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Which of the following will not represent zero?
(a) 1 + 0 (b) 0 × 0
(c) 
(d) 
a) 1+0 = 1 - it does not represents 0.
b) 0x0 = 0 - it represents 0.
c) 0/2 = 0- it represents 0.
d) 10-10/2 = 0/2 = 0- it represents 0.
If the product of two whole numbers is zero, can we say that one or both of them will be zero? Justify through examples.
If the product of 2 whole numbers is 0, it is important that one or both of them will be zero.
Example - 0x0 = 0 (product is 0 if both numbers are 0)
0x 2 - 0 (product is 0 if one number is 0)
2x 3 - 6 (product is not 0 as no number is 0)
If the product of two whole numbers is 1, can we say that one of both of them will be 1? Justify through examples.
If the product of 2 numbers is 1, then both the numbers have to be equal to 1.
For example, 1 × 1 = 1
However, 1 × 6 = 6
Clearly, the product of two whole numbers will be 1 in the situation when both numbers to be multiplied are 1.
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 = 73528
(b) 5437 × 1001 = 5437 × (1000 + 1)
= 5437 × 1000 + 5437 × 1
= 54,37,000 + 5437 = 54,42,437
(c) 824 × 25 = (800 + 24) × 25
= (800 + 25 − 1) × 25
= 800 × 25 + 25 × 25 − 1 × 25
= 20,000 + 625 − 25
= 20,000 + 600 = 20600
(d) 4275 × 125 = (4000 + 200 + 100 − 25) × 125
= 4000 × 125 + 200 × 125 + 100 × 125 − 25 × 125
= 5,00,000 + 25000 + 12500 − 3125
= 534375
(e) 504 × 35 = (500 + 4) × 35
= 500 × 35 + 4 × 35
= 17500 + 140 = 17640
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).
1,23,456 × 8 + 6 = 9,87,648 + 6 = 9,87,654
12,34,567 × 8 + 7 = 98,76,536 + 7 = 98,76,543
Yes, the pattern works.
As 1,23,456 = 111111 + 11111 + 1111 + 111 + 11 + 1,
1,23,456 × 8 = (111111 + 11111 + 1111 + 111 + 11 + 1) × 8
= 1,11,111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8
= 8,88,888 + 88,888 + 8888 + 888 + 88 + 8 = 9,87,648
1,23,456 × 8 + 6 = 9,87,648 + 6 = 9,87,654
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