What is the converse statement of "If a number is divisible by 3, then it is divisible by 9."?

Understanding the Converse Statement

The converse of a statement of the form "If P, then Q" is "If Q, then P." In this case, we have:

• P: A number is divisible by 3.
• Q: A number is divisible by 9.

Formulating the Converse

Therefore, the converse statement of "If a number is divisible by 3, then it is divisible by 9" would be:

"If a number is divisible by 9, then it is divisible by 3."

Explanation

This converse statement is true because any number that is divisible by 9 can also be expressed as $9k$ for some integer $k$, which can be factored to show that it is also divisible by 3 (since $9k = 3(3k)$). Thus, divisibility by 9 implies divisibility by 3.