Whole Numbers Ex 2.3
Q1. Which of the following will not represent zero:
(a) 1 + 0
(b) 0 × 0
(c) 0 / 2
(d) (10 – 10) / 2
Solutions:
(a) 1 + 0 = 1
Hence, it does not represent zero
(b) 0 × 0 = 0
Hence, it represents zero
(c) 0 / 2 = 0
Hence, it represents zero
(d)(10 – 10) / 2 = 0
Hence, it represents zero
Q2. If the product of two whole numbers is zero, can we say that one or both of them will be zero? Justify through examples.
Solutions:
If product of two whole numbers is zero, definitely one of them is zero
Example: 0 × 3 = 0 and 15 × 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
Q3. If the product of two whole numbers is 1, can we say that one or both of them will be 1? Justify through examples.
Solutions:
If the product of two whole numbers is 1, both the numbers should be equal to 1
Example: 1 × 1 = 1
But 1 × 5 = 5
Hence, its clear that the product of two whole numbers will be 1, only in situation when both numbers to be multiplied are 1
Q4. Find using distributive property:
Q4. Find using distributive property:
(a) 728 × 101
(b) 5437 × 1001
(c) 824 × 25
(d) 4275 × 125
(e) 504 × 35
Solutions:
(a) Given 728 × 101
= 728 × (100 + 1)
= 728 × 100 + 728 × 1
= 72800 + 728
= 73528
(b) Given 5437 × 1001
= 5437 × (1000 + 1)
= 5437 × 1000 + 5437 × 1
= 5437000 + 5437
= 5442437
(c) Given 824 × 25
= (800 + 24) × 25
= (800 + 25 – 1) × 25
= 800 × 25 + 25 × 25 – 1 × 25
= 20000 + 625 – 25
= 20000 + 600
= 20600
(d) Given 4275 × 125
= (4000 + 200 + 100 – 25) × 125
= (4000 × 125 + 200 × 125 + 100 × 125 – 25 × 125)
= 500000 + 25000 + 12500 – 3125
= 534375
(e) Given 504 × 35
= (500 + 4) × 35
= 500 × 35 + 4 × 35
= 17500 + 140
= 17640
Q5. 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)
Solutions:
123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543
Given 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
