Question
Evaluate using BODMAS. Why does the order of operations matter?
(CBSE 6 Board pattern)
Solution — Step by Step
| Letter | Operation | Priority |
|---|---|---|
| B | Brackets (parentheses) | 1st (highest) |
| O | Orders (powers, roots) | 2nd |
| D | Division | 3rd (left to right) |
| M | Multiplication | 3rd (left to right) |
| A | Addition | 4th (left to right) |
| S | Subtraction | 4th (left to right) |
D and M have the SAME priority — work left to right. Same for A and S.
Brackets:
Expression becomes:
and
Expression becomes:
, then
If we had ignored BODMAS and gone left to right blindly: , , , . A completely wrong answer.
flowchart TD
A["Given an expression"] --> B["Step 1: Solve BRACKETS first"]
B --> C["Step 2: Evaluate ORDERS - powers, roots"]
C --> D["Step 3: Do DIVISION and MULTIPLICATION left to right"]
D --> E["Step 4: Do ADDITION and SUBTRACTION left to right"]
E --> F["Final Answer"]Why This Works
Without a fixed order, the same expression gives different answers. BODMAS is a universal agreement so that everyone reading "" gets the same result (14, not 20). Multiplication and division are “stronger” operations because they represent repeated addition — they naturally come before simple addition and subtraction.
Brackets override everything because they are explicit instructions: “do this first.” That is why we use brackets to force a specific order when needed.
Alternative Method
PEMDAS is the American version of the same rule: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. The rules are identical — just different names.
A common memory trick: “Big Oranges Don’t Make Apples Sweet” for BODMAS.
When in doubt, add brackets to make your intention clear. Writing vs removes all ambiguity. Examiners sometimes test whether you know that D and M have equal priority — solve them left to right, not “D before M.”
Common Mistake
Many students think Division always comes before Multiplication because D appears before M in BODMAS. This is wrong. D and M have EQUAL priority — you work left to right. Example: (left to right), NOT (doing multiplication first). The same applies to Addition and Subtraction.