● A number is called an odd number if it cannot be grouped equally in twos. 1, 3, 5, 7, …, 73, 75, …, 2009,… are
odd numbers.
● A number is called an even number if it can be grouped equally in twos. 2, 4, 6, 8, ..., 68, 70, . . , 4592,... are even numbers.
● All odd numbers end with any one of the digits 1, 3, 5, 7 or 9.
● All even numbers end with any one of the digits 0, 2, 4, 6 or 8.
●In whole numbers, odd and even numbers come alternatively.
● 1 is odd, its successor 2 is even and so its predecessor 0 is also even.
●The first natural number 1 is odd and the first whole number 0 is even.
Observe the following additions :
1 + 3 = 4
5 + 11 = 16
21 + 47 = 88
From this observation, we conclude that “the sum of any two odd numbers is always an even number".
Observe the following additions :
4 + 5 = 9
7 + 12 = 19
35 + 56 = 93
From this observation, we conclude that “the sum of any odd number and any even number is always an odd number".
Observe the following products :
5 x 3 = 15
7 x 9 = 63
11 x 13 = 143
From this observation, we conclude that “the product of any two odd numbers is always an odd number”
Observe the following products :
2 x 4 = 8
9 x 6 = 36
12 x 8 = 96
15 x 12 = 180
From this observation, we conclude that “the product of any number (odd or even) and an even number is always an even number”
Observe the following products :
1 x 3 x 5 = 15
7 x 9 x 11 = 693
13 x 17 x 21 = 4641
From this observation, we conclude that “the product of any three odd numbers is always an odd number.”
Problem 1 :
Find the sum of the smallest and largest two-digit even numbers?
Solution :
Smallest two-digit even number = 10
Largest two-digit even number = 98
Sum of the smallest and largest two-digit even numbers :
= 10 + 98
= 108
Problem 2 :
Find the sum of the smallest and largest two-digit odd numbers?
Solution :
Smallest two-digit odd number = 11
Largest two-digit even number = 99
Sum of the smallest and largest two-digit odd numbers :
= 11 + 99
= 110
Problem 3 :
Find the sum of the smallest two-digit even number and the largest three-digit odd number?
Solution :
Smallest two-digit even number = 10
Largest three-digit odd number = 999
Sum of the smallest two-digit even number and the largest three-digit odd number :
= 10 + 999
= 1009
Problem 4 :
What is the difference between the largest three-digit even number and the smallest three-digit odd number?
Solution :
Largest three-digit even number = 998
Smallest three-digit odd number = 101
Difference between the largest three-digit even number and the smallest three-digit odd number :
= 998 - 101
= 897
Problem 5 :
What is the difference between the largest four-digit odd number and the smallest three-digit even number?
Solution :
Largest four-digit odd number = 9999
Smallest three-digit even number = 100
Difference between the largest three-digit even number and the smallest three-digit odd number :
= 9999 - 100
= 9899
Problem 6 :
Write all the two-digit odd numbers which are multiples of 7.
Solution :
21, 35, 49, 63, 77, 91
Problem 7 :
Write all the two-digit even numbers which are multiples of 7.
Solution :
14, 28, 42, 56, 70, 84, 98
Problem 8 :
Write all the two-digit odd numbers which are multiples of 5.
Solution :
10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95
Problem 9 :
Find the sum of all two-digit even numbers which are multiples of 12.
Solution :
Sum of all two-digit even numbers which are multiples of 12 :
= 12 + 24 + 36 + 48 + 60 + 72 + 84 + 96
= 432
Problem 10 :
Find the sum of all three-digit even numbers which are multiples of 100.
Solution :
Sum of all three-digit even numbers which are multiples of 100 :
= 100 + 200 + 300 + 400 + 500 + 600 + 700 + 800 + 900
= 4500
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