## 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.