A2 — divide last because multiplication comes before division in PEMDAS
B8 — multiplication and division have equal priority, so evaluate left to right
C18 — multiply 3 × 2 first because M comes before D in the acronym
D4 — work right to left when operations have the same letter pair
Multiplication and division are the same priority level — neither always comes first. The rule is to evaluate them left to right. So: 12 ÷ 3 = 4, then 4 × 2 = 8. Option A is the most common wrong answer — treating PEMDAS as six separate ranked levels causes students to always multiply before dividing, which is incorrect.
Question 2 Multiple Choice
A student evaluates 20 − 4 + 3 by doing 4 + 3 = 7 first, then 20 − 7 = 13. What went wrong?
AThey should have subtracted before adding because subtraction comes before addition
BThey should have added before subtracting because A comes before S in PEMDAS
CAddition and subtraction have equal priority and must go left to right; 20 − 4 should come first, giving 16 + 3 = 19
DNothing went wrong; 13 is the correct answer
Addition and subtraction, like multiplication and division, are equal-priority partners — neither always precedes the other. The correct approach is left to right: 20 − 4 = 16, then 16 + 3 = 19. The student treated 'AS' as meaning 'addition first,' which is a misreading of the acronym. PEMDAS has four levels, not six.
Question 3 True / False
Placing parentheses around part of an expression can change its value even if the operations inside are the same.
TTrue
FFalse
Answer: True
Parentheses override the default priority order. Without parentheses, 2 + 3 × 4 = 14 (multiply first). With parentheses, (2 + 3) × 4 = 20 (add first). The parentheses force the addition to happen before the multiplication, producing a different result. This is precisely their purpose: communicating which operation should happen first.
Question 4 True / False
In PEMDAS, multiplication typically comes before division because M appears before D in the acronym.
TTrue
FFalse
Answer: False
This is one of the most common misconceptions about order of operations. M and D represent a single priority level, not two separate ones. When an expression contains both multiplication and division (with no parentheses separating them), you evaluate left to right — whichever appears first gets done first. The acronym groups them together for a reason: MD is one level, AS is one level.
Question 5 Short Answer
Why does 2 + 3 × 4 equal 14 and not 20? Explain using the purpose of the order of operations convention.
Think about your answer, then reveal below.
Model answer: The order of operations is a shared convention that ensures every mathematical expression has exactly one value. Under the convention, multiplication is evaluated before addition, so 3 × 4 = 12 is computed first, then 2 + 12 = 14. If we added first, (2 + 3) × 4 = 20 — a different answer. The convention exists so writers and readers of expressions always agree on meaning.
The key insight is that the order of operations is not an arbitrary rule but a necessary agreement. Without it, an expression like 2 + 3 × 4 would be ambiguous — two mathematicians could read it and get different answers. The convention resolves that ambiguity by specifying which operations bind more tightly. Parentheses let you override the convention when you need a different grouping.