You have an expression like 20 − 4 × 3 ÷ 2 + 1 in front of you. Where does the division happen? Does it come before or after the multiplication? Before or after the subtraction? The answer to those questions is the order of operations — and getting it wrong means getting the wrong answer, even if every individual calculation is correct.
This post explains exactly where division fits, why it shares a step with multiplication, and how to work through any expression confidently using PEMDAS or BODMAS.
What Is the Order of Operations?
The order of operations is a set of rules that tells you which part of a mathematical expression to calculate first. Without these rules, the same expression could produce different answers depending on who solved it. The rules exist so that there is exactly one correct answer to any written expression.
Two acronyms teach the same rule in different countries:
Parentheses, Exponents, Multiplication & Division, Addition & Subtraction
Brackets, Orders (powers/roots), Division & Multiplication, Addition & Subtraction
Both acronyms describe exactly the same rule. The different words — Parentheses vs. Brackets, Exponents vs. Orders — just reflect regional vocabulary. The mathematics underneath is identical.
Where Division Sits in the Order
Division is the third step — but it shares that step with multiplication. This is the detail that trips people up the most.
| Step | PEMDAS | BODMAS | What you do |
|---|---|---|---|
| 1 | Parentheses () | Brackets () | Solve everything inside brackets first |
| 2 | Exponents | Orders | Calculate powers and roots |
| 3 | Multiplication & Division | Division & Multiplication | Work left to right — whichever comes first |
| 4 | Addition & Subtraction | Addition & Subtraction | Work left to right — whichever comes first |
The key insight: division does not come after multiplication. They are equal. When you see both in the same expression, you simply read from left to right and handle whichever one you encounter first.
Why Multiplication and Division Share a Step
Division is actually multiplication in disguise. Dividing by 4 is the same as multiplying by ¼. Because of this mathematical equivalence, the two operations have the same priority — neither can outrank the other. The left-to-right rule is the tiebreaker.
Many students see M before D in PEMDAS and conclude that multiplication always happens first. It does not. The letter order in the acronym is just a memory aid, not a ranking. Multiplication and Division are on the same level — always resolved left to right.
Worked Examples
Example 1 — Division before multiplication (left to right)
If you multiplied first you'd get 24 ÷ 12 = 2 — wrong. The left-to-right rule is what separates the right answer from the wrong one.
Example 2 — Division after parentheses
Without the parentheses, 3 + 9 ÷ 4 would give a different result — division happens first, giving 3 + 2.25 = 5.25. Parentheses change everything.
Example 3 — Division inside a longer expression
Example 4 — Multiple divisions in a row
If you reversed the order and calculated 4 ÷ 3 first, then 48 ÷ (4/3), you'd get 36 — a completely different result. Division is not associative, so left-to-right is not just a convention, it's essential for a consistent answer. You can check individual division steps on 48 ÷ 4.
Need to verify a division step inside a longer calculation?
Use the Division Calculator →How Parentheses Interact with Division
Parentheses are the most powerful tool for controlling where division happens. They override every other rule. Whatever is inside the brackets gets resolved first, no exceptions.
This is useful in real situations. If you want to divide the sum of two numbers rather than just one of them, you group them in parentheses:
The parentheses change the meaning entirely. This is why being careful about where you write division signs — and where you add brackets — matters so much, especially in fractions where the fraction bar acts as a grouping symbol. See our post on how to divide fractions for more.
Division and Negative Numbers
Order of operations doesn't change when negative numbers are involved, but the signs require attention. A negative sign that isn't inside parentheses applies only to the number immediately next to it, not to an entire operation.
For a full guide on how signs behave when dividing, see our post on dividing negative numbers.
A Word on Long Division and Order of Operations
When you use long division to work out a single division step inside a larger expression, you're still following the same priority rules — you're just using a method to complete one step at a time. Order of operations tells you which step to do when; long division tells you how to do a single division step when the numbers are large. The two ideas work together, not against each other.
Quick Reference: Division in Order of Operations
Division happens after parentheses and exponents. Division happens at the same time as multiplication — left to right. Division happens before addition and subtraction. Parentheses can move division to any priority level you need. Multiple divisions in a row are always resolved left to right.
🔢 For even more worked examples of division in action, visit the long division examples page to see the method applied to different types of numbers.