**Whole Numbers Class 6 Ex. 2.3**

**Ncert Class 6 Math Free Solution.**

**Exercise 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 1:-**

(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 ).

**Question 2 :- f the product of two whole numbers is zero, can we say that one or both of them will be zero? Justify through examples. **

**Solution 2:-**

Yes,

Examples :-

7 x 0 = 0

0 x 6 = 0

0 x 0 = 0

**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 3:-**

Only when all of the numbers are 1 is this true.

1 x 1 = 1

1 x 0 = 0

0 x 1 = 0

So, condition only true, when each of the number are 1.

**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 4:-**

(a) 728 x 101 = 728 x (100 + 1)

= 728 x 100 + 728 x 1

= 72800 + 728

= 73,528

(b) 5437 x 1001 = 5437 x (1000 + 1)

= 5437 x 1000 + 5437 x 1

= 54,37,000 + 5,437

= 54,42,437

(c) 824 x 25 = 824 x (20 + 5)

= 824 x 20 + 824 x 5

= 16480 + 4120

= 20,600

(d) 4275 x 125 = 4275 x (100 + 20 + 5)

= 4275 x 100 + 4275 x 20 + 4275 x 5

= 427500 + 85500 + 21375

= 5,34,375

(e) 504 x 35 = (500 + 4) x 35

= 500 x 35 + 4 x 35

= 17500 + 140

= 17,640

**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 5:-**

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 = 98,765.