Why is the product of 2 odd numbers, odd?

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Answer 1 · 2018-03-14T18:10:48

See an explanation below:

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:

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

$"odd number"$