BODMAS Rules: Comprehensive Guide with Definitions, Formula & Examples for Students and Parents

What is the BODMAS rule?

So, you’ve likely heard about the BODMAS rule, right? It’s basically a sequence to solve Maths problems. When we talk about BODMAS, we’re talking about the order of operations. The BODMAS rule is essential in many mathematical problems. The full form of BODMAS is

• B – Brackets, 
• O – Order of powers or roots,
• D – Division, 
• M – Multiplication,
• A – Addition, 
• S – Subtraction.

S – Subtraction. The BODMAS theory solves problems that have multiple operations. So when you see addition, multiplication, subtraction, and division together, you are prepared to find the correct answer following the proper sequence of operations.

When to use BODMAS?

Think of any time you’re faced with a maths problem that has a mix of operations. BODMAS is your roadmap to navigate it. It’s like your maths GPS!

Maths is all about logical interpretations and systematic solving of problems. Hence it requires a specific set of procedures to be observed. It is easy to perform one function, like addition, with two or three numbers. But if a question involves more than one operation, it can be confusing to solve the problem without guidance.

You can utilise the BODMAS formula whenever there is more than one operation in a mathematical equation or expression. We have to follow the set sequence so that the results are correct. We cannot just calculate from left to right or in a haphazard manner. The BODMAS rule in Maths identifies the correct order or sequence to be followed while solving the Maths problem.

DODMAS Rule

If you’re familiar with BODMAS, think of DODMAS as its close relative. DODMAS stands for Division, Order, Division, Multiplication, Addition, and Subtraction. You might be thinking, “Wait, why Division twice?

D	Division ÷, /
O	Order of Square roots, indices, exponents and powers
D	Division  ÷, /
M	Multiplication  ×, *
A	Addition +
S	Subtraction –

BODMAS vs PEMDAS

You might have heard of another term called PEMDAS used to solve mathematical expressions. It is a similar sequence of operations you must follow, just like the BODMAS theory. Let us look into what PEMDAS means:

• P – Parenthesis
• E – Exponents
• M – Multiplication
• D – Division
• A – Addition
• S – Subtraction

So it is nearly the same sequence of operations but with a different name. Why another name? Because some countries have specific terms for the operations. So ‘Brackets’ become Parenthesis, and ‘Of’ becomes Exponents. A critical difference between the BODMAS rule and PEMDAS is that in PEMDAS, multiplication should be done before division, unlike in BODMAS.

Conditions of BODMAS

You cannot understand Maths concepts without examples. And to understand the conditions of the BODMAS rule, we have some BODMAS examples below :

• If there is any bracket, open the bracket first, then add or subtract the terms. 

            x + (y + z) = x + y + z,
            a + (b – c) = a + b – c

• If there is a negative sign, open the bracket first, then multiply the negative sign with each term inside the bracket.

            x – (y + z) ⇒ x – y – z

• When there is a term outside the bracket, multiply it with each of the terms inside the bracket

            a (b + c) = ab + ac

Easy Ways to Remember BODMAS Rules

Specific tips can help you remember the conditions and rules of BODMAS. The meaning of BODMAS and the BODMAS rule questions are a convenient way to remember the rules:

• ALWAYS simplify the brackets first.
• If there are any exponents and roots, solve those.
• Perform division or multiplication (go from left to right)
• Perform addition or subtraction (go from left to right)

Explain BODMAS with examples

After understanding the BODMAS rule, it is time to test the waters and apply the BODMAS formula to Maths questions. But, again, keep the conditions in mind to get the correct answer.

428 – 60 ( 6 x 7 – 12 x 4)
428 – 60 (42 – 48)
428 – 60 – 6

The property of integers suggests – and – becomes +, therefore

428 – 66 = 362
Thus, the answer is 362.

How to deal with brackets?

Brackets mean simplifying terms inside the brackets can be done directly before any other calculation. We must perform the operations inside the bracket in the order of division, multiplication, addition and subtraction.

Note: The order of brackets to be simplified is (), {}, [].

The following BODMAS examples will help you grasp the rule of BODMAS brackets:

BODMAS without Brackets

DODMAS or BODMAS?

Both are paths leading to the same destination. The idea is to understand the hierarchy of operations in maths. Whether you choose DODMAS, BODMAS, or even PEMDAS (for our friends across the pond), the essential thing is the structured approach to crunching those numbers.

The BODMAS Rule: Common Mistakes & How to Avoid Them

We’ve all been in that spot where we confidently solve a problem, only to realise our answer is…well, way off the mark. More often than not, this happens because of simple errors while applying the BODMAS rules. Let’s chat about some of these common mistakes and how to avoid them.

Brackets First, Always: 

One of the classic errors is diving straight into multiplication or division and overlooking the brackets. Remember, those brackets (whether they’re round, curly, or square) take priority. Always resolve what’s inside them first.

Mixing Up the Order: 

After brackets, it’s the orders (powers and square roots). Then, you move to division and multiplication (from left to right), followed by addition and subtraction (again, left to right). Mixing up this sequence? You’ll end up in a mathematical confusion.

Forgetting Left to Right Rule: 

Say you have both multiplication and division in a problem. Don’t just start anywhere. Begin from the left and work your way to the right. The same goes for addition and subtraction.

Overcomplicating: 

Keep it simple. Break down complex problems into smaller parts, tackle them step by step, and you’re less likely to make a mistake.

Not Double-Checking: 

Once you’ve solved the problem, take a moment to go over it. A quick review can catch any errors in the sequence you might have made.

In the end, remember that practice makes perfect. The more you familiarise yourself with the BODMAS rules and recognise where you might be going wrong, the sharper your maths skills will become.

Conclusion

Understanding mathematical rules might seem a bit difficult at first, but with tools like BODMAS and DODMAS, it becomes much more manageable. Whether you’re a student trying to ace your maths test or a parent helping out with homework, these rules are your go-to guides. They offer a clear pathway, ensuring you solve problems in the right order, every time. So, the next time you’re faced with a tricky equation, remember these handy tools. With practice and understanding, maths can indeed become a lot less intimidating.

Mathematics is all about comprehending and handling its concepts. If your child has a strong foundation in Maths, you can rest assured that the child will score well in higher grades. And a good record in Maths will assist your child in college and even afterwards. A successful career can rely on the ability of your child to do well in Maths.