Question

Why is the product of 2 odd numbers, odd?

Answer 1

See an explanation below:

Explanation:

The same odd number added together will always produce and even number.

If `a` is odd (or even for that matter) then

`a + a = 2a`

Because 2 times a number is always even.

If `a` and `b` are odd numbers then we can write their product as:

`a xx b`

This can be rewritten as:

`a xx (b - 1 + 1) =>`

`a xx ((b - 1) + 1) =>`

`(a xx (b - 1)) + (a xx 1)`

Because `b` is odd, therefore `(b - 1)` is even.

Because `(b - 1)` is even, therefore `a xx (b - 1)` is even.

Because `a` is odd and `(a xx 1) = a`, therefore, `(a xx 1)` is also add.

Therefore:

Because an odd number plus an even number equal and odd number, therefore:

`(a xx (b - 1)) + (a xx 1) = "even number" + "odd number" =`

`"odd number"`