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A high-level explanation: Every odd number is equal to an even number plus 1. For example, 3 is equal to 2+1, 11 is equal to 10+1. So when you add together two odd numbers, you are adding the two even numbers that come right before them and you are adding the two extra ones. Adding two even numbers gives an even number, adding two ones gives you 2 which is also an even number.

For example, 3 + 11 is the same as (2+1) + (10+1). Since we can add in any order, this is the same as (2+10) + (1 + 1) or 12 + 2. Adding two to an even number always gives another even number.

A more formal proof:

Every odd number can be expressed as 2n + 1, where n is an integer.

So take two odd numbers, they can be expressed as 2a+1 and 2b+1, where a and b are integers. (2a+1)+(2b+1)= 2a + 2b + 2 = 2(a+b+1). Since a and b are integers, a+b+1 is an integer. So the sum of the two odd numbers is divisible by 2 which makes it an even number.

Simply because of basic arithmetic ! ANY odd number plus another odd number HAS to equal an even number !

Let m, n, and p be real numbers.

the representation of the 1st odd number: 2m + 1

the representation of the 2nd odd number: 2n + 1

the sum = 2m + 1 + 2n + 1 = 2(m + n) + 2

since m + n is also a real number, let's say equals to p, the sum representation of the two odd numbers becomes 2p + 2 which is an even number (the consecutive even number of even number 2p)

Q: Why is an odd number plus an odd number equal to an even number?

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Your question is incomplete. Adding an even number with an odd number will always result in an odd number. Multiplying an even number with an odd number will always result in an even number.

An odd number plus an odd number will be an even number. Odd number A is (even number + 1) Odd number B is (even number + 1) A + B = (even number + 1) + (even number + 1) = even number + even number + 2 Since all even numbers are divisible by 2 and 2 is divisible by 2, each part of the result is divisible by 2, so the sum as a whole is divisible by 2, which means it is an even number.

For any even number n, the following integer is odd (n+1), so for any odd number other than 1, you are adding the preceding even number, plus 1. Because all even numbers are multiples of 2, their sum is even, and 1 more will be an odd number.---Think of the odd number as an even number plus one and remember that all even numbers are multiples of two.Therefore:- Any two even numbers added together will always be a multiple of two and therefore even. Any two odd numbers added together will be the same as adding two even numbers plus 1 plus 1. (A multiple of two plus two which is still a multiple of two).An odd number added to an even number will be the same as two even numbers plus 1 in other words a multiple of two (even) plus one making the result odd.Extrapolating further it's easy to see that by the above reasoning that for all positive integers...Any number of even numbers added together will always be even.An odd number of odd numbers added together will always be odd.Any even number of odd numbers added together will always be even,Adding any number of even numbers to any number of odd numbers will make no difference to the outcome, the odd or even outcome will still be determined by the number of odd numbers being added together.---Another approach:Let n, r be real numbers even number representation: 2nodd number representation: 2n + 1sum = 2n + 2n + 1 = 4n + 1 = 2(2n) + 1let 2n = rsum representation becomes: 2r + 1, which is a representation of an odd number.

Always an even number. Think of an odd number as an even number plus a half. Add them up and the two halves make an even.

Only integers are even or odd. If a decimal is equal to an integer (for example 24.0 is equal to 24), then it can be even or odd. If a decimal is not equal to an integer (for example, 24.1 is not an integer), then it is neither even nor odd.

Related questions

An odd number plus an even number will always be an odd number.

An even number

Yes.

An even number.

In normal arithmetic, never.

Any odd number can be written as an even number plus one. Any even number plus any other even number makes an even number. Add one makes an odd number. So an odd number plus an even number is always an odd number. Algebraically, any odd number can be written as 2a+ 1 where a is a whole number. Any even number can be written as 2b, where b is a whole number. Add them together, the sum is 2(a + b) + 1, which is odd.

All even numbers can be divided by two, while odd numbers can't. Also, an even number plus an even number is always even. An odd number plus an odd number is always even. An even number plus an odd number is always odd.

You'll get an odd number when adding two evens (which will be even) and an odd number.

It doesn't. An even number(for example 2) plus an odd number(for example 3) would give you an odd number for the answer. Comment: Im sorry but you are mistaken, 2 is an odd number 2/2 2/1 so 2+4=6 see?

Yes, an even number plus an even number is always even. Also, and odd number plus an odd number is always even.

Yes it would Even + even = even Even + odd = odd Odd + odd = even

What! Even numbers never equal an odd number. Not ever!