CBSE Class VI ( 6th) Mathematics Chapter 2. Whole Numbers : Exercise 2.3
Question 1. Which of the following will not represent zero:
Answer:
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
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:
Question 4. Find using distributive property :
(a) 728 × 101 (b) 5437 × 1001 (c) 824 × 25 (d) 4275 × 125 (e) 504 × 35
Question 5. Study the pattern :
Write the next two steps. Can you say how the pattern works?
(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).
Answer:
| (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 = 0 | Here second number is a Zero, and its product with 1 is also Zero |
| 2. | 0 × 12 = 0 | Here first number is a Zero and its product with 12 is also Zero |
| 3. | 0 × 0 = 0 | Here 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 | ||
1? Justify through examples.
Answer:
| 1. | 15 × 1 = 15 | Here second number is 1 and its product with 15 is 15 |
| 2. | 1 × 23 = 23 | Here first number is 1 and its product with 23 is 23 |
| 3. | 1 × 1 = 1 | Here 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+4×35 | ||
| = 500×(30+5)+4×(30+5) | ||
| = 500×30+500×5+4×30+4×5 | ||
| = 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 |
(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 ?: | |
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