Question

PLEASE ANSWER ASAP! IMPORTANT! MUST BE CORRECT! GIVING OUT POINTS!

John stated that when you add an even and an odd integer the answer will be odd. Use these numbers to answer the questions: –13, –8, 16, 23, –7

Is John’s statement always true, sometimes true, or always false? Write two equations to support your answer.

Answer 1

Try adding some of these together to look for the pattern:

-13 +16 = 3 odd+even = odd

-7 + 16 = 9

how about -13 + -7 = -20

-8 + 16 = 8

It looks like

even + even = even
odd + odd = even

even + odd = odd

So, we only get an odd result in this case. It seems that it is always true.

Answer 2

so an even number is represented as 2n where n= a whole number
an odd is 1 more than an even so 2n+1 is odd

so even+odd=2n+2n+1=4n+1=
we see 2 2n's in there which are even
(even)+(even)+1
we know that even+even=even try that withe any 2 even numbers
then +1 means it's odd so therefor it is always true