Chapter 2 Whole Numbers Exercise 2.3
Question 1: Which of the following will not represent zero:a) 1 + 0
b) 0 × 0
c) 0/2
d) 10 - 10/2
Answer:
a) 1 + 0 = 1
Therefore, it does not represent zero
b) 0 × 0 = 0
Therefore, it represents zero
c) 0/2 = 0
Therefore, it represents zero
d) 10 - 10/2 = 0/2 = 0
Therefore, it represents zero
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: If product of two whole numbers is zero, definitely one of them is zero. Example: 0 × 5 = 0 and 1560 × 0 = 0. If product of two whole numbers is zero, both of them may be zero. Example: 0 × 0 = 0. Yes, if the product of two whole numbers is zero, then 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: If the product of two whole numbers is 1, both the numbers should be equal to 1. Example: 1 × 1 = 1 but 1 × 15048 = 15048. Therefore, it’s clear that the product of two whole numbers will be 1, only in situation when both numbers to be multiplied are 1.
Question 4: Find using distributive property:
a) 728 × 101
b) 5437 × 1001
c) 824 × 25
d) 4275 × 125
e) 504 × 35
Answer:
a)
= 728 × 101
= 728 × (100 + 1)
= 728 × 100 + 728 × 1
= 72800 + 728
= 73528
b)
= 5437 × 1001
= 5437 × (1000 + 1)
= 5437 × 1000 + 5437 × 1
= 5437000 + 5437
= 5442437
c)
= 824 × 25
= (800 + 24) × 25
= (800 + 25 - 1) × 25
= 800 × 25 + 25 × 25 - 1 × 25
= 20000 + 625 - 25
= 20000 + 600
= 20600
d)
= 4275 × 125
= (4000 + 200 + 100 - 25) × 125
= (4000 × 125 + 200 × 125 + 100 × 125 - 25 × 125)
= 500000 + 25000 + 12500 – 3125
= 534375
e)
= 504 × 35
= (500 + 4) × 35
= 500 × 35 + 4 × 35
= 17500 + 140
= 17640
Question 5: Study the pattern:
1 × 8 + 1 = 9
12 × 8 + 2 = 98
123 × 8 + 3 = 987
1234 × 8 + 4 = 9876
12345 × 8 + 5 = 98765
Write the next two steps. Can you say how the pattern works? (Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).
Answer:
123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543
123456 = (111111 + 11111 + 1111 + 111 + 11 + 1)
123456 × 8 = (111111 + 11111 + 1111 + 111 + 11 + 1) × 8
= 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8
= 888888 + 88888 + 8888 + 888 + 88 + 8
= 987648
123456 × 8 + 6 = 987648 + 6
= 987654
Yes, here the pattern works.
1234567 × 8 + 7 = 9876543
Given 1234567 = (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1)
1234567 × 8 = (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1) × 8
= 1111111 × 8 + 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8
= 8888888 + 888888 + 88888 + 8888 + 888 + 88 + 8
= 9876536
1234567 × 8 + 7 = 9876536 + 7
= 9876543
Yes, here the pattern works.
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