Step by step
The question
Question: prove that the sum of two even numbers is even.
1 Write it with letters
x is even, so x = 2a, where a is a whole number.
That is what even means.
y is even, so y = 2b, where b is a whole number.
A new letter, b: y can be a different number from x.
Careful!
The same letter would make x and y the same number.
Two numbers need two letters.
2 Put them in
Now put them in: x + y becomes (2a) + (2b).
3 Work it out
Open the brackets: 2a + 2b.
4 Show the form
Every term has a 2 in it.
We take out 2: 2(a + b).
a + b is a whole number, because whole numbers added and multiplied stay whole.
2 times a whole number: so x + y is even.
The square at the end means: the proof is done.
5 Check
An example: x = 2 and y = 4.
It gives 6.
6 is 2 times 3: even, as the proof says.
Right!
Let's look back.
First: write it with letters.
Then: put them in.
Then: work it out.
Then: show the form.
Last: check.