The question states:
"If $m$ is a digit and the number $46m23$ is divisible by 9, then the digit $m$ is equal to:"

Solution:

To determine the value of $m$, we need to use the divisibility rule for 9. The rule states that a number is divisible by 9 if the sum of its digits is divisible by 9.

Step 1: Write down the digits of the number $46m23$

The digits are $4, 6, m, 2,$ and $3$.

Step 2: Express the sum of the digits

$4 + 6 + m + 2 + 3 = 15 + m$

Step 3: Find the value of $m$ such that the sum is divisible by 9

We want $15 + m$ to be divisible by 9. Let's try different values for $m$ (since $m$ is a single-digit number from 0 to 9).

• $m = 0$: $15 + 0 = 15$ (Not divisible by 9)
• $m = 1$: $15 + 1 = 16$ (Not divisible by 9)
• $m = 2$: $15 + 2 = 17$ (Not divisible by 9)
• $m = 3$: $15 + 3 = 18$ (Divisible by 9)

Thus, the correct value of $m$ is $m = 3$.

Final Answer:

$m = 3$

Do you have any questions or need further details?

Here are some follow-up questions for deeper understanding:

1. What is the divisibility rule for 3, and how does it compare with the rule for 9?
2. How would the solution change if the number were $46m2$ instead of $46m23$?
3. If the number were divisible by 11, what condition would $m$ need to satisfy?
4. Can a number be divisible by both 9 and 6 at the same time? Why or why not?
5. How does divisibility play a role in cryptography or data validation?

Tip: Always double-check your sums when working with divisibility rules to avoid small calculation errors.