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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.
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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.
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Another approach:
Let n, r be real numbers even number representation: 2n
odd number representation: 2n + 1
sum = 2n + 2n + 1 = 4n + 1 = 2(2n) + 1
let 2n = r
sum representation becomes: 2r + 1, which is a representation of an odd number.
What else can I help you with?
Why is a even number plus an even number equal to an even number?
You can simply take the lowest even numbers and subtract it i.e. 4-2=2
Does x squared plus x plus 41 always equal a prime number?
No. it's not a prime number when x = 40, 41, 81,82 ...
When you add two odd number together is your answer an even or 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.
Why is an even number plus an even number always even?
An even number + another even number are always even because if you think in terms of a number line, an even number always skips the odd numbers, when adding, so to speak. If you have 2+2 you are skipping 3. Think of every addition of even numbers broken down into 2's for a minute. 12+4 = 12+2+2, so you start at 12, skip 13, then skip 15.
A number plus twice the number is equal to three times the number?
A + 2a = 3a
What does odd plus even equal?
An odd number plus an even number will always be an odd number.
What does odd plus odd always equal?
An even number
Does a odd number plus a odd number always equal a even number?
Yes.
Is an even number plus an even number always even?
Yes, an even number plus an even number is always even. Also, and odd number plus an odd number is always even.
Is a even plus a even equal a odd or a even?
Even. Always
What is an even number plus an even number equal to?
An even number.
What is even plus an even number?
always even
When does a negative number plus a negative number equal a negative?
Always.
Does an irrational plus a rational number equal an irrational number?
Yes, always.
When does the sum odd number plus even number equal even number?
In normal arithmetic, never.
The sum of two odd numbers is always odd?
The sum of any two odd numbers is always even. This is because (a) any odd number can always be expressed as an even number plus 1, and (b) the sum of two even numbers is always even. So if X is even and Y is even then X+1 added to Y+1 will equal X+Y+2
When odd number plus an even number is equal even numbers?
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.
