PEMDAS is a common math acronym that helps students remember the correct order for solving mathematical expressions.
It stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
Following PEMDAS helps you solve equations consistently and avoid mistakes when an expression contains several different mathematical operations.
In this guide, you’ll learn what PEMDAS means, how to use it, examples with answers, and how it compares with other order-of-operations rules.
What Does PEMDAS Mean?
PEMDAS stands for:
- P — Parentheses: Solve expressions inside parentheses first.
- E — Exponents: Calculate powers and roots where applicable.
- M — Multiplication: Perform multiplication.
- D — Division: Perform division.
- A — Addition: Perform addition.
- S — Subtraction: Perform subtraction.
Quick answer: PEMDAS is a rule for determining the order in which mathematical operations should be performed.
One important detail: multiplication and division have the same priority, as do addition and subtraction. When operations have equal priority, work from left to right.
1. How Does PEMDAS Work?
Follow these steps when solving an expression:
- Evaluate expressions inside parentheses or other grouping symbols.
- Calculate exponents.
- Perform multiplication and division from left to right.
- Perform addition and subtraction from left to right.
For example:
(6+3\times4)
First, multiply:
(3\times4=12)
Then add:
(6+12=\boxed{18})
The answer is 18, not 36, because multiplication comes before addition.
2. PEMDAS Examples With Answers
Example 1: Addition and Multiplication
(5+2\times6)
Step 1: Multiply first.
(2\times6=12)
Step 2: Add.
(5+12=\boxed{17})
Answer: 17
Example 2: Parentheses
((5+2)\times6)
Step 1: Solve the parentheses.
(5+2=7)
Step 2: Multiply.
(7\times6=\boxed{42})
Answer: 42
Notice that adding first changes the answer because the parentheses specify the order.
Example 3: Exponents
(3+2^3\times2)
Step 1: Calculate the exponent.
(2^3=8)
Step 2: Multiply.
(8\times2=16)
Step 3: Add.
(3+16=\boxed{19})
Answer: 19
Example 4: Division and Subtraction
(20\div5-2)
Step 1: Divide.
(20\div5=4)
Step 2: Subtract.
(4-2=\boxed{2})
Answer: 2
Example 5: Multiplication and Division Together
(24\div6\times2)
Multiplication and division have equal priority, so work from left to right.
Step 1:
(24\div6=4)
Step 2:
(4\times2=\boxed{8})
Answer: 8, not 2.
Example 6: Addition and Subtraction Together
(15-6+2)
Addition and subtraction have equal priority, so work from left to right.
Step 1:
(15-6=9)
Step 2:
(9+2=\boxed{11})
Answer: 11
3. What Is the Difference Between PEMDAS and BODMAS?
PEMDAS and BODMAS are two different acronyms for remembering the same general order of operations.
| PEMDAS | BODMAS |
| P — Parentheses | B — Brackets |
| E — Exponents | O — Orders |
| M — Multiplication | D — Division |
| D — Division | M — Multiplication |
| A — Addition | A — Addition |
| S — Subtraction | S — Subtraction |
The wording differs, but the rules are effectively the same when interpreted correctly.
Important: Neither acronym means that multiplication must always be performed before division. Multiplication and division share the same priority and are evaluated from left to right. Addition and subtraction follow the same rule.
4. Common PEMDAS Mistakes
Students sometimes misunderstand PEMDAS in these ways:
- Doing addition before multiplication: In (4+3\times2), multiply first to get 10.
- Always multiplying before dividing: In (18\div3\times2), work left to right to get 12.
- Always adding before subtracting: In (10-4+1), work left to right to get 7.
- Ignoring parentheses: In ((4+3)\times2), calculate the parentheses first to get 14.
Remember that PEMDAS is about priority levels, not six completely separate steps that must always happen in the printed order.
FAQs
1. What does PEMDAS stand for?
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
2. What is the main purpose of PEMDAS?
It tells you which mathematical operations to perform first when solving an expression containing multiple operations.
3. Is PEMDAS the same as BODMAS?
Yes. They are different memory aids for the same general order-of-operations rules.
4. Does multiplication always come before division?
No. Multiplication and division have equal priority. Evaluate them from left to right.
5. Does addition always come before subtraction?
No. Addition and subtraction have equal priority. Evaluate them from left to right.
6. What is the correct answer to 10 + 2 × 3?
The answer is 16. Multiply first: (2\times3=6), then add: (10+6=16).
7. Why is PEMDAS important?
PEMDAS provides a consistent method for interpreting mathematical expressions, helping everyone arrive at the same answer.
Conclusion:
PEMDAS means Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
It helps you solve mathematical expressions in the correct order.
The most important rule to remember is that multiplication and division share the same priority, as do addition and subtraction.
When operations have equal priority, always work from left to right.
Kevin Turner researches English words, expressions, and language trends to create educational content that is both informative and accessible. His work emphasizes clarity, factual accuracy, and practical language usage for global audiences.