Is BODMAS different from PEMDAS?

No. BODMAS and PEMDAS describe the same rule. "Brackets" means the same as "Parentheses," and "Orders" means the same as "Exponents." In BODMAS, Division is listed before Multiplication, and in PEMDAS, Multiplication is listed before Division, but both systems treat division and multiplication as equal priority — you always work left to right at that level. The same goes for addition and subtraction.

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

Order of Operations (BODMAS) is the rule that tells you the sequence in which to perform calculations in a mathematical expression. BODMAS stands for Brackets, Orders (exponents), Division, Multiplication, Addition, and Subtraction.

BODMAS is a convention that establishes a hierarchy for evaluating arithmetic expressions: first evaluate expressions inside grouping symbols (brackets/parentheses), then apply exponents (orders/powers), then perform division and multiplication from left to right, and finally perform addition and subtraction from left to right. This convention ensures that every well-formed numerical expression yields a single, unambiguous result.

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. BODMAS provides that rule. Work through each level in order: simplify anything inside Brackets first, then evaluate Orders (exponents), then carry out Division and Multiplication scanning left to right, and finally handle Addition and Subtraction scanning left to right. Note that Division and Multiplication share the same priority — whichever appears first from left to right gets done first. The same applies to Addition and Subtraction. The acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) describes exactly the same rule using different names.

Worked Example

Problem: Evaluate

6 + 2 \times (5 - 3)^2

Brackets: Simplify the expression inside the brackets first.

5 - 3 = 2

Orders (Exponents): Next, evaluate the exponent.

2^2 = 4

Multiplication: Now perform the multiplication.

2 \times 4 = 8

Addition: Finally, perform the addition.

6 + 8 = 14

Answer:

6 + 2 \times (5 - 3)^2 = 14

Another Example

Problem: Evaluate

18 \div 3 \times 2 + 5

Division and Multiplication (left to right): Division and multiplication have equal priority, so work left to right. Division comes first.

18 \div 3 = 6

Continue Multiplication: Now multiply.

6 \times 2 = 12

Addition: Finally, add.

12 + 5 = 17

Answer:

18 \div 3 \times 2 + 5 = 17

Why It Matters

Order of operations is foundational to every math course from middle-school pre-algebra through calculus. Spreadsheet formulas, programming languages, and scientific calculators all follow these same rules, so entering a formula incorrectly can produce wrong answers in real-world work. Understanding BODMAS also prepares you for writing and simplifying algebraic expressions, where misapplying the order leads to errors that cascade through multi-step problems.

Common Mistakes

Mistake: Always doing multiplication before division (because M comes before D in PEMDAS)

Correction: Multiplication and division have equal priority. Evaluate them left to right. For example, in

12 \div 4 \times 3

, divide first to get

3 \times 3 = 9

, not

12 \div 12 = 1

Mistake: Ignoring brackets and jumping straight to multiplication or exponents

Correction: Brackets always come first. In

2 \times (3 + 4)

, you must add inside the brackets to get

7

before multiplying, giving

14

— not

2 \times 3 + 4 = 10

Related Terms

Arithmetic — The branch of math where BODMAS applies
Exponent — The 'O' (Orders) step in BODMAS
Exponentiation — Operation evaluated at the Orders stage
Power — Another term for exponent or order
Product — Result of multiplication in BODMAS
Quotient — Result of division in BODMAS
Difference — Result of subtraction, last BODMAS level
Formula — Requires BODMAS to evaluate correctly