Even and odd numbers
Even and odd numbers are straightforward concepts. I will start easy, but I will try to challenge the topic a little bit
Even numbers
An even number is any number that can be divided by 2.For example, 12 can be divided by 2, so 12 is even.
We saw in
divisibility rules
that a number is divisible by 2 if its last digit is 0,2,4,6,or 8.
Therefore, any number whose last digit is 0, 2, 4, 6, or 8 is an even number
Other examples of even numbers are 58, 44884, 998632, 98, 48, and 10000000
Formal definition of an even number:
A number n is even if there exist a number k, such that n = 2k where k is an
integer
This is formal way of saying that if n is divided by 2, we always get a quotient k with no remainder
Having no remainder means that n can in fact be divided by 2
Odd numbers
An odd number is any number that
cannot be divided by 2.For example, 25 cannot be divided by 2, so 25 is odd.
We saw in
divisibility rules
that a number is divisible by 2 if its last digit is 0,2,4,6,or 8.
Therefore, any number whose last digit is
not 0, 2, 4, 6, or 8 is an odd number
Other examples of odd numbers are 53, 881, 238637, 99, 45, and 100000023
Formal definition of an odd number:
A number n is odd if there exist a number k, such that n = 2k + 1 where k is an
integer
This is formal way of saying that if n is divided by 2, we always get a quotient k with a remainder of 1
Having a remainder of 1 means that n cannot in fact be divided by 2
Basic operations with even and odd numbers
Addition
even + even = even
4 + 2 = 6
even + odd = odd
6 + 3 = 9
odd + odd = even
13 + 13 = 26
Multiplication
even × even = even
2 × 6 = 12
even × odd = even
8 × 3 = 24
odd × odd = odd
3 × 5 = 15
Subtraction
even − even = even
8 − 4 = 4
even − odd = odd
6 − 3 = 3
odd − odd = even
13 − 3 = 10
If you have any questions about this even and odd numbers lesson, just contact me.