BODMAS Rule: Examples, Full form, Practice Questions
BODMAS is an acronym for priority of mathematical operation rules. Bodmas rule states that division and multiplication must be done before addition and subtraction in any mathematical operation.
BODMAS Full form
- B – Brackets: Used to Solve expressions within brackets first.
- O – Orders: Evaluate expressions with exponents or roots next.
- D – Division: Perform division from left to right.
- M – Multiplication: Perform multiplication from left to right.
- A – Addition: Perform addition from left to right.
- S – Subtraction: Perform subtraction from left to right.
In this article, We have explained the BODMAS rule in detail. we have also covered every important concept related to the BODMAS rule with examples, practice questions, the Difference between PEDMAS and BODMAS, How you can use the BODMAS rule in your real life, and many more.
Table of Content
BODMAS Rule Definition
BODMAS rule set of guidelines which is used to determine the sequence in which mathematical operations must be performed when solving an expression. Maintaining the order of operations is important while solving the mathematical operations to get the correct result. The following is the order by which mathematical operations can be performed.
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 |
---|---|---|
1. B – Brackets |
| Example: 2^{3} + (5 – 3) – 16/2 + 4×3 + 1 First solve (5 – 3) |
2. O – Orders |
| Example: 2^{3} + 2 – 16/2 + 4×3 + 1 Then solve (2^{3}) |
3. D – Division |
| Example: 8 + 2 – 16/2 + 4×3 + 1 Then solve (16/2) |
4. M – Multiplication |
| Example: 8 + 2 – 8 + 4×3 + 1 Then solve (4×3) |
5. A – Addition |
| Example: 8 + 2 – 8 + 12 + 1 Then solve 8 + 2 + 12 + 1 |
6. S – Subtraction |
| Example: 23 – 8 At last, solve 23 – 8 = 15 |
BODMAS Full form
Basic rule for solving multiple operations in an equation is the BOADMAS and the full form of BODMAS is “B” stands for Brackets, “O” Stands for Order of, “D” stands for Division, “M” stands for Multiplication, “A” stands for Addition, and “S” stands for Subtraction. BODMAS full form by letter given as the following:
BODMAS Full Form – Each Letter Representation | ||
---|---|---|
B | [{( )}] | Brackets |
O | x² | Order of Powers or Roots, (in some cases, ‘of’) |
D | ÷ | Division |
M | × | Multiplication |
A | + | Addition |
S | – | Subtraction |
How to Solve Problems using BODMAS Rule
BODMAS Rule is used when there are multiple 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
Conditions and Rules
Below are provided several conditions and rules for the purpose of general simplification:
Condition | Rule |
---|---|
x + (y + z) ⇒ x + y + z | Uncover the bracket and combine the terms inside. |
x – (y + z) ⇒ x – y – z | When you see numbers inside brackets and a minus sign in front, change the signs of those numbers – if they were adding, make them subtract, and if they were subtracting, make them add. |
x(y + z) ⇒ xy + xz | Take term outside the bracket and multiply it with each term inside the bracket. |
Solving Problems using BODMAS Rule, Follow teps:
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.
Tips to Remember BODMAS Rule
Here are the steps to simplify an expression using the BODMAS rule:
- Start with Brackets
- Deal with Exponents or Roots
- Do Division or Multiplication (left to right)
- Finish with Addition or Subtraction (left to right)
What is PEMDAS?
PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right). It is almost as BODMAS but differ in some way. Full form of PEDMAS given below:
PEMDAS Full Form
- P: Parenthesis
- E: Exponent
- M: Multiplication (whichever comes first between M and D)
- D: Division
- A: Addition
- S: Subtraction (whichever comes first between A and S)
Difference between BODMAS and PEMDAS
PEMDAS or BODMAS are the names given to the two rules which are used to solve the order of the operation. There is no big difference between PEMDAS and BODMAS basic difference between them is the priority of (multiplication or division) and the priority of (addition or subtraction)
Basic order of operation in BODMAS and PEMDAS is discussed in image below,
Order of Operations PEMDAS
- P is for Parentheses ( ), { }, [ ]
- E is for Exponents (x^{n})
- M is for Multiplication (×)
- D is for Division (÷)
- A is for Addition (+)
- S is for Subtraction (-)
Order of Operations BODMAS
- B is for Brackets ( ), { }, [ ]
- O is for Order
- D is for Division (÷)
- M is for Multiplication (×)
- A is for Addition (+)
- S is for Subtraction (-)
Ways to Remember Order of Operations in PEDMAS
PEDMAS can easily be learned by using phrase,
“Please Excuse My Dear Miss Aunt Sally”.
Here, order of operations means “Parentheses, Exponents, Division and Multiplication, and Addition and Subtraction”.
Also, BODMAS can be understood as, Brackets, Orders, Division, Multiplication, Addition, and Subtraction.
Tips to Remember PEDMAS Rule
To simplify using PEDMAS rule use the following tips,
- Solve for brackets first.
- Then solve for exponents or root terms (order).
- Then solve division or multiplication operations (whichever comes first from left to right).
- Then solve addition or subtraction operations (whichever comes first 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 Rule without Bracket
If in any simplification problem we are not given bracket we use BODMAS rule without bracket, i.e. ODMAS rule to solve problem. This is explained by example added below,
Example: Simplify, 5 of 15/3 × 2 – 6 + 4
= 5 of 15/3 × 2 – 6 + 4
= (5 × 15)/3 × 2 – 6 + 4
= 75/3 × 2 – 6 + 4
= 25 × 2 – 6 + 4
= 50 – 6 + 4
= 48
Real-Life Applications of BODMAS Rule
BODMAS Rule is widely used in our daily life to solve various problems. Let’s learn about an example that will explain to us the use of BODMAS in real life.
Example: Suppose you purchased 8 cricket balls each costing 25 rupees and a cricket bat costing 450 rupees and now you have to distribute the total bill among your 5 friends. How much does each friend have to pay?
Required equation for above situation is,
= {(8 × 25) + 450} / 5
Using BODMAS rule we get,
= {200 + 450} / 5
= {650} / 5
= 130
Thus, each friend has to pay Rupees 130.
Related Resources
BODMAS Solved Examples
Some examples on BOADMAS Rule are,
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) = 41
So, 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 first
= 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
FAQS on BODMAS Rule
What is BODMAS Rule in Maths?
BODMAS rule in mathematical expression stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction and is used to solve multiple operation in one equation.
Why BODMAS Rule was Invented?
BODMAS rule was invented for solving the equation in mathematics which include multiple operations. This rule provide the correct sequence in which a equation has to be solved.
Who Created BODMAS Rule?
Achilles Reselfelt a mathematician is the one who created BODMAS rule.
What is Trick for Remembering PEDMAS?
PEDMAS can be remembered by phrase “Please Excuse my Dear Miss Aunt Sally”
Are BODMAS and PEDMAS Same?
BODMAS and PEDMAS both are same they are acronyms for remembering the order of operations and are different name for same rules. In UK, Australia, and India it is called BODMAS and in US it is called PEDMAS.
Why is BODMAS important?
Order of operation is important to solve the complex arithmetic problems in right order, without order of operations it is very difficult to solve arithmetic equations.
What is the Use of BODMAS Rule?
BODMAS rule assists in accurately simplifying mathematical expressions. By following this rule, we can correctly calculate the provided expression to ensure an accurate answer.
What does S Mean in Order of Operations?
In BODMAS rule of mathematics, letter ‘S’ represents subtraction.