Step by step
The question
Question: prove that the product of two multiples of 4 is a multiple of 16.
1 Write it with letters
x is a multiple of 4, so x = 4a, where a is a whole number.
That is what a multiple of 4 means.
y is a multiple of 4, so y = 4b, 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: xy becomes (4a)(4b).
3 Work it out
Every part times every part: 16ab.
4 Show the form
Every term has a 16 in it.
We take out 16: 16ab.
ab is a whole number, because whole numbers added and multiplied stay whole.
16 times a whole number: so xy is a multiple of 16.
The square at the end means: the proof is done.
5 Check
An example: x = 4 and y = 8.
It gives 32.
32 is 16 times 2: a multiple of 16, 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.