Brackets, Orders, Division, Multiplication, Addition, Subtraction

BODMAS Full Form in English, letter by letter

BODMAS is the rule for the order of operations in arithmetic: Brackets, Orders, Division, Multiplication, Addition, Subtraction.

BODMAS Full Form in Indian Languages

Every Indian schoolchild learns BODMAS before simplifying an expression. Here is Brackets, Orders, Division, Multiplication, Addition, Subtraction and where it goes wrong.

The full form and what each letter does

The BODMAS rule stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. It is a memory aid for the order in which operations must be worked, so that everyone gets the same answer from the same expression. Older Indian textbooks write the O as 'Of' and the first letter as Bracket.

Brackets come first, and you handle inner brackets before outer ones. Orders means powers and roots, such as squares and cube roots. In Indian textbooks, the word 'of' (as in half of 8) is worked out at this stage, before the surrounding division. Division and multiplication share one level, and addition and subtraction share the next.

The order of letters does not mean division outranks multiplication or addition outranks subtraction. Within each pair, work from left to right as written.

Three worked examples

Take 12 + 8 ÷ 4 × 2 - 3. Division and multiplication go left to right: 8 ÷ 4 = 2, then 2 × 2 = 4. Now 12 + 4 - 3 = 13. A student who adds 12 and 8 first, or multiplies before dividing, will get a wrong answer.

Take (3 + 5)² ÷ 4 - 2. The bracket gives 8, the square gives 64, 64 ÷ 4 = 16, and 16 - 2 = 14. The square sits outside the bracket, so it applies only after the bracket is resolved.

Take 3 + (1/2) of 8. In Indian textbooks 'of' acts at the Orders level, so half of 8 is 4 before the addition, giving 7. When a fraction bar is used, solve the top and bottom first as though each were inside brackets.

The 8 ÷ 2(2 + 2) argument

One expression has been argued over online for years: 8 ÷ 2(2 + 2). Working left to right with division and multiplication at the same level, 8 ÷ 2 = 4 and 4 × 4 = 16. Most calculators and programming languages return 16.

Others treat a number written directly against a bracket as binding more tightly than the division sign, which gives 1. Some style guides allow that reading, so the expression really is ambiguous. For exams, follow the convention your board teaches, and when you write maths yourself, add brackets to remove the doubt.

BODMAS, PEMDAS and the other names

The rule is the same everywhere. Only the letters change. British schools use BIDMAS (Indices), American schools use PEMDAS (Parentheses, Exponents), and Canadian textbooks use BEDMAS. All describe the same precedence.

One trap survives every renaming. Students taught PEMDAS think M must come before D, and students taught BODMAS think D must come before M. They share a level, so only the written left-to-right order decides: 10 - 3 + 2 is 9, not 5, and 12 ÷ 3 × 2 is 8, not 2.

Common mistakes and how to avoid them

The most common error is solving an expression strictly in the order of the letters, which gives wrong answers whenever subtraction comes before addition or multiplication before division. The second is ignoring the sign in front of a bracket: 10 - (3 + 2) is 5, not 9.

Negative numbers cause the third mistake. In -3², the square applies only to 3, so the result is -9, while (-3)² is 9. When you are unsure, rewrite the expression with extra brackets and solve one step at a time.

Where BODMAS shows up in Indian exams

Simplification and approximation questions built on this rule appear in SSC CGL and CHSL, bank PO and clerk papers, railway exams and state service tests. Speed decides marks there, and most errors come from skipping the bracket step rather than from weak arithmetic.

Watch for brackets inside brackets, fractions where top and bottom each need solving first, and decimals hidden in long chains. Writing each step on rough paper costs a second and prevents the sign slips that cost a whole question. Knowing squares, cubes and common fraction-percentage pairs speeds things up, but only once the order is secure.

BODMAS is the shortest route to correct answers in school maths and competitive papers. Solve in order, work left to right within each level, and write the steps down.

BODMAS Full Form: Common Questions