 + 1)× 8 + 2
= 11 × 8 + 1 × 8 + 2
= 88 + 8 + 2
= 98

123 × 8 + 3 = 987
(111 + 11 + 1) × 8 + 3 = 111 × 8 + 11 × 8 + 1 × 8 + 2
= 888 + 88 + 8 + 3
= 987

1234 × 8 + 4 = 9876
=(1111 + 111 + 11 + 1)× 8 + 4
= 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8 + 4
= 8888 + 888 + 88 + 8 + 4
= 9876

12345 × 8 + 5 = 98765
(11111 + 1111 + 111 + 11 + 1) × 8 + 5
= 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8 + 5
= 88888 + 8888 + 888 + 88 + 8 + 5
= 98765

Extending the pattern, we have

123456 × 8 + 6
= (111111 + 11111 + 1111 + 111 + 11 + 1) × 8 + 5
= 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8 + 5
= 888888 + 88888 + 8888 + 888 + 88 + 8 + 6
= 987654

1234567 × 8 + 7
= (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1) × 8 + 7
= 1111111 × 8 + 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8 + 7
= 8888888 + 888888 + 88888 + 8888 + 888 + 88 + 8 + 7
= 9876543