Question: Determine the order of operation of the following algebraic expression.
a + \frac{b - c \times d}{f}
Which of the following operations should be done first?
A. addition
1. **State the problem:** We need to determine the order of operations for the expression $$a + \frac{b - c \times d}{f}$$ and identify which operation should be done first.
2. **Recall the order of operations (PEMDAS/BODMAS):**
- Parentheses/Brackets
- Exponents/Orders
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
3. **Analyze the expression:**
- The numerator is $$b - c \times d$$ inside the fraction.
- The denominator is $$f$$.
- The entire fraction $$\frac{b - c \times d}{f}$$ is added to $$a$$.
4. **Apply order of operations:**
- Inside the numerator, multiplication $$c \times d$$ must be done before subtraction.
- Then subtract the result from $$b$$.
- Next, divide the numerator by $$f$$.
- Finally, add $$a$$ to the result of the fraction.
5. **Conclusion:**
- The first operation to perform is the multiplication $$c \times d$$.
**Final answer:** The first operation to be done is multiplication, not addition.