why do an odd number added with an even number turns out to be an odd answer?

Question

i find this funny....

Answer 1

Because every other number is odd. There for if you are only adding the number in between them, then they are going to skip the even numbers.

Answer 2

Well, a little algebra will show you why. It is pretty straightforward.

Why is a number "even?" Because it is a multiple of 2. That is, every even number can be written as 2n for some n. So,

10 = 2 x 5
46 = 2 x 23
10456 = 2 x 5228

You get the idea. Now why is an integer odd? Because it is some even number plus 1, or 2t + 1. So,

11 = 2 x 5 + 1
47 = 2 x 23 + 1
10457 = 2 x 5228 + 1

Ok, now let answer your question. Let's add an even number to an odd on and see what we get. Here is our even number:

2k

and here is our odd one

2r + 1

Add them together

2k + 2r + 1 Let's rewrite this factoring out the 2

2(k + r) + 1 Now let's let k + r = n

2n + 1 Is that even, or odd? Right! It is odd. So, any even number added to any odd number is odd.

HTH

Charles

Answer 3

Because odd numbers occur every other number:

ONE, two, THREE, four, FIVE, etc etc

So if you are at an odd number (say on the number line) and you move a multiple of some even number you will, once again, land on an odd number.

Same thing is true of even numbers.

Answer 4

Án odd number is written as 2n+1 .An even number is written as 2h. The sum is 2(n+h) +1 which is an even number plus 1=An ODD number