K-5 friendly lesson

One small step at a time.Read the idea, try the activity, and celebrate each win as you go.

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.

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

Lesson 33 of 216

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. Parentheses: Solve everything inside parentheses first. 2. Exponents: Handle any powers or square roots. 3. Multiplication and Division: Work from left to right. 4. Addition and Subtraction: 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

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