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Standard VII

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Shahajiraje and Jijabai

What pattern ...

Question

What pattern can you observe in a 3 table ?

The product alternate between odd and even numbers

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The sum of the product adds up either to 3, 6 and 9

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All the numbers end in zero

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Only (1) and (2) are true

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Solution

The correct option is D
Only (1) and (2) are true

When we observe the table, then we have the products which follow a pattern i.e starting from an odd number and then even number and so on.

Also when we observe the product of the numbers and add the digits, we get the sum as either 3, 6 or 9, basically it is a multiple of 3.

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Similar questions

Q. (i) Take any three consecutive odd numbers and find their product; for example,

1 \times 3 \times 5 = 15, 3 \times 5 \times 7 = 105, 5 \times 7 \times 9 - . . . . . .

(ii) Take any three consecutive even numbers and add them, say,

2 + 4 + 6 = 12, 4 + 6 + 8 = 18, 6 + 8 + 10 = 24, 8 + 10 + 12 = 30

and so on.
Is there any pattern you can guess in these sums? What can you conjecture about them?

State whether the following statements are True or False:

(a) The sum of three odd numbers is even.

(b) The sum of two odd numbers and one even number is even.

(d) If an even number is divided by 2, the quotient is always odd.

(e) All prime numbers are odd.

(f) Prime numbers do not have any factors.

(g) Sum of two prime numbers is always even.

(h) 2 is the only even prime number.

(i) All even numbers are composite numbers.

(j) The product of two even numbers is always even.

Q. Even and Odd Number Patterns

91
81
71
61
51
41
31
21
11
1

92
82
72
62
52
42
32
22
12
2

93
83
73
63
53
43
33
23
13
3

94
84
74
64
54
44
34
24
14
4

95
85
75
65
55
45
35
25
15
5

96
86
76
66
56
46
36
26
16
6

97
87
77
67
57
47
37
27
17
7

98
88
78
68
58
48
38
28
18
8

99
89
79
69
59
49
39
29
19
9

100
90
80
70
60
50
40
30
20
10

Half these numbers are in yellow. What patterns do you see in these numbers? Continue the same pattern and fill in the blanks:
96, 98, _____, 102, _____, _____, _____, _____, _____
How far can you continue this pattern?
These numbers have a special name. They are called even numbers.
Do any of these even numbers end with 3 or 5?
What do even numbers end with?
Look at the pattern of numbers in blue. Continue the pattern and fill in the blanks:
99, 101, _____, 105, 107, _____, _____, _____
What do the numbers in blue end with?
All numbers that end with 1, 3, 5, 7 or 9 are called odd numbers.
Write all odd numbers between 400 and 410.
_________________________________________________________________
Write all even numbers between 155 and 165.
_________________________________________________________________
If we add 1 to any odd number we get an _________ (even/odd) number.
If we add 1 to any even number we get an _________ (even/odd) number.
What do you get if you add an even number to an odd number?

Q. Multiplication Patterns

9 × 1 = 9
9 × 2 = 18	1 + 8 = 9
9 × 3 = 27	2 + 7 = 9
9 × 4 = 36	3 + 6 = 9
9 × 5 = 45	4 + 5 = 9
9 × __ = __	__ + __ = __
9 × __ = __	__ + __ = __
9 × 8 = __	__ + __ = __

Did you see the pattern in the 9 times table? What numbers are adding up to 9?

Q. A box contains

9

tickets numbered

1

9

inclusive. If

3

tickets are drawn from the box without replacement. The probability that they are alternatively either {odd, even, odd} of {even, odd, even} is

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