Is this statement true? Give an example to support your answer. "If two numbers are divisible by another number then their difference is also divisible by that number".

Question

I think that its like this:
3 and 4 is divisible by 12 then 4-3=1 so the answer is no?

Answer 1

You have your thinking backwards.
an example of the above would be

both 12 and 30 are divisible by 3
then their difference is divisible by 3

check:
difference = 30-12 = 18
is 18 divisible by 3 ? YES

actual proof:
let the two numbers be kx and ky.
kx and ky are both divisible by k, since we can factor out k from each of them

their difference is kx - ky
= k(x-y)
This number is divisible by k, since k is a factor

So the statement is true in all cases.
btw, it would also be true for the sum of the 2 numbers.