To solve the expression \(45 + 27 / 25 : 2\), we need to follow the correct order of operations, which is typically expressed by the acronym PEMDAS:

- **P**arentheses
- **E**xponents
- **M**ultiplication and **D**ivision (from left to right)
- **A**ddition and **S**ubtraction (from left to right)

Let's break down the expression step by step:

\[
45 + 27 / 25 : 2
\]

### Step 1: Division
Perform the division operations first:

1. **27 divided by 25:**

\[
27 / 25 = 1.08
\]

2. **1.08 divided by 2:**

\[
1.08 / 2 = 0.54
\]

### Step 2: Addition
Now, add the result to 45:

\[
45 + 0.54 = 45.54
\]

Therefore, the result of the expression \(45 + 27 / 25 : 2\) is:

\[
\boxed{45.54}
\]

### Conclusion
- The expression simplifies to 45.54 when following the correct order of operations.

### Verification
To verify, let's revisit the operations:

1. Calculate \(27 / 25\):

\[
27 / 25 = 1.08
\]

2. Divide the result by 2:

\[
1.08 / 2 = 0.54
\]

3. Add this result to 45:

\[
45 + 0.54 = 45.54
\]

This confirms that the answer is indeed \(\boxed{45.54}\).

---

### Do you have any questions or would you like more details on a specific part of the process?

### Further Questions:
1. How can the order of operations affect the outcome of mathematical expressions?
2. What are some common mistakes people make when evaluating expressions with division and addition?
3. Can you explain why multiplication and division are performed from left to right?
4. What would be the result if parentheses were used in the expression, e.g., \(45 + (27 / (25 : 2))\)?
5. How does division by a fraction affect the result of an expression?
6. What role does PEMDAS play in complex algebraic equations?
7. Can you provide a similar example and solve it using the order of operations?
8. Why is it important to understand the distinction between division and multiplication in expressions?

### Tip:
Always write out each step clearly and double-check your operations to ensure accuracy, especially when dealing with complex expressions.

Learn how to solve the expression 45 + 27 / 25 : 2 step-by-step with a detailed explanation of order of operations. This problem covers mathematical concepts including division and addition, suitable for students in Grades 6-8.

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