BODMAS rule is a set of guidelines used to determine the sequence in which mathematical operations must be performed when solving an expression. Following the correct order of operations is vital to getting accurate results.
The term BODMAS is an acronym used to remember the order of operations to be followed when solving arithmetic expressions involving multiple operations. It stands for Brackets, Orders (i.e., powers and roots), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
Here’s the order of operations according to BODMAS:
Brackets → Orders (Exponents and Roots) → Division → Multiplication → Addition → Subtraction.
BODMAS Rule - Order of Operations
To get accurate results always follow the order sequence to avoid confusion. Order and Operations in BODMAS rule is shown below as,
Rules of BODMAS in Order | Operations Rules | Examples |
|---|---|---|
B - Brackets | Evaluate expressions within brackets first. | Example: 23 + (5 - 3) - 16/2 + 4×3 + 1 |
O - Orders | Evaluate expressions with exponents or roots. | Example: 23 + 2 - 16/2 + 4×3 + 1 |
D - Division | Perform division from left to right. | Example: 8 + 2 - 16/2 + 4×3 + 1 |
M - Multiplication | Perform multiplication from left to right. | Example: 8 + 2 - 8 + 4×3 + 1 |
A - Addition | Perform addition from left to right. | Example: 8 + 2 - 8 + 12 + 1 |
S - Subtraction | Perform subtraction from left to right. | Example: 23 - 8 |
When to Use BODMAS Rule?
BODMAS Rule is used when there are multiple arithmetic operations (Divide, Multiply, Addition, and Subtraction) in one equation only and the preference of solving then impact the result of the equation then we use the BODMAS rule to solve are equation correctly.
Conditions to follow while solving using the BOADMAS rule are the following
- Bracket is to be simplified first. In bracket also first —(Bar) is simplified then ()(Parentheses) is simplified, then {}(Curly bracket) is simplified, and at last [](square bracket) are simplified.
- Negative sign ahead of any bracket changes the internal sign of the bracket(positive to negative and vice-versa) when the bracket is opened.
Example: - (b - c + d) = - b + c - d
- Any term outside the bracket is multiplied using the distributive property of multiplication.
Example: a(b + c) = ab + ac
Steps for Solving Problems using BODMAS Rule
- Step 1: Brackets: Evaluate expressions within brackets first.
- Step 2: Orders: Simplify expressions with exponents or roots.
- Step 3: Division: Perform division from left to right.
- Step 4: Multiplication: Perform multiplication from left to right.
- Step 5: Addition: Add numbers from left to right.
- Step 6: Subtraction: Subtract numbers from left to right.
Simplification of Bracket
BODMAS is used to simplify various arithmetic problems and simplifying the bracket is the first priority and the priority order of the bracket is (), {}, and [].
That is we first solve for the bracket (), then {} and last we solve the bracket []. This is explained by the example added below as,
Example: Simplify [2 + {3 × 4}]/(5-2)
= [2 + {3 × 4}]/(5-3)
= [2 + 12]/2
= 14/2 = 7
BODMAS, PEMDAS and BIDMAS
PEMDAS and BIDMAS are variations of the BODMAS acronym, each emphasizing the same order of operations but using slightly different terminology.
BODMAS | BIDMAS | PEMDAS |
|---|---|---|
B - Brackets ( ( ), { }, [ ] ) | B - Brackets ( ), { }, [ ] | P - Parentheses ( ), { }, [ ] |
O - Order ( √ ) | I - Indices ( xn) | E - Exponents (xn) |
D - Division (÷) | D - Division (÷) | M - Multiplication (×) |
M - Multiplication (×) | M - Multiplication (×) | D - Division (÷) |
A - Addition (+) | A - Addition (+) | A - Addition (+) |
S - Subtraction (-) | S - Subtraction (-) | S - Subtraction (-) |
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BODMAS Rule Solved Examples
Example 1: Solve 2+7×8-5
Solution:
Applying BODMAS
2 + (7 × 8) - 5
= 2 + 56 -5
= (2 + 56) - 5
= 58 - 5
= 53
Example 2: Find the value of the expression : (8 × 6 - 7) + 65
Solution:
As brackets are provided here, solve them first
(8 × 6 - 7) in this, multiplication operator has the highest priority therefore it will be
= (48 - 7)
= 41So, the final result will be 41 + 65 = 106
Example 3: Find the value of 6× 6+ 6× 6+ 6× 6
Solution:
Here, only have two operators that is addition and multiplication.
Therefore, solve multiplication first6× 6+ 6× 6+ 6× 6
= 36 + 36 + 36
=108
Example 4: Evaluate 8/4 × 6/3 × 7 + 8 - (70/5 - 6)
Solution:
Evaluate 8/ 4 × 6/3 × 7 + 8 - (70/5 - 6 )
We can rewrite expression as
(8/4 × 6/3 × 7 + 8) - (70/5 - 6)Now we will solve respective brackets ,
= (2 × 2 × 7 + 8) - (14 - 6)
= (4 × 7 + 8) - (8)
= (28 + 8) - (8)
= (36) - (8)
= 28