Consider the numerical expression: 3 + 6 × (5 + 4) ÷ 3 − 7.
Question 1
To evaluate the numerical expression, what is the first step in the order of operations?Evaluate the given numerical expression.
Responses
A	99
B	1212
C	1414
D	21

To evaluate the expression \(3 + 6 \times (5 + 4) \div 3 - 7\), we follow the order of operations, often remembered by the acronym PEMDAS:

1. **Parentheses**
2. **Exponents**
3. **Multiplication and Division** (from left to right)
4. **Addition and Subtraction** (from left to right)

### Step-by-Step Solution

#### Step 1: Parentheses
Evaluate \(5 + 4\) inside the parentheses:
\[
3 + 6 \times 9 \div 3 - 7
\]

#### Step 2: Multiplication and Division (from left to right)
1. Evaluate \(6 \times 9\):
   \[
   3 + 54 \div 3 - 7
   \]
2. Next, evaluate \(54 \div 3\):
   \[
   3 + 18 - 7
   \]

#### Step 3: Addition and Subtraction (from left to right)
1. Add \(3 + 18\):
   \[
   21 - 7
   \]
2. Subtract \(7\):
   \[
   14
   \]

The final answer is:
\[
\boxed{14}
\]

### Answer: 
The correct choice is **C. 14**.

Would you like further explanation on any of these steps?

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### Additional Questions

1. What would the result be if we changed \(5 + 4\) to \(5 - 4\)?
2. How does changing the division symbol to multiplication alter the answer?
3. What if we evaluated the expression without following the order of operations?
4. Can you create a similar expression that equals 21 instead?
5. How would inserting additional parentheses alter the outcome?

**Tip:** Remember to always perform multiplication and division from left to right, rather than completing one type before the other.

Consider the numerical expression: 3 + 6 × (5 + 4) ÷ 3 − 7. To evaluate the numerical expression, what is the first step in the order of operations? Evaluate the given numerical expression.

Learn how to evaluate the numerical expression 3 + 6 × (5 + 4) ÷ 3 − 7 by following the order of operations (PEMDAS). This problem involves arithmetic expressions and is suitable for students in Grades 5-7. The final answer is 14, and the process includes step-by-step guidance.

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