Does multiplication always come before division?

No. Despite the M appearing before D in PEMDAS, multiplication and division have equal priority. You perform whichever comes first as you read the expression from left to right. The same rule applies to addition and subtraction—they share equal priority and are handled left to right.

Order of Operations (PEMDAS) — Definition, Formula & Examples

Order of Operations (PEMDAS) is the set of rules that tells you which calculations to perform first when an expression has more than one operation. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

The order of operations is a convention that establishes a hierarchy for evaluating mathematical expressions: (1) evaluate expressions inside grouping symbols (parentheses, brackets, braces) first, working from the innermost group outward; (2) evaluate exponents and roots; (3) perform multiplication and division from left to right; (4) perform addition and subtraction from left to right. Multiplication and division share the same priority, as do addition and subtraction.

How It Works

When you see an expression like

3 + 4 \times 2

, you need a rule to decide whether to add first or multiply first—different choices give different answers. PEMDAS provides that rule. Start by simplifying anything inside parentheses, then handle exponents. Next, scan left to right and perform all multiplication and division in the order you encounter them. Finally, scan left to right again for addition and subtraction. The key detail many students miss is that multiplication and division are equal in rank (same for addition and subtraction), so you resolve ties by working left to right.

Worked Example

Problem: Evaluate:

6 + 2 \times (5 - 1)^2 \div 4

Parentheses: Simplify inside the parentheses first.

5 - 1 = 4 \quad\Rightarrow\quad 6 + 2 \times 4^2 \div 4

Exponents: Evaluate the exponent next.

4^2 = 16 \quad\Rightarrow\quad 6 + 2 \times 16 \div 4

Multiplication and Division (left to right): Multiply first (it appears before the division when reading left to right), then divide.

2 \times 16 = 32 \quad\Rightarrow\quad 32 \div 4 = 8 \quad\Rightarrow\quad 6 + 8

Addition: Finally, add.

6 + 8 = 14

Answer:

14

Another Example

Problem: Evaluate:

18 \div 3 \times 2 - 1

Division and Multiplication (left to right): Division comes first when reading left to right, then multiplication.

18 \div 3 = 6 \quad\Rightarrow\quad 6 \times 2 = 12 \quad\Rightarrow\quad 12 - 1

Subtraction: Subtract last.

12 - 1 = 11

Answer:

11

Why It Matters

Every math course from 6th-grade pre-algebra onward assumes you follow the order of operations. Without it, formulas in science, finance, and engineering would be ambiguous—two people could read the same expression and get different results. Standardized tests like the SAT and ACT regularly include problems designed to test whether you apply PEMDAS correctly.

Common Mistakes

Mistake: Always doing multiplication before division (or addition before subtraction) because of the letter order in PEMDAS.

Correction: Multiplication and division share the same rank. So do addition and subtraction. Within each pair, work left to right. For example,

8 \div 2 \times 3 = 12

, not

8 \div 6

Mistake: Forgetting to simplify everything inside parentheses before moving to the next step.

Correction: Resolve all operations inside grouping symbols first, including nested parentheses (innermost first), before applying exponents or anything outside.

Related Terms

Arithmetic — The branch of math where PEMDAS applies
Exponent — Evaluated in the second step of PEMDAS
Exponentiation — The operation of raising to a power
Product — Result of multiplication, step three in PEMDAS
Quotient — Result of division, same rank as multiplication
Difference — Result of subtraction, the last PEMDAS step
Formula — Requires PEMDAS to evaluate correctly
Power — Another term for an exponent expression