Why Adding or Subtracting Odd Numbers Always Results in Even Numbers | Algebraic Proof

odd +/- odd=

even

When we add or subtract two odd numbers, the result is always an even number.

For example:

3 + 5 = 8 (which is an even number)
9 – 7 = 2 (which is also an even number)

We can prove this mathematically using algebraic expressions:

Let’s assume that x and y are odd numbers.

An odd number can be represented as 2n+1, where n is any integer.

So, x = 2a+1 and y = 2b+1, where a and b are any integers.

Now, let’s add or subtract these two odd numbers:

x + y = 2a+1 + 2b+1
= 2(a+b) + 2
= 2(a+b+1)

We can see that the result is always an even number (2 multiplied by any integer)

Similarly, if we subtract two odd numbers:

x – y = 2a+1 – (2b+1)
= 2(a-b)

Again, we can see that the result is always an even number (2 multiplied by any integer).

Therefore, odd +/- odd always equals an even number.

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