Even and odd numbersEven 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 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. 




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