Even and odd numbers are straightforward concepts. I will start easy, but I will try to challenge the topic a little bit

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

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

An odd number is any number that

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

Other examples of odd numbers are 53, 881, 238637, 99, 45, and 100000023

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

even + even = even

4 + 2 = 6

even + odd = odd

6 + 3 = 9

odd + odd = even

13 + 13 = 26

even × even = even

2 × 6 = 12

even × odd = even

8 × 3 = 24

odd × odd = odd

3 × 5 = 15

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.