To solve the expression $100 \div 4(2+3)$, we need to follow the order of operations (PEMDAS/BODMAS):

1. Parentheses: First, calculate inside the parentheses.
2. Exponents: Then, deal with exponents (if any).
3. Multiplication and Division: Next, perform multiplication and division from left to right.
4. Addition and Subtraction: Finally, perform addition and subtraction from left to right.

Let's solve it step-by-step:

1. Calculate inside the parentheses: $2 + 3 = 5$

   Now the expression becomes: $100 \div 4(5)$

2. Interpret the multiplication: Here, $4(5)$ means $4 \times 5$.

   So, the expression now is: $100 \div 20$

3. Perform the division: $100 \div 20 = 5$

Final Answer:

$100 \div 4(2+3) = 5$

Would you like more details or have any questions about this?

Here are some related questions you might find interesting:

1. What is the order of operations and why is it important in mathematics?
2. How would the answer change if there were different operations involved?
3. What if the expression was written differently, such as $100 \div (4(2+3))$?
4. Can the order of operations change depending on the context?
5. How does one handle division and multiplication when they appear consecutively?

Tip: Always remember to perform operations inside parentheses first and follow the correct order to avoid mistakes.