Order of Operations (PEMDAS)
Learn the correct order to solve math problems with multiple operations using PEMDAS.
Definition
- P = Parentheses (do these first)
- E = Exponents (powers and roots)
- M/D = Multiplication and Division (left to right)
- A/S = Addition and Subtraction (left to right)
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Worked Examples
Solve:
Look for Parentheses
No parentheses → Move to next step
Look for Exponents
No exponents → Move to next step
Do Multiplication first
→
Do Addition
→
Answer:
Common Mistakes
Adding before multiplying
Why it's wrong: Students often work left to right, doing before the multiplication in
Correct: Always do multiplication and division before addition and subtraction. The answer is , not
Thinking M comes before D
Why it's wrong: PEMDAS lists M before D, making students think multiplication always comes first
Correct: Multiplication and Division have EQUAL priority. Work left to right. In , do first, then
Forgetting to work inside parentheses completely
Why it's wrong: Students may only do part of what is inside parentheses
Correct: Solve EVERYTHING inside parentheses before moving on. In , you must do first, then
Ignoring exponents
Why it's wrong: Students sometimes treat exponents like regular multiplication
Correct: Exponents come before multiplication. In , first calculate , then
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Practice Problems
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Why It Matters
- Science - calculating formulas correctly
- Programming - computers follow strict operation orders
- Finance - calculating interest, taxes, and budgets
- Engineering - designing safe structures and systems
Real World Applications
Shopping Discounts
When shopping, you often need to calculate final prices after discounts and additional costs. The order in which you apply these calculations matters!
Example:
A 50 dollar shirt is 20% off, then you add 5 dollar shipping. Calculate: dollars
You want to buy a video game that costs 60 dollars. The store has a 25% off sale, and there is a 4 dollar tax added at the end.
What is the final price you will pay?
Step 1: Write the mathematical expression
Write the mathematical expression using the numbers from the problem:
Cooking & Recipes
When scaling recipes or combining ingredients, the order of operations ensures you get the right amounts.
Example:
A recipe needs cups total (2 cups flour + 1 cup sugar, tripled)
You are making cookies. The recipe calls for 2 cups of flour plus 1 cup of sugar, and you want to make 4 batches.
How many total cups of dry ingredients do you need?
Step 1: Write the mathematical expression
Write the expression using parentheses to group what goes in one batch:
Video Game Scoring
Video games use mathematical formulas to calculate damage, scores, and rewards. Understanding order of operations helps you predict outcomes.
Example:
Damage = base × multiplier + bonus: damage
In a game, your base attack is 15, you have a 3× critical hit multiplier, and a +10 bonus from your weapon.
How much total damage do you deal?
Step 1: Write the mathematical expression
Write the damage formula (base × multiplier + bonus):
Key Takeaways
- 1PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
- 2Always solve inside Parentheses first, starting with the innermost
- 3Exponents (powers) come after parentheses
- 4Multiplication and Division have equal priority - work left to right
- 5Addition and Subtraction have equal priority - work left to right
- 6When in doubt, use parentheses to make your intention clear
- 7BODMAS and PEMDAS are the same thing - different regions use different names
Frequently Asked Questions
Glossary
- Order of Operations
- A set of rules that determines which calculations are performed first in an expression
- PEMDAS
- An acronym to remember the order: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
- BODMAS
- British version of PEMDAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction
- Expression
- A mathematical phrase containing numbers and operations, like 3 + 4 × 2
- Parentheses
- Symbols ( ) used to group parts of an expression that should be calculated first
- Exponent
- A number that shows how many times to multiply a base by itself, written as a superscript
Formula Card
PEMDAS Order
The order to follow: Parentheses, Exponents, then Multiplication/Division (left to right), then Addition/Subtraction (left to right)