Step by Step
P
Parentheses first
Solve everything inside ( ) before doing anything else, working from the innermost parentheses outward if there are several.
E
Exponents next
Handle all powers and roots after parentheses are cleared.
M/D
Multiplication and Division — left to right
These two operations share equal priority. Whichever one appears first (reading left to right) gets done first — multiplication does NOT automatically beat division.
A/S
Addition and Subtraction — left to right
Same rule applies here: equal priority, left to right, regardless of which symbol looks like it should "come first."
Applied Walkthrough
1
Solve 10 ÷ 2 × 5 using PEMDAS. There are no parentheses or exponents, so you move straight to the M/D tier.
2
Since multiplication and division share equal priority, you work strictly left to right: 10 ÷ 2 = 5 first, not 2 × 5.
3
Then finish: 5 × 5 = 25. The final answer is 25 — not 1, which is what you'd get if you mistakenly did the multiplication first.
4
This exact left-to-right trap is the single most common PEMDAS mistake on exams.
Exam Application
Exams test whether you can apply PEMDAS in strict order, and specifically whether you know that M/D and A/S are each equal-priority pairs solved left to right — not "multiplication always before division."
⚠ Common Trap
The most common trap: assuming multiplication always happens before division (or addition always before subtraction). Both pairs are actually equal priority — you resolve them strictly left to right, in whichever order they appear in the problem.
✓ Quick Self-Check
1. What does PEMDAS stand for?
Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Tap to reveal / hide
2. Solve 10 ÷ 2 × 5. What's the answer?
25 — divide first (10÷2=5), then multiply (5×5=25), left to right.
Tap to reveal / hide
3. Does multiplication always come before division in PEMDAS?
No — they're equal priority and are solved left to right, whichever appears first.
Tap to reveal / hide
4. Solve 2 + 3 × 4. What's the answer?
14 — multiply first (3×4=12), then add (2+12=14).
Tap to reveal / hide
5. If a problem has nested parentheses, which do you solve first?
The innermost parentheses first, working outward.
Tap to reveal / hide