Parent asking for grade 4 student.

Why is the sum of an odd number and an even number always odd?

Thank you
James

Let's ignore negative integers to keep it simple.

The even integers are the multiples of 2:

The remaining integers 1, 3, 5, 7, 9, 11, 13, ... are the odd integers - each odd number is one more than an even number, that is they all have the form

Thus if we add an even and an odd integer we have

even + odd = even + (even +1) = (even + even) +1 = even + 1 = odd.

For a grade 4 some examples would help

4 + 7 = 4 + (6 + 1) = (4 + 6) + 1 = 10 + 1 = 11

8 + 11 = 8 + (10 + 1) = (8 + 10) + 1 = 18 + 1 = 19,

Hope this helps,

Penny Nom