Step by step
The question
Question: prove that the sum of two multiples of 7 is a multiple of 7.
1 Write it with letters
x is a multiple of 7, so x = 7a, where a is a whole number.
That is what a multiple of 7 means.
y is a multiple of 7, so y = 7b, 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 (7a) + (7b).
3 Work it out
Open the brackets: 7a + 7b.
4 Show the form
Every term has a 7 in it.
We take out 7: 7(a + b).
a + b is a whole number, because whole numbers added and multiplied stay whole.
7 times a whole number: so x + y is a multiple of 7.
The square at the end means: the proof is done.
5 Check
An example: x = 7 and y = 14.
It gives 21.
21 is 7 times 3: a multiple of 7, 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.