Why is the product of 2 odd numbers, odd?

1 Answer
Mar 14, 2018

Answer:

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"#