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.
What are even numbers?
An even number is any number that gives a remainder of zero when divided by 2. For example, 12 gives a remainder of 0 when divided by 2, so 12 is even.
We saw in
divisibility rules
that a number is divisible by 2 or gives a remainder of zero 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.
What are odd numbers?
An odd number is any number that gives a remainder of 1 when divided by 2. For example, 25 gives a remainder of 1 when divided by 2, so 25 is odd.
Again, we saw in
divisibility rules
that a number is divisible by 2 or gives a remainder of zero 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.

Sep 17, 20 03:57 PM
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