Instructions
Follow these steps to master the Order of Operations. In math, we don't just solve from left to right! We follow a special set of rules called PEMDAS to ensure everyone gets the same answer.
- P - Parentheses ( ): Solve everything inside brackets or parentheses first.
- E - Exponents ²: Solve small numbers like "squared" or "cubed."
- MD - Multiplication & Division: Solve these from left to right (they are equal partners).
- AS - Addition & Subtraction: Solve these from left to right (they are equal partners).
Section 1: The Step-by-Step Breakdown
Complete the table below. Use the first row as your guide to see how to break the problem into pieces.
| Expression | Step 1: Parentheses | Step 2: Multiply/Divide | Step 3: Add/Subtract | Final Answer |
|---|---|---|---|---|
| Example: 5 + (2 x 3) | 5 + 6 | N/A | 11 | 11 |
| 10 - (4 + 2) | ||||
| (8 / 2) + 7 | ||||
| 3 x (10 - 4) | ||||
| 15 / (3 + 2) | ||||
| (6 x 2) - 5 |
Section 2: Operation Detective
Solve these problems by checking off the operations as you go. Remember: Multiplication and Division happen at the same time, moving from left to right!
1. 12 + 4 ÷ 2
- Division first: 4 ÷ 2 = __
- Then Addition: 12 + __ = Answer: __
2. (10 - 2) x 3
- Parentheses first: 10 - 2 = __
- Then Multiplication: __ x 3 = Answer: __
3. 20 ÷ 4 + 2 x 3
- Division first: 20 ÷ 4 = __
- Multiplication next: 2x3 = __
- Finally, add them: __ + __ = Answer: __
Section 3: The Snack Bar Scenario
You are working at the school snack bar. Use the Order of Operations to calculate the total cost for these orders.
- Apples: $2 each
- Juice: $3 each
- Popcorn: $5 each
Scenario: A customer buys 2 apples and 3 juices. They have a $2 discount coupon that is taken off the total at the very end.
The Equation: (2 x 2) + (3 x 3) - 2
Show your work:
- Solve the first parentheses (Apples): __
- Solve the second parentheses (Juice): __
- Add them together: __
- Subtract the coupon: __
Total Cost: $__
Section 4: The Mystery Parentheses (Challenge!)
In these problems, the answer is already there, but the parentheses are missing! Draw the parentheses in the correct spot to make the equation true.
Example: 2 + 3 x 4 = 20 → (2 + 3) x 4 = 20
- 5 + 2 x 3 = 21
- 10 - 4 / 2 = 3
- 8 + 2 x 5 - 3 = 12
Section 5: Brain Buster
Create your own math expression that equals 10. You must use at least three different operations (+, -, x, or ÷) and at least one set of parentheses.
Your Expression: __
Answer Key
Section 1:
- 10 - (4+2) -> 10 - 6 = 4
- (8 / 2) + 7 -> 4 + 7 = 11
- 3 x (10 - 4) -> 3 x 6 = 18
- 15 / (3 + 2) -> 15 / 5 = 3
- (6 x 2) - 5 -> 12 - 5 = 7
Section 2:
- 12 + 2 = 14
- 8 x 3 = 24
- 5 + 6 = 11
Section 3: (4) + (9) - 2 = 11. Total Cost: $11
Section 4:
- (5 + 2) x 3 = 21
- (10 - 4) / 2 = 3
- 8 + 2 x (5 - 3) = 12
Section 5: Answers will vary. Example: (2 + 3) x 4 / 2 = 10