Step by step
The question
Question: prove that the sum of three consecutive integers is a multiple of 3.
1 Write it with letters
Call the first number n, a whole number.
The next integers are 1 more each time: n + 1, n + 2.
Careful!
An example shows one number.
The letters show every number at once.
2 Put them in
Add them up.
3 Work it out
Open the brackets: n + n + 1 + n + 2.
Like terms together: 3n + 3.
4 Show the form
Every term has a 3 in it.
We take out 3: 3(n + 1).
n + 1 is a whole number, because whole numbers added and multiplied stay whole.
3 times a whole number: so the sum is a multiple of 3.
The square at the end means: the proof is done.
5 Check
An example: 3, 4, 5.
It gives 12.
12 is 3 times 4: a multiple of 3, 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.