Order of Operations (PEMDAS) — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
(3 + 5) × 2 = 13
Corrected: (3 + 5) × 2 = 16
The corrected sentence is: "(3 + 5) × 2 = 16". The original sentence "(3 + 5) × 2 = 13" contained an error that needed to be fixed.
2. Fix the sentence:
4 × (6 - 2) = 22
Corrected: 4 × (6 - 2) = 16
The corrected sentence is: "4 × (6 - 2) = 16". The original sentence "4 × (6 - 2) = 22" contained an error that needed to be fixed.
3. Fix the sentence:
(10 + 2) ÷ 4 = 10.5
Corrected: (10 + 2) ÷ 4 = 3
The corrected sentence is: "(10 + 2) ÷ 4 = 3". The original sentence "(10 + 2) ÷ 4 = 10.5" contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. (4 + 6) × 3 = 30.
Parentheses first: (4 + 6) = 10. Then multiply: 10 × 3 = 30.
2. 5 × (8 - 3) = 25.
Parentheses first: (8 − 3) = 5. Then multiply: 5 × 5 = 25.
3. (9 + 1) ÷ 2 = 5.
Parentheses first: (9 + 1) = 10. Then divide: 10 ÷ 2 = 5.
4. (7 - 4) × (2 + 3) = 15.
Both parentheses first: (7 − 4) = 3 and (2 + 3) = 5. Then multiply: 3 × 5 = 15.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Compare 3 × 4 + 2 and 3 × (4 + 2). Are they equal? Explain.
Sample answer: 3 × 4 + 2 = 14 because you multiply first: 12 + 2 = 14. But 3 × (4 + 2) = 18 because parentheses come first: 3 × 6 = 18. They are not equal.
Without parentheses, multiply before adding: 3 × 4 + 2 = 12 + 2 = 14. With parentheses, add inside first: 3 × (4 + 2) = 3 × 6 = 18. Different results.
2. Where would you place parentheses in 2 + 3 × 4 to make it equal 20?
Sample answer: Place parentheses around 2 + 3 to get (2 + 3) × 4 = 5 × 4 = 20.
Without parentheses, 2 + 3 × 4 = 2 + 12 = 14. Adding parentheses: (2 + 3) × 4 forces the addition first: 5 × 4 = 20.