Order of Operations Introduction — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
16 / 2 * 4 = 2 because 2 * 4 = 8 and 16 / 8 = 2.
Corrected: 16 / 2 * 4 = 32: divide first to get 8, then multiply by 4.
Reading equal-priority operations from left to right keeps PEMDAS results consistent and correct.
2. Fix the sentence:
((3+2)*5) is solved by doing 2*5 first, getting 3+10=13.
Corrected: ((3+2)*5) is solved by doing 3+2 first inside parens, getting 5*5=25.
Parentheses always rank above multiplication, so grouped expressions must finish first.
3. Fix the sentence:
I solved 30 / 5 * 2 as 30 / 10 because multiplication should be done before division.
Corrected: I solved 30 / 5 * 2 left to right: 30 / 5 = 6, then 6 * 2 = 12.
Multiplication and division share rank, so position decides which is evaluated first.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. ((9-3)*2) equals 12 after solving the inner parentheses.
Innermost parentheses must be simplified before any operation outside reaches them.
2. 40 / 4 * 5 = 50 when computed in correct order.
Tied operations are resolved left to right to keep PEMDAS fair and predictable.
3. In 14 / 7 * 2, the first step is to divide because it appears first.
Equal-priority operations always follow the order they appear when reading from left.
4. ((8+2)/5) equals 2 after using parentheses correctly.
Parentheses rank highest, so the inside sum must finish before division begins.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain how to evaluate ((12-2)*3) step by step.
Sample answer: Solve inside parens first: 12-2=10. Then multiply: 10*3=30. Innermost parens always come before outside operations.
Working inside out is the foundation of PEMDAS and prevents layered-expression mistakes.
2. Why does 36 / 9 * 2 = 8 instead of 2?
Sample answer: Because division and multiplication tie in rank, you go left to right: 36 / 9 = 4, then 4 * 2 = 8.
Left-to-right ordering for tied operations is essential for matching the correct answer.