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Evaluate Numerical Expressions with Parentheses in Different Places

Parentheses are like VIP passes in math - they tell you what to do first! Moving parentheses to different places can completely change the answer. Let's see how powerful punctuation can be in math!

Do this: Read the concept below, then try the quiz or activity.

Lesson 34 of 216

Concept

Parentheses change the order of operations and can dramatically change your answer!

🎯 The Golden Rule: Whatever is inside parentheses gets done FIRST, no matter what!

📊 Compare These Expressions:

Example 1: • (8 + 2) × 5 = ? → 10 × 5 = 50

• 8 + (2 × 5) = ? → 8 + 10 = 18

Same numbers, different parentheses, TOTALLY different answers!

Example 2: • (15 - 5) ÷ 2 = ? → 10 ÷ 2 = 5

• 15 - (5 ÷ 2) = ? → 15 - 2.5 = 12.5

💡 Order of Operations Review (PEMDAS): Parentheses - Do these FIRST! Exponents - Next Multiplication and Division - Left to right Addition and Subtraction - Left to right

But parentheses OVERRIDE everything else!

🌟 Real Examples:

Problem: (6 + 4) × (3 + 2) Step 1: Do left parentheses: 6 + 4 = 10 Step 2: Do right parentheses: 3 + 2 = 5 Step 3: Multiply: 10 × 5 = 50

Problem: 20 - (3 + 4) + 2 Step 1: Parentheses first: 3 + 4 = 7 Step 2: Now: 20 - 7 + 2 Step 3: Left to right: 13 + 2 = 15

🎨 Parentheses as Grouping: Think of parentheses as containers: • Do what's in the container first • Then use that result in the bigger problem • Multiple parentheses? Do each container separately

Testing Understanding: Does 3 × (4 + 5) = (3 × 4) + 5? • Left side: 3 × 9 = 27 • Right side: 12 + 5 = 17 • NO! Different parentheses = different answers

Try it

Practice evaluating expressions with parentheses!

📝 Evaluate These: 1. (12 + 8) ÷ 4 = ? 2. 12 + (8 ÷ 4) = ? 3. (15 - 6) × 2 = ? 4. 15 - (6 × 2) = ?

🎯 Compare:
5. Solve BOTH:
   a) (5 + 3) × 2 = ?
   b) 5 + (3 × 2) = ?
   Which is larger?

6. Solve BOTH:
   a) (20 - 8) ÷ 4 = ?
   b) 20 - (8 ÷ 4) = ?

💡 Multiple Parentheses: 7. (7 + 3) × (10 - 6) = ? 8. (25 - 5) ÷ (12 - 8) = ? 9. (6 × 2) + (8 ÷ 4) = ?

📊 Complex Expressions: 10. 100 - (25 + 15) + 10 = ? 11. (18 ÷ 3) + (4 × 5) = ? 12. 50 - (10 + 5) × 2 = ? (Careful!)

🏆 Create Your Own:
13. Place parentheses to make this TRUE:
    6 + 3 × 2 = 18
    (Where do parentheses go?)

14. Place parentheses to make this TRUE:
    20 - 4 + 6 = 10

💪 Challenge: 15. Evaluate: (15 + 5) ÷ (8 - 3) + 2 × (6 - 4)

16. Why do these give different answers?
    • 4 × 3 + 2
    • 4 × (3 + 2)
    Explain in your own words.

17. Write an expression where moving the parentheses changes the answer from 20 to 40.

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