## 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