Key to "Why is the product of 2 odd numbers,..."

High School
Algebra
Algebra I
Forms of linear equations

blackdivcp

Answered question

2022-10-14

Why is the product of 2 odd numbers, odd?

Answer & Explanation

Kash Osborn

Beginner2022-10-15Added 18 answers

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 \times b

This can be rewritten as:

a \times (b - 1 + 1) \Rightarrow

a \times ((b - 1) + 1) \Rightarrow

(a \times (b - 1)) + (a \times 1)

Because b is odd, therefore (b−1) is even.
Because (b−1) is even, therefore

a \times (b - 1)

is even.
Because a is odd and

(a \times 1) = a

, therefore,

(a \times 1)

is also add.
Therefore:
Because an odd number plus an even number equal and odd number, therefore:

(a \times (b - 1)) + (a \times 1) = even number + odd number =

odd number

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