Monday, 5 March 2012

CBSE Class VI ( 6th) Mathematics Chapter 2. Whole Numbers : Exercise 2.3

Question 1. Which of the following will not represent zero:
(a) a + 0
(b)  0 × 0
(c)  0
2
(d)   10×10
2


Answer:
(a)a + 0 and (d)    10×10
2



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
1.5 × 0 = 0Here second number is a Zero, and its product with 1 is also Zero
2.0 × 12 = 0Here first number is a Zero and its product with 12 is also Zero
3.0 × 0 = 0Here both numbers are a Zeros and their product is also Zero
Hence If the product of two whole numbers is zero, we can say that one or both of them will be zero
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.
Answer:
1.15 × 1 = 15Here second number is 1 and its product with 15 is 15
2.1 × 23 = 23Here first number is 1 and its product with 23 is 23
3.1 × 1 = 1Here both numbers are 1s and their product is 1
Hence If the product of two whole numbers is 1,we can say that one or both of them will be 1

Question 4. Find using distributive property :
(a) 728 × 101 (b) 5437 × 1001 (c) 824 × 25 (d) 4275 × 125 (e) 504 × 35
(a)728 × 101= 728×( 100 + 1 )
= 728 × 100 + 728 × 1
= 72800 + 728
= 72800 + 700 +28
= 73528
(b)5437 × 1001= 5437×( 1000 + 1 )
= 5437 × 1000 + 5437 × 1
= 5437000 + 5437
= 5437000 + 5000 + 400 + 37
= 5442000 + 400 + 37
= 5442400 + 37
= 54312437
(c)824 × 25= 824 × (20 + 5)
= 824 × 20 + 824 × 5
= 824×10×2+4120
= 8240×2 + 4120
= 16480+4120
= 16000+480+4000+120
= 20000+480+120
= 20600
(d)4275 × 125= 4275 × (100 + 25)
= 4275 × 100 + 4275 × 25
= 427500 + 4275 ×(20+5)
= 427500 + 4275×20+4275×5
= 427500 + 4275×10×2+21375
= 427500 + 42750×2+21375
= 427500 + 85550 + 21375
= 427000 + 500 + 85000 + 550 + 21000 + 375
= 560000 + 500 + 550 + 375
= 560000 + 1425
= 561425
(e)4504 × 35= (500+4) × 35
= 500×35+4&times35
= 500×(30+5)+4×(30+5)
= 500×30+500×5+4×30+4&times5
= 15000+25000+120+20
= 40140

Question 5. Study the pattern :

(i)1 × 8 + 1 = 9
(ii)12 × 8 + 2 = 98
(iii)123 × 8 + 3 = 987
(iv)1234 × 8 + 4 = 9876
(v)12345 × 8 + 5 = 98765
Write the next two steps. Can you say how the pattern works?
(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).
Answer:

(i)1 × 8 + 1 = 9
(ii)12 × 8 + 2 = 98
(iii)123 × 8 + 3 = 987
(iv)1234 × 8 + 4 = 9876
(v)12345 × 8 + 5 = 98765
(v)123456 × 8 + 6 = 987654
(v)1234567 × 8 + 7 = 9876543
How the Pattern works ?:
  • 10-1
  • 100-(1+1)
  • 1000-(10+3)
  • 10000-(100+20+4)
  • 100000-(100+100+30+5)

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