To solve the expression $\frac{100}{4}(2+3)$, we'll follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (PEMDAS).

Step-by-Step Solution

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

2. Perform the division and multiplication from left to right: $\frac{100}{4} = 25$

   Then multiply by 5: $25 \times 5 = 125$

Final Answer

$\frac{100}{4}(2+3) = 125$

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How would the result change if the expression were written as $100 \div [4(2+3)]$?
2. What if the expression was $100/(4+2) + 3$?
3. How does the order of operations affect calculations involving both multiplication and division?
4. What is the difference between $100/(4 \cdot (2+3))$ and $100/4 \cdot (2+3)$?
5. Can you show how PEMDAS applies to more complex equations?

Tip: Always remember to follow the order of operations to avoid common mistakes in calculations!