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:
7 + 8 ÷ 2 = 7.5
Corrected: 7 + 8 ÷ 2 = 11
The corrected sentence is: "7 + 8 ÷ 2 = 11" The error was left-to-right error — added before dividing: the original sentence "7 + 8 ÷ 2 = 7.5" needed to be fixed.
2. Fix the sentence:
15 - 3 × 3 = 36
Corrected: 15 - 3 × 3 = 6
The corrected sentence is: "15 - 3 × 3 = 6" The error was left-to-right error — subtracted before multiplying: the original sentence "15 - 3 × 3 = 36" needed to be fixed.
3. Fix the sentence:
2 + 10 ÷ 5 × 3 = 7.2
Corrected: 2 + 10 ÷ 5 × 3 = 8
The corrected sentence is: "2 + 10 ÷ 5 × 3 = 8" The error was left-to-right error — added first then divided and multiplied incorrectly: the original sentence "2 + 10 ÷ 5 × 3 = 7.2" needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In PEMDAS, the E stands for Exponents.
E stands for Exponents, which is the second step in PEMDAS, right after Parentheses and before Multiplication.
2. 3 × 7 - 10 = 11.
Multiply first: 3 × 7 = 21, then subtract 10 to get 11. Multiplication always comes before subtraction.
3. 18 ÷ 9 + 6 × 2 = 14.
Handle division and multiplication first: 18 ÷ 9 = 2 and 6 × 2 = 12, then add to get 2 + 12 = 14.
4. 4 + 16 ÷ 4 - 1 = 7.
Divide first: 16 ÷ 4 = 4, then work left to right: 4 + 4 = 8, and 8 - 1 = 7.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A student wrote 6 + 3 × 2 = 18. What mistake did the student make?
Sample answer: The student added 6 + 3 first to get 9, then multiplied by 2. The correct way is to multiply first: 3 × 2 = 6, then 6 + 6 = 12.
A good answer includes: The student added 6 + 3 first to get 9, then multiplied by 2. The correct way is to multiply first: 3 × 2 = 6, then 6 + 6 = 12.
2. Addition and subtraction are done left to right in PEMDAS. Show how to solve 20 - 5 + 3 - 1.
Sample answer: Work left to right: 20 - 5 = 15, then 15 + 3 = 18, then 18 - 1 = 17. The answer is 17.
A good answer includes: Work left to right: 20 - 5 = 15, then 15 + 3 = 18, then 18 - 1 = 17. The answer is 17.