What Is BODMAS Rule? | Solved Examples

The BODMAS rule is a fundamental principle that dictates the correct sequence of operations when solving an expression or equation. But what is BODMAS in maths? Let's explore.

What is BODMAS?

BODMAS in maths stands for Brackets, Orders, Division and Multiplication, Addition and Subtraction. It is a mathematical rule used to determine the correct order of operations when solving expressions. According to BODMAS, operations inside brackets should be solved first. After that, any exponents or orders (such as squares, cubes, etc.) are dealt with. Next, division and multiplication are performed from left to right, followed by addition and subtraction, also from left to right. This rule ensures that mathematical expressions are simplified correctly and consistently. By following BODMAS, you avoid confusion and achieve the correct result in calculations involving multiple operations. So, if someone asks, "What is BODMAS in maths?", you can now explain it like a pro.

Also Check: Perimeter of Rectangle

What is the BODMAS Rule

Numbers

1. Natural Numbers : The set of positive integers, starting from 1 (1, 2, 3, 4, …).
2. Whole Numbers : Similar to natural numbers but include 0 (0, 1, 2, 3, …).
3. Integers : Whole numbers and their negative counterparts (-3, -2, -1, 0, 1, 2, 3, …).
4. Rational Numbers : Numbers that can be expressed as fractions or ratios (1/2, 3/4, 0.5, etc.).
5. Irrational Numbers : Numbers that cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions (√2, π).
6. Real Numbers : The set of all rational and irrational numbers, representing any value on the number line.
7. Complex Numbers : Numbers that include both real and imaginary components, often represented as a + bi (where "i" is the imaginary unit).

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Operators or Operations

1. Addition (+) : Combining two numbers to get their total.
2. Subtraction (-) : Finding the difference between two numbers.
3. Multiplication (×) : Combining numbers through repeated addition.
4. Division (÷) : Splitting one number by another to determine how many times the divisor fits into the dividend.

Why Do We Use the BODMAS Rule in Maths?

In maths, we use different signs to add, subtract, multiply, or divide numbers. If we mix up the steps, we’ll get a wrong answer. That's why we follow the maths BODMAS rule. It keeps our solving steps in the correct order. Let’s take an example:

Solve 5 + 2 × 3.

Without using the maths BODMAS rule, we might first add 5 + 2 and get 7 × 3 = 21. That’s wrong. But with BODMAS in maths, we do multiplication first: 2 × 3 = 6, then add 5 + 6 = 11.

See? The correct answer is 11. That’s the power of using the maths BODMAS rule. Now lets study briefly about the order in the next heading.

Order of Operations in BODMAS Rule

• B rackets: First, solve expressions inside brackets (parentheses).
• O rders: Next, handle orders (exponents or powers).
• D ivision: Perform division from left to right.
• M ultiplication: Perform multiplication from left to right.
• A ddition: Perform addition from left to right.
• S ubtraction: Finally, perform subtraction from left to right.

Easy Ways to Remember the BODMAS Rule

• Big Old Ducks Make Apple Sauce – A fun sentence to remember!

• Draw a pyramid with brackets at the top and subtraction at the bottom.

• Practice solving BODMAS equations every day.

The more you practice, the better you’ll understand how to explain BODMAS rule. 

Expression or an Equation of BODMAS

Example of an Expression

Expression: ( 8 + 2 \times (3^2 - 1) \div 2 )

1. Brackets : Solve inside the brackets first.
   • ( 3^2 - 1 = 9 - 1 = 8 )
   • The expression now becomes: ( 8 + 2 \times 8 \div 2 )
2. Orders : There are no further orders to solve.
3. Division and Multiplication : From left to right.
   • First, perform the multiplication: ( 2 \times 8 = 16 )
   • Then, perform the division: ( 16 \div 2 = 8 )
   • The expression now becomes: ( 8 + 8 )
4. Addition : Finally, perform the addition.
   • ( 8 + 8 = 16 )

Example of an Equation

Equation: ( 4x + 3 = 19 )

1. Isolate the variable: Start by subtracting 3 from both sides.
   • ( 4x = 19 - 3 )
   • ( 4x = 16 )
2. Division: Divide both sides by 4 to solve for ( x ).
   • ( x = \frac{16}{4} )
   • ( x = 4 )

Final Result: ( x = 4 )

Vertical Line

Easy Ways to Remember the BODMAS Rule

1. A Simple Mnemonic: Use the phrase "BODMAS" itself or create a memorable sentence:
   • B rackets
   • O rders (Exponents)
   • D ivision
   • M ultiplication
   • A ddition
   • S ubtraction
2. Example : "Big Old Dogs Make Amazing Sounds." This simple phrase helps you recall the order of operations.
3. Visualize the Process: Imagine the BODMAS steps as a series of "layers," starting with brackets as the innermost layer that gets solved first, then orders, followed by multiplication/division, and finally, addition/subtraction.
4. Use Acronyms or Rhymes: Create an acronym that’s easy to remember. For example, "Please Excuse My Dear Aunt Sally" is a popular mnemonic for PEMDAS, the same rule used in the US (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
5. Practice with Examples: The more you practice solving problems following the BODMAS rule, the easier it will become to recall the order naturally. Regular practice helps reinforce the concept.
6. Focus on the Importance of Order: The BODMAS rule is all about maintaining the right sequence. By focusing on the priority of operations (brackets first, then orders, followed by division/multiplication, and lastly addition/subtraction), you’ll get a sense of how to approach problems methodically.

BODMAS and PEMDAS

BODMAS

• B rackets
• O rders (Exponents or Powers)
• D ivision
• M ultiplication
• A ddition
• S ubtraction

PEMDAS

• P arentheses
• E xponents
• M ultiplication
• D ivision
• A ddition
• S ubtraction

Key Differences Between BODMAS and PEMDAS:

• BODMAS is commonly used in the UK and other parts of the world.
• PEMDAS is more commonly used in the United States.
• Brackets in BODMAS are the same as Parentheses in PEMDAS.
• Orders in BODMAS refers to Exponents in PEMDAS.

How Both Rules Work:

How BODMAS Helps in Everyday Maths

Every time you do shopping or share chocolates, you are using the BODMAS rule full form without even knowing it! If you divide candies and then add some more, the order matters. That's where bodmas in maths become useful. The maths BODMAS rule helps you decide what to do first so you don’t get confused.

Common Mistakes Without Using BODMAS

When you forget the BODMAS rule full form, you may:

• Add before multiplying

• Ignore brackets

These mistakes can give you wrong answers in BODMAS equations. That’s why it's important to ask, "What is BODMAS in maths?" every time you solve something tricky. Join Online Tuition for Kids Now !!