Key takeaways
PEMDAS is a concept that students learn in middle school. This concept has different names in different mathematics systems across countries. Many students understand it wrong, and this causes mistakes in math later. So it is important to understand and use this concept correctly.
- Use YouTube videos to see some examples and to better understand how it works
- Always check your steps, especially when you subtract
- Practice a little every day so you can calculate faster
Contents
What Is PEMDAS?
“Students often memorize PEMDAS as a fixed sequence, but it’s more accurate to think of it as a structure for organizing mathematical operations”
The letters stand for:
- P = Parentheses
- E = Exponents
- M = Multiplication
- D = Division
- A = Addition
- S = Subtraction
A common memory device is the phrase “Please Excuse My Dear Aunt Sally,” where the first letter of each word matches the acronym.
PEMDAS is a mnemonic that tells you the correct order to perform operations and simplify complex expressions correctly when solving a math expression that contains more than one type of operation. Without an agreed-upon sequence, the expression 8 + 2 x 3 could equal 30 (if you add first) or 14 (if you multiply first). PEMDAS eliminates this problem.
How PEMDAS Actually Works?
Step 1: Parentheses: Solve everything inside parentheses first. Brackets and braces count as grouping symbols too. Remember: whatever is inside a grouping symbol gets resolved before it interacts with anything outside it.
Example: 3 x (2 + 4) = 3 x 6 = 18, not 6 + 4 = 10 or any other sequence.
Step 2: Exponents: After clearing parentheses, evaluate all exponents and roots. Square roots, cube roots, and any radical expressions belong at this stage.
Example: 2 + 3² = 2 + 9 = 11, not 5² = 25.
Step 3: Multiplication AND Division: This is where students run into trouble. Multiplication does not come before division. Students should remember that multiplication and division have equal priority and must always be solved from left to right.
Example: 12 ÷ 4 x 3.
First divide, then multiply when moving left to right. Wrong approach (doing multiplication first): 12 ÷ 12 = 1 Correct approach (left to right): 12 ÷ 4 = 3, then 3 x 3 = 9.
The correct answer is 9. The acronym implies multiplication goes first, but that reading is incorrect.
Step 4: Addition AND Subtraction: The same principle applies here. Addition and subtraction share equal priority and are worked left to right.
Example: 10 – 3 + 2.
Wrong approach (doing addition first): 10 – 5 = 5 Correct approach (left to right): 10 – 3 = 7, then 7 + 2. The answer is 9.
Priorities of Steps
| Priority | Operations | Rule |
|---|---|---|
| 1 (highest) | Parentheses, brackets, braces | Innermost first, then outward |
| 2 | Exponents and roots | Left to right |
| 3 | Multiplication and Division | Left to right, equal priority |
| 4 (lowest) | Addition and Subtraction | Left to right, equal priority |
BODMAS vs PEMDAS
BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. BIDMAS replaces “Orders” with “Indices,” which is another word for exponents and powers. All three acronyms, PEMDAS and BODMAS describe the same mathematical convention.
PEMDAS or BODMAS: Which One Should You Use?
PEMDAS or BODMAS, the answer depends entirely on where you are studying. American schools teach PEMDAS. British, Australian, and many international schools teach BODMAS or BIDMAS.
What About BEDMAS?
BEDMAS is the Canadian version of the same acronym. It stands for Brackets, Exponents, Division, Multiplication, Addition, Subtraction. Structurally it sits between PEMDAS and BODMAS: it uses “Brackets” like the British systems but “Exponents” like the American one, and lists Division before Multiplication in the same way BODMAS does.
One thing worth noting about BEDMAS specifically: because it lists Division before Multiplication and the Canadian curriculum tends to be explicit about the left-to-right rule within each tier, students taught on BEDMAS sometimes have a cleaner intuition about equal-priority operations than students who learned PEMDAS and assumed M always beats D.
PEMDAS vs BODMAS vs BEDMAS: A Quick Reference
| Feature | PEMDAS (US) | BODMAS (UK, Australia) | BIDMAS (UK variant) | BEDMAS (Canada) |
|---|---|---|---|---|
| Origin | United States | UK, Australia | UK | Canada |
| First letter | Parentheses | Brackets | Brackets | Brackets |
| Second letter | Exponents | Orders | Indices | Exponents |
| M and D order | M listed first | D listed first | D listed first | D listed first |
| Mathematical result | Identical | Identical | Identical | Identical |
The Most Common PEMDAS Mistakes
Most mistakes with order of operations follow a few simple patterns:
- Some students think PEMDAS has six steps and always do multiplication before division and addition before subtraction.
- When there are no parentheses, some students get confused or add them where they are not needed.
- PEMDAS works for numbers, but in algebra, students sometimes try to combine terms that are not the same.
Why PEMDAS Is Important Beyond the Classroom?
Because it is used in everyday life, and here are the most common areas:
- Computer programming
- Scientific calculations
- Financial math
- Standardized tests
PEMDAS Practice
Seeing the rules applied to actual problems is the fastest way to internalize them.
Example 1
Solve: 5 + 3 x 2² – (8 ÷ 4)
Step 1: (8 ÷ 4) = 2 Expression becomes: 5 + 3 x 2² – 2
Step 2: 2² = 4 Expression becomes: 5 + 3 x 4 – 2
Step 3: 3 x 4 = 12 Expression becomes: 5 + 12 – 2
Step 4: 5 + 12 = 17, then 17 – 2 = 15
Answer: 15
Example 2
Solve: 18 ÷ 6 x 3
Many students multiply 6 x 3 first (because M comes before D in the acronym) and get 18 ÷ 18 = 1. That is wrong.
Working left to right: first divide 18 ÷ 6 = 3, then multiply 3 x 3 = 9.
Answer: 9
Example 3
Solve: 6 + 18 ÷ 3² × (5 − 2)
Parentheses: (5 − 2) = 3 → 6 + 18 ÷ 3² × 3
Exponents: 3² = 9 → 6 + 18 ÷ 9 × 3
Multiplication/Division left to right: 18 ÷ 9 = 2, then 2 × 3 = 6 → 6 + 6
Answer: 12
PEMDAS in Online Math Courses at Legacy Online School
Online math learning can be hard with PEMDAS. At Legacy Online School, teachers help students understand it step by step. Students see math problems in a clear format and learn the correct order of operations. They also practice common mistakes, like how to do multiplication and division from left to right. Students can open their materials anytime and repeat PEMDAS examples before tests.
For parents supporting students through online math, PEMDAS is one of the concepts worth checking in on early in the school year. A quick review of how your student solves an expression like 12 – 4 ÷ 2 + 3 x 2 reveals whether they understand the rules or are applying the acronym too literally.
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Top Tips from Our Expert
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Maya Robinson, Math Curriculum Specialistl
Sources: College Board
