Chapter - 2- EXERCISE 2.3 - Basic Geometrical Ideas (NCERT Class 6th Maths Solution)

1. Which of the following will not represent zero: 

Solution/Explanation:

(a) 1+0 =1      It does not represent zero


(b) 0 x 0 = 0   It represents zero


(c) 0/2 = 0      It Represents zero


(d) 10-10/ 2 = 0   It represents 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/Explanation:

2⋅0=0${\displaystyle 2\cdot 0=0}$
15⋅0=0${\displaystyle 15\cdot 0=0}$
0⋅0=0${\displaystyle 0\cdot 0=0}$
so, we can say that the one or both of them will be zero, if the product of 2 whole nos is zero

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/Explanation:

If the product of two whole numbers is 1, then both the numbers should be 1.

Let us consider two numbers, for example, 55 and 1.

55 × 1 = 55

We see that the product is not 1.

But, 1 × 1 = 1.

Thus, if the product of any two whole numbers is 1, then both of them should be 1.

4. Find using distributive property : 

(a) 728 × 101            (b) 5437 × 1001               (c) 824 × 25 (d) 4275 × 125          (e) 504 × 35 

Solution/Explanation: 

(a) We have, 728 x 101 = 728 x (100 + 1) = 728 x 100 + 728 x 1 [by distributive property of multiplication over addition] = 72800 + 728 = 73528 

(b) We have, 5437 x 1001 = 5437 x (1000 + 1) = 5437 x 1000 + 5437 x 1 [by distributive property of multiplication over addition] = 5437000 + 5437 = 5442437 

(c) We have,   824 x 25 = 824 x (20 + 5) = 824 x 20 + 824 x 5 [by distributive property of multiplication over addition] = 16480 + 4120 = 20600 

(d) We have, 4275 x 125 = 4275 x (100 + 20 +5) = 4275 x 100 + 4275 x 20 + 4275 x 5 [by distributive property of multiplication over addition] = 427500 + 85500 + 21375 = 513000 + 21375 = 534375 (e) We have, 504 x 35 = 35 x 504    [by commutative property] = 35 x (500 + 4) = 35 x 500 + 35 x 4 [By distributive property of multiplication over addition] = 17500 + 140 = 17640

5. Study the pattern : 

         1 × 8 + 1 = 9                                  1234 × 8 + 4 = 9876                   12 × 8 + 2 = 98                                12345 × 8 + 5 = 98765             123 × 8 + 3 = 987 

Write the next two steps. Can you say how the pattern works?
(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1). 

Solution/Explanation:

The given pattern works as,

123456=111111+11111+1111+111+11+1123456×8=(111111+11111+1111+111+11+1)×8=888888+88888+8888+888+88+8=987648

Now next step of given pattern will be,

123456×8+6=987648+6=987654

Second next step will be,

1234567×8+7=9876536+7=9876543