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:
For 12 / 3 * 2, do 3 * 2 first to get 12 / 6 = 2.
Corrected: For 12 / 3 * 2, work left to right: 12 / 3 = 4, then 4 * 2 = 8.
Multiplication and division share equal priority, so order of appearance decides which one happens first.
2. Fix the sentence:
In ((2+3)*4), I solve 3*4 first because multiplication beats addition.
Corrected: In ((2+3)*4), I solve the inside parens first: 2+3=5, then 5*4=20.
Parentheses outrank multiplication, so grouped sums must be finished before any outside operation.
3. Fix the sentence:
20 / 4 * 5 equals 1 because 4 * 5 = 20 and 20 / 20 = 1.
Corrected: 20 / 4 * 5 equals 25: divide first to get 5, then multiply by 5.
Skipping the left-to-right rule gives the wrong answer because order changes the result.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Solve ((6+2)*3): inner parens give 8, so the answer is 24.
Nested parentheses are solved from the inside out before any outer operation.
2. 12 / 3 * 2 = 8 when worked left to right correctly.
Multiplication and division have equal rank, so the leftmost one happens first.
3. In ((10-4)/2), the first operation to perform is subtraction.
Innermost parentheses are always evaluated before any other step in the expression.
4. 24 / 6 * 1 equals 4 using the left-to-right rule.
Left-to-right keeps tied operations fair and produces the correct result every time.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why must you solve 18 / 2 * 3 from left to right?
Sample answer: Because division and multiplication share the same priority, so order of appearance decides; 18 / 2 = 9, then 9 * 3 = 27.
Treating tied operations equally and reading left to right prevents common PEMDAS mistakes.
2. Which operation in ((4+1)*6) do you do first, and why?
Sample answer: Addition inside the inner parentheses comes first because innermost groupings always rank highest, giving 5*6=30.
Nested grouping symbols force you to work outward, securing accuracy in layered problems.