PEMDAS Power Tool
Enter a math problem to see the step-by-step magic.
Visual Solution Path
Mastering the Order of Operations
Imagine trying to bake a cake but reading the instructions in the wrong order. If you put the eggs in the oven before cracking them, you would have a mess! Mathematics works the same way. To get the correct answer, everyone must follow a specific set of rules known as the Order of Operations.
Without these rules, a simple problem like $3 + 4 \times 2$ could have two different answers. If you add first ($3+4=7$), you get $14$. If you multiply first ($4\times2=8$), you get $11$. To avoid confusion, mathematicians agreed on a universal hierarchy.
Meet PEMDAS
The most common mnemonic used in the United States to remember this hierarchy is PEMDAS. You can remember it by the phrase: “Please Excuse My Dear Aunt Sally.”
- P Parentheses: Solve what is inside grouping symbols first $( )$.
- E Exponents: Calculate powers and square roots next $x^2$.
- MD Multiply & Divide: These are tied! Work from left to right.
- AS Add & Subtract: These are also tied. Work from left to right.
The Golden Rule
Multiplication does NOT always come before division.
Addition does NOT always come before subtraction.
Left $\rightarrow$ Right
Using this tool, you can verify your homework or create your own complex expressions to test your skills. Just remember: scan the problem from left to right, identify the highest priority operation, solve it, and rewrite the line. Repeat until you have a single number!
Frequently Asked Questions
Why is the answer different on my calculator?
Basic calculators often calculate immediately as you type (doing $3+4=7$, then $\times 2=14$). Scientific calculators and this tool use the correct hierarchy to give you $11$.
What if there are nested parentheses?
Always work from the innermost set of parentheses outward. Think of it like peeling an onion—start from the center.
Do fractions count as division?
Yes! The fraction bar acts as a grouping symbol. You must solve the entire numerator (top) and the entire denominator (bottom) before dividing them.