Evaluate numerical expressions with parentheses
Parentheses in math mean "Do this first!" They are the VIP section of a math problem. Following the order of operations (PEMDAS) is the secret to getting the right answer every time.
Concept
Parentheses are used to group parts of a long math expression to show what needs to be done first. Changing the parentheses can completely change the answer. **The Order of Operations: PEMDAS** This is the rule for the order in which you solve a math problem: 1. **P**arentheses: Solve everything inside parentheses first. 2. **E**xponents: Handle any powers or square roots. 3. **M**ultiplication and **D**ivision: Work from left to right. 4. **A**ddition and **S**ubtraction: Work from left to right. (A common way to remember this is "Please Excuse My Dear Aunt Sally"). **Example 1: How Parentheses Change Everything** * **Problem A: (10 + 2) x 5** 1. Parentheses first: 10 + 2 = 12 2. Then multiply: 12 x 5 = **60** * **Problem B: 10 + (2 x 5)** 1. Parentheses first: 2 x 5 = 10 2. Then add: 10 + 10 = **20** See? Same numbers, totally different answers. **Example 2: A More Complex Problem** * **Problem: 3 + [20 ÷ (7 - 2)]** *Sometimes you see brackets [] which work just like parentheses.* 1. **Innermost Parentheses:** (7 - 2) = 5 2. **Next Level Parentheses/Brackets:** [20 ÷ 5] = 4 3. **Final Step:** 3 + 4 = **7** **Key Idea:** Think of parentheses as creating a mini-problem that you have to solve before you can continue with the main problem. Once it's solved, the parentheses disappear.
Try it
Practice with parentheses! **Solve the expression:** 1. (5 + 4) x 3 = ? 2. 20 - (8 ÷ 2) = ? 3. 12 + (6 x 2) = ? 4. (30 ÷ 3) - 5 = ? **Compare the two expressions:** 5. Which is greater? a) (8 - 3) x 4 b) 8 - (3 x 4) 6. Are these equal? a) 2 + (5 x 6) b) (2 + 5) x 6 **Solve with multiple steps:** 7. (4 + 6) ÷ (1 + 1) = ? 8. 5 x (10 - (2 + 4)) = ? 9. [(15 - 5) x 2] ÷ 4 = ? **Word Problems:** 10. You buy 3 packs of stickers. Each pack has 5 red and 4 blue stickers. Write an expression to find the total number of stickers. (3 x (5 + 4)) 11. You have $50. You buy a book for $12 and a game for $25. Write an expression to show how much money you have left. (50 - (12 + 25)) **Challenge Problems:** 12. Place parentheses to make this equation true: 8 x 5 - 3 = 16 13. Place parentheses to make this equation true: 30 ÷ 5 + 1 x 2 = 12