Scott stated that when you add an even and an odd integer the answer will be odd.

Use these numbers to answer the questions:
–15, –6, 18, 21, –4

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

Write a rule for adding an even and an odd integer.

PLEASE HELP!! I HAVE TO BE 1000% RIGHT!

Question

Scott stated that when you add an even and an odd integer the answer will be odd.

Use these numbers to answer the questions:
–15, –6, 18, 21, –4

Is Scott’s statement always true, sometimes true, or always false? Write two equations to support your answer.

Write a rule for adding an even and an odd integer.

PLEASE HELP!! I HAVE TO BE 1000% RIGHT!

oaktree · Answer

Scott is 100% right - his statement is always true. Let's look at why this is with some examples from the given numbers.
$$-15 + -6 = -21$$$$21 + 18 = 39$$Both of these are sums of an even number and an odd number, but they give us odd numbers!
A more technical reason why this is is the following. Let an even number be $$2n$$and an odd number be $$2n+1$$These are obviously even an odd, respectively, since 2 divides the first evenly and not the second. So when we add the two, we get $$2n+2n+1 = 4n+1$$which is decidedly odd, since 2 does not divide one plus a multiple of 4! So Scott's right.

anonymous · Answer

omg thank you so much