## Chapter 2: Whole Numbers

## Exercise 2.3

**Q1. Which of the following will not represent zero:**

(a) 1 + 0

(b) 0 x 0

(c)

(d)

**Answer.**

(a) is equal to 1

**Q2. 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 we multiply any number with zero the resultant product will be zero.

Example: 2 x 0 = 0, 5 x 0 = 0, 8 x 0 = 0

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

0 x 0 = 0

**Q3. If the product of two whole number is 1, can we say that one or both of them will be 1? Justify through examples. **

**Answer.** If only one number be 1 then the product cannot be 1.

Examples: 4 x 1 = 4, 6 x 1 = 6, 8 x 1 = 8

If both number are 1, then the product is 1

1 x 1 = 1

**Q4. Find using distributive property: **

**(a) 728 x 101 **

**(b) 5437 x 1001 **

**(c) 824 x 25 **

**(d) 4275 x 125 **

**(e) 504 x 35 **

**Answer. **

(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 x5

= 427500 + 85500 + 21375 = 534375

(e) 504 x 35

= (500 + 4) x 35

= 500 x 35 + 4 x 35

= 17500 + 140

= 17640

**Q5. 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? **

**Answer.**

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

Pattern works like this:

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

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9875643