If n is an integer, explain why 2n is an even number?

Question

Sorry, this is a really dumb question but an integer is a whole number, right? So that would be saying any whole number times itself is even, which is isn't e.g. 9x9 = 81.

Then write down, in terms of n, an expression for an odd number.

Oops! I feel really thick now!

Answer 1

An integer is a whole number, that is correct. An whole number times itself is not even, you even gave a counter example. You have mixed times by 2 with times by iteself.

If n is an integer than 2n is an even number because it has a factor of 2 as even number have a factor of 2.

Expression for odd number is 2n+1

Answer 2

Even numbers are any whole number divisible by 2. So 2n is always divisible by 2. An odd number is not divisible by 2 so 2n + 1 is odd. When I say divisible, the result must be a whole number with no remainder.

Answer 3

Multiply each and every little thing by using (n - a million)(n - 2) to cancel out all denominators: 2n(n - 2) - 2(n - a million) = (n - a million)(n - 2) escalate the brackets: 2n^2 - 4n - 2n + 2 = n^2 - 3n + 2 combine each and every of the like words: 2n^2 - 6n + 2 = n^2 - 3n + 2 flow each and every little thing to a minimum of one factor: n^2 - 3n = 0 element out n: n(n - 3) = 0 n = 0, 3

Answer 4

2 n means you multiply any number, represented by n, times two. since 2 is even, any number multiplied by an even number will also be even--two times any number, even or odd, equals an even result. This is also true of 4n, 6n, 8n etc. for the same reason. To get an odd number you'd have to multiply one odd number times another odd number, e.g. 9x 9, 7 x 5, etc.

Answer 5

9x9 is n² not 2n

if n=9, then 2n is 9x2 = 18

18 is an even number

in general, 2n is an even number because it is divisible by 2, and has a factor of 2.

Answer 6

You know, when I was starting out in algebra this confused me, too. It is all about what 2n means as opposed to n^2.

2n = n + n, which makes it easy to see why it is even (there's two of them, right? Right!)

What you have in mind is n * n which is n^2 (n-squared), and as you have discovered that in no way is always an even number.

This, BTW, is a fine way to learn algebra. Personal discoveries like this (n*n is never always an even number) will stay with you.

HTH

Charles

Answer 7

its not true that if your multiply a number by itself would be even.

but it is true that if you multiply a whole number to 2 or any even number.. the answer would always be an even..