To solve the expression $100 \div 4(2 + 3)$, we will follow the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication/Division (from left to right), Addition/Subtraction (from left to right)):

Step 1: Simplify the parentheses

$2 + 3 = 5$ Now the expression becomes: $100 \div 4(5)$

Step 2: Multiply or divide from left to right

Next, we divide first since division and multiplication are done from left to right: $100 \div 4 = 25$ Now the expression becomes: $25 \times 5$

Step 3: Perform the multiplication

$25 \times 5 = 125$

So, the value of $100 \div 4(2 + 3)$ is 125.

Do you have any further questions or would you like additional details?

Here are 5 related questions:

1. What is the result of $120 \div 6(2 + 4)$?
2. How does the order of operations affect calculations in complex expressions?
3. If the parentheses were different, such as $100 \div (4(2 + 3))$, what would the result be?
4. What happens if you have multiple parentheses in an equation?
5. How do exponents interact with multiplication and division in order of operations?

Tip: Always handle parentheses first in any expression before moving on to multiplication, division, addition, or subtraction!