Which expression would produce the largest answer?

3(9 + 3) + 4(6 ÷ 2)

2(32) + 3(2 • 2)

12(8 ÷ 1) + 5(4 - 5)

15(2 + 3) - 3(1 + 3)

To determine which expression produces the largest answer, we can evaluate each one step by step using the order of operations (parentheses, exponents, multiplication and division, addition and subtraction, often remembered by the acronym PEMDAS).

Let's evaluate each expression:

1. **Expression 1: \( 3(9 + 3) + 4(6 \div 2) \)**  
   - Calculate inside the parentheses: \( 9 + 3 = 12 \)  
   - Calculate inside the second parentheses: \( 6 \div 2 = 3 \)  
   - Now substitute these back into the expression: \( 3(12) + 4(3) \)  
   - Multiply: \( 3 \times 12 = 36 \) and \( 4 \times 3 = 12 \)  
   - Add: \( 36 + 12 = 48 \)

2. **Expression 2: \( 2(3^2) + 3(2 \cdot 2) \)**  
   - Calculate the exponent: \( 3^2 = 9 \)  
   - Calculate inside the parentheses: \( 2 \cdot 2 = 4 \)  
   - Now substitute these back into the expression: \( 2(9) + 3(4) \)  
   - Multiply: \( 2 \times 9 = 18 \) and \( 3 \times 4 = 12 \)  
   - Add: \( 18 + 12 = 30 \)

3. **Expression 3: \( 12(8 \div 1) + 5(4 - 5) \)**  
   - Calculate inside the parentheses: \( 8 \div 1 = 8 \) and \( 4 - 5 = -1 \)  
   - Now substitute these back into the expression: \( 12(8) + 5(-1) \)  
   - Multiply: \( 12 \times 8 = 96 \) and \( 5 \times -1 = -5 \)  
   - Add: \( 96 - 5 = 91 \)

4. **Expression 4: \( 15(2 + 3) - 3(1 + 3) \)**  
   - Calculate inside the parentheses: \( 2 + 3 = 5 \) and \( 1 + 3 = 4 \)  
   - Now substitute these back into the expression: \( 15(5) - 3(4) \)  
   - Multiply: \( 15 \times 5 = 75 \) and \( 3 \times 4 = 12 \)  
   - Subtract: \( 75 - 12 = 63 \)

Now that we've calculated all four expressions:

1. Expression 1: \( 48 \)
2. Expression 2: \( 30 \)
3. Expression 3: \( 91 \)
4. Expression 4: \( 63 \)

**The expression that produces the largest answer is Expression 3, which equals 91.**

Would you like to see more details or have any questions?

Here are five related questions:

1. How would the answers change if the parentheses were altered in any of the expressions?
2. What happens if the order of operations is not followed correctly?
3. How can you determine the smallest answer among multiple expressions?
4. What is the impact of negative numbers on these types of calculations?
5. How would the expressions change if additional arithmetic operations, such as square roots or factorials, were introduced?

**Tip:** Always remember the order of operations (PEMDAS) when solving mathematical expressions to ensure accurate results.

Explore which expression produces the largest answer among given mathematical expressions. Step-by-step evaluation using the order of operations (PEMDAS) is demonstrated. Suitable for students in Grades 6-8.

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