Question

Prove that if a divides b and c divides d, then ac divides bd?

Answer 1

To prove that if a divides b and c divides d, then ac divides bd, we can use the properties of divisibility.

Step-by-step explanation:

To prove that if a divides b and c divides d, then ac divides bd, we can use the properties of divisibility.

1. Given that a divides b, we can write b = ax, where x is an integer.
2. Similarly, c divides d, so we can write d = cy, where y is an integer.
3. Multiplying both sides of these equations, we get bd = acxy.
4. Since x and y are integers, we can say that ac divides bd.

Therefore, we have proved that if a divides b and c divides d, then ac divides bd.