How do you prove: If a/b, then a/bc
So far I have: Since a/b, then b=ac where c is an integer. Now where do i go?
To prove the statement "If a/b, then a/bc," you need to show that if a is divisible by b, then a is also divisible by bc.
To proceed with the proof, you have assumed that a/b, which means there exists an integer c such that b = ac.
Now, to prove that a/bc, you need to show that there exists an integer d such that bc = ad.
To find d, you can rearrange the equation b = ac to solve for a:
b = ac
Dividing both sides by c: b/c = a
Now, let's substitute this value of a into the equation bc = ad:
bc = (b/c)d
Multiplying both sides by c: bc^2 = bd
Dividing both sides by b: c^2 = d
So, we have found that d = c^2. Since c is an integer, c^2 is also an integer. Hence, for d = c^2, we have bc = ad.
Therefore, we have proven that if a/b, then a/bc.