Even Number :
An even number is an integer which is a multiple of 2.
Examples :
2, 4, 6, 8, 10
Odd Number :
An odd number is an integer which is not a multiple of 2.
Examples :
1, 3, 5, 7
Note :
In a two digit number or three digit number or four digit number, to check whether it is even or odd, look at the digit at the ones place.
If the digit at the one's place is 0 or 2 or 4 or 6 or 8, then the number is even.
Examples :
138, 28596, 325670
If the digit at the ones place is 1 or 3 or 5 or 7, then the number is odd.
Examples :
261, 39485, 150867
1. The sum or difference of two even numbers is always an even number.
4 + 8 = 12
16 - 10 = 6
2. The sum or difference of two odd numbers is always an even number.
3 + 7 = 10
13 - 7 = 6
3. The sum or difference of an odd number and an even number is always an odd number.
3 + 8 = 11 6 + 7 = 13 |
13 - 6 = 7 8 - 5 = 3 |
4. The product of two even numbers is always an even number.
2 x 6 = 12
5. The product of an even number and an odd number is always an even number.
3 x 6 = 18
4 x 7 = 28
6. The product of two odd numbers is always an odd number.
3 x 7 = 21
Addition odd + odd = even even + even = even odd + even = odd even + odd = odd |
Multiplication odd x odd = odd even x even = even odd x even = even even x odd = even |
Example 1 :
Is 9 + 49 even or odd?
Solution :
9 = odd number
49 = odd number
Rule :
odd + odd = even
Moreover,
9 + 49 = 58
(58 is an even number)
So, 9 + 49 is even.
Example 2 :
Is 36 + 120 even or odd?
Solution :
36 = even number
120 = even number
Rule :
even + even = even
Moreover,
36 + 120 = 156
(156 is an even number)
So, 36 + 120 is even.
Example 3 :
Is 5 + 114 even or odd?
Solution :
5 = odd number
114 = even number
Rule :
odd + even = odd
Moreover,
5 + 114 = 119
(119 is an odd number)
So, 5 + 114 is odd.
Example 4 :
Is 146 + 289 even or odd?
Solution :
146 = odd number
289 = even number
Rule :
even + odd = odd
Moreover :
146 + 289 = 435
(435 is an odd number)
So, 146 + 289 is odd.
Example 5 :
Is 120 x 146 even or odd?
Solution :
120 = even number
146 = even number
Rule :
even x even = even
Moreover,
120 x 146 = 17520
(17520 is an even number)
So, 17520 is even.
Example 6 :
Is 121 x 14 even or odd?
Solution :
121 = odd number
14 = even number
Rule :
odd x even = even
Moreover,
121 x 14 = 1694
(1694 is an even number)
So, 121 x 14 is even.
Example 7 :
Is 151 x 17 even or odd?
Solution :
151 = odd number
17 = odd number
Rule :
odd x odd = odd
Moreover,
151 x 17 = 2567
(2567 is an odd number)
So, 151 x 17 is odd.
Example 8 :
Is 160 x 7 even or odd?
Solution :
160 = even number
7 = odd number
Rule :
even x odd = even
Moreover,
160 x 7 = 1120
(1120 is an even number)
So, 160 x 7 is even.
Example 9 :
Is 2x^{2} even or odd?
Solution :
In 2x^{2}, 'x' is a variable and it can take any value.
Whatever value we substitute for x, when x^{2} is multiplied by 2, it becomes a multiple of 2.
So, 2x^{2 }is even.
Example 10 :
Is 2x^{2} + 3 even or odd?
Solution :
From the above example 9, it is clear that 2x^{2 }is even.
And 3 is an odd number.
2x^{2} + 3 = even + odd
Rule :
even + odd = odd
So, 2x^{2} + 3 is odd.
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