Question

This is the example my teacher used. However, I still don't understand what makes the integers even or odd. I was hoping someone here could help me understand the difference.

Answer 1

Here's what makes an integer odd:

• It is NOT a multiple of 2.

• When divided by 2, the quotient would be a decimal or have a remainder or fraction.

Here's what makes an integer even:

• It is a multiple of 2.

• When divided by 2, the quotient has a whole number.

The odd numbers from one to 10 are: 1, 3, 5, 7, 9.

The even numbers from one to 10 are: 2, 4, 6, 8, 10.

• With big numbers, if it ends with any of the odd numbers from one to ten, listed above, it would be odd. This goes for the same with even.

With the x + 2, x + 4, etc:

• An odd number and even number has a pattern....

[odd, even, odd, even, odd...] [1, 2, 3, 4, 5]

• So, if x was an odd number, adding it by 2, 4, 6, etc. will result in another odd number.

Here's an example:

`x= 17\\x + 2 = ?\\(17) + 2 = 19`

See how x is an odd number and the sum of the number and two makes another odd number?

The same can go with an even number:

`x=2\\x + 6 = ?\\(2) + 6= 8`

See how x is an even number and the sum of the number and six makes another even number?

I hope my answer helps you understand even and odd numbers.