Is the sum of two odd numbers always going to be even?

Answer 1

Yes!

Let's think about it. If we let x = any odd number. Then any other odd number could be written as x+2y or in other words x+(some multiple of 2 let's say 2y).

If we add the original odd number x, and the new odd number x+2y then we get

x + x + 2y, which is 2x + 2y! Using a little bit of factoring we get 2(x + y), which implies that we are multiplying by 2 which will always result in an even number.

Why does multiplying by 2 imply that the number is even? Well that would mean that the final product is divisible by 2, which would make that number by definition even.