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!
Concept
Parentheses change the order of operations and can dramatically change your answer! šÆ **The Golden Rule:** Whatever is inside parentheses gets done FIRST, no matter what! š **Compare These Expressions:** **Example 1:** ā¢ (8 + 2) Ć 5 = ? ā 10 Ć 5 = 50 ā¢ 8 + (2 Ć 5) = ? ā 8 + 10 = 18 Same numbers, different parentheses, TOTALLY different answers! **Example 2:** ā¢ (15 - 5) Ć· 2 = ? ā 10 Ć· 2 = 5 ā¢ 15 - (5 Ć· 2) = ? ā 15 - 2.5 = 12.5 š” **Order of Operations Review (PEMDAS):** **P**arentheses - Do these FIRST! **E**xponents - Next **M**ultiplication and **D**ivision - Left to right **A**ddition and **S**ubtraction - Left to right But parentheses OVERRIDE everything else! š **Real Examples:** **Problem:** (6 + 4) Ć (3 + 2) **Step 1:** Do left parentheses: 6 + 4 = 10 **Step 2:** Do right parentheses: 3 + 2 = 5 **Step 3:** Multiply: 10 Ć 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 šØ **Parentheses as Grouping:** Think of parentheses as containers: ā¢ Do what's in the container first ā¢ Then use that result in the bigger problem ā¢ Multiple parentheses? Do each container separately **Testing Understanding:** Does 3 Ć (4 + 5) = (3 Ć 4) + 5? ā¢ Left side: 3 Ć 9 = 27 ā¢ Right side: 12 + 5 = 17 ā¢ NO! Different parentheses = different answers
Try it
Practice evaluating expressions with parentheses! š **Evaluate These:** 1. (12 + 8) Ć· 4 = ? 2. 12 + (8 Ć· 4) = ? 3. (15 - 6) Ć 2 = ? 4. 15 - (6 Ć 2) = ? šÆ **Compare:** 5. Solve BOTH: a) (5 + 3) Ć 2 = ? b) 5 + (3 Ć 2) = ? Which is larger? 6. Solve BOTH: a) (20 - 8) Ć· 4 = ? b) 20 - (8 Ć· 4) = ? š” **Multiple Parentheses:** 7. (7 + 3) Ć (10 - 6) = ? 8. (25 - 5) Ć· (12 - 8) = ? 9. (6 Ć 2) + (8 Ć· 4) = ? š **Complex Expressions:** 10. 100 - (25 + 15) + 10 = ? 11. (18 Ć· 3) + (4 Ć 5) = ? 12. 50 - (10 + 5) Ć 2 = ? (Careful!) š **Create Your Own:** 13. Place parentheses to make this TRUE: 6 + 3 Ć 2 = 18 (Where do parentheses go?) 14. Place parentheses to make this TRUE: 20 - 4 + 6 = 10 šŖ **Challenge:** 15. Evaluate: (15 + 5) Ć· (8 - 3) + 2 Ć (6 - 4) 16. Why do these give different answers? ā¢ 4 Ć 3 + 2 ā¢ 4 Ć (3 + 2) Explain in your own words. 17. Write an expression where moving the parentheses changes the answer from 20 to 40.