How PEMDAS Works: A Complete Guide for Students

What Does PEMDAS Stand For?

PEMDAS is an acronym that helps you remember the order in which to perform mathematical operations. Each letter represents a step:

P - Parentheses (solve what is inside brackets first)
E - Exponents (powers and square roots)
M - Multiplication
D - Division
A - Addition
S - Subtraction

Some people remember it with the phrase "Please Excuse My Dear Aunt Sally." Whatever helps you remember works!

The Most Important Rule: MD and AS Are Equal Partners

Here is where many students get confused: Multiplication and Division have the SAME priority. Addition and Subtraction also have the SAME priority. When you have operations with equal priority, you work from LEFT to RIGHT.

Think of it this way:

Step 1: P - Parentheses
Step 2: E - Exponents
Step 3: M/D - Multiplication and Division (left to right)
Step 4: A/S - Addition and Subtraction (left to right)

Example 1: Basic PEMDAS

Let us solve: 3 + 4 × 2

Wrong approach: 3 + 4 = 7, then 7 × 2 = 14 (INCORRECT)
Right approach: Do multiplication first: 4 × 2 = 8
Then add: 3 + 8 = 11

Example 2: With Parentheses

Let us solve: (3 + 4) × 2

Parentheses first: 3 + 4 = 7
Then multiply: 7 × 2 = 14

See how parentheses change the answer? That is why they are so important!

Example 3: Left-to-Right Rule

Let us solve: 24 ÷ 6 × 2

Division and multiplication have equal priority
Work left to right: 24 ÷ 6 = 4
Then: 4 × 2 = 8
NOT: 6 × 2 = 12, then 24 ÷ 12 = 2 (This is wrong!)

Example 4: Complex Expression

Let us solve: 2 + 3 × (8 - 4) ÷ 2

Step 1 - Parentheses: (8 - 4) = 4
Now we have: 2 + 3 × 4 ÷ 2
Step 2 - Multiplication/Division left to right: 3 × 4 = 12
Now we have: 2 + 12 ÷ 2
Continue M/D: 12 ÷ 2 = 6
Now we have: 2 + 6
Step 3 - Addition: 2 + 6 = 8

Common PEMDAS Mistakes to Avoid

Mistake 1: Always multiplying before dividing

M comes before D in PEMDAS, but they have equal priority. Always work left to right.

Mistake 2: Forgetting implied multiplication

In expressions like 2(3+4), the multiplication is implied. Solve parentheses first, then multiply.

Mistake 3: Not recognizing nested parentheses

Work from the innermost parentheses outward: ((2+3) × 4) - solve 2+3 first.

Why PEMDAS Matters in Real Life

You might wonder when you will ever use this. The truth is, PEMDAS appears everywhere:

Calculating sale prices with multiple discounts
Programming and spreadsheet formulas
Science equations and chemistry calculations
Financial calculations with interest and fees
Standardized tests like the SAT and ACT

How to Practice PEMDAS

The best way to master PEMDAS is through consistent practice. Here are some tips:

Start with simple expressions and gradually increase complexity
Write out each step so you can track your work
Play math games that require quick order-of-operations thinking
Create your own problems and solve them
Practice daily, even if just for 5-10 minutes