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.
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.
Can you find two other cases to support your answer?