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What is BODMAS in Math and How Is It Applied?

Wondering what is BODMAS in math? In the world of arithmetic, it’s a mnemonic your child can use to learn the correct order of operations in a mathematical expression. As they follow BODMAS, they can navigate through addition, subtraction, multiplication, and division more easily and find the correct answer every time. In this article, I’ll break down this important rule and show how it’s applied in practice.

Key points

• The BODMAS rule is a method that guides orders of operations and helps to solve mathematical expressions consistently. 
• BODMAS stands for brackets, orders, division, multiplication, addition, and subtraction, and establishes a clear hierarchy of steps to be taken in each expression.
• BODMAS and PEMDAS are two different acronyms with the same mathematical logic behind and the same sequence of steps students need to take.
• Brighterly offers structured and engaging lessons with experienced math tutors, who will help your child make order of operations intuitive and fun.

What is BODMAS?

Think of BODMAS as a helpful acronym that tells you exactly which order to follow when you are solving math problems with multiple operations. BODMAS stands for Brackets, Order of Powers or Roots, Division, Multiplication, Addition, and Subtraction. The rule makes sure that everyone solves expressions in the same order.

What do Americans use instead of BODMAS?

While the BODMAS math rule is quite well-known, in the United States, another acronym is typically used –– PEMDAS. Even though the BODMAS rule vs PEMDAS rule have different names, both acronyms follow the same mathematical logic to help your child arrive at the correct answer. In reality, the primary difference between BODMAS and PEMDAS is simply the regional terminology. For example, where BODMAS refers to Brackets, in the US, they are referred to as Parentheses. Instead of Orders in BODMAS, you have the Exponents in the US to describe a power or square roots. Despite the slight change in letters, you need to remember that the order of operations remains identical across both systems, as they are simply representing the existing math rules and not creating different rules. I’ll go deeper into the logic of the operations and their sequence shortly.

What is BODMAS rule? 

I like to think of it as a mathematical compass, which gives a standardized guideline for solving math expressions that contain multiple operations. You can also think of it as the grammar of math. Just as the order of the words and the punctuation you use helps to understand the meaning of a sentence, the order of operations helps to interpret the value of mathematical problems. This is a good way to think about it, as what is the BODMAS rule is one of the most common BODMAS-related questions.

The reason it is necessary is that without BODMAS math, our world would turn into chaos. Imagine a situation where two people look at the same string of numbers and operations, but arrive at completely different answers, because one thought to add the numbers on the left, and the other started to multiply on the right. Without a rule, how do you calculate which answer is correct? This would lead to total confusion in engineering, science, finance, and so many other aspects of life. So, the primary objective of the BODMAS order of operations is to dictate which part of the expression your child must tackle first get answers that are accurate and consistent.

What is the logic behind BODMAS?

BODMAS rule in math acts like a universal “grammar” for arithmetic, in that it establishes a clear hierarchy of operations based on their mathematical power or complexity. For example, multiplication is essentially repeated addition, and exponents are repeated multiplication. So, to maintain the logical integrity of the expression, when solving it, we prioritize them. 

One of the biggest necessities in mathematics is eliminating ambiguities as much as possible. And the logic behind the BODMAS method is rooted in this necessity, so that every person solving the same problem arrives at the same correct answer. Without a standardized rule, even simple math questions that contain more than one operation could be interpreted in multiple ways, leading to inconsistent and wrong results. 

Are there any cases when BODMAS rule is not applicable?

The BODMAS rule is always applicable for standard arithmetic. Sometimes it may not apply in non-standard systems where operations are evaluated strictly from left to right, or when an expression lacks clear mathematical operators. These points of contention happen much later, during higher mathematics classes.

The BODMAS rule explanation step by step

• First are (B)rackets. Your child needs to learn to always look for brackets (or parentheses) first and solve the arithmetic inside them before anything else. The logic behind this is that it helps them to group specific parts of the equation that need to be treated as a single unit.
• Next up are (O)rders. If the expression at hand has exponents, square roots, or numbers raised to a power, students need to calculate them next.
• Third comes multiplication (*) and division (/), and your child needs to work through them left to right. This is a critical step, and one of the more common BODMAS questions. Multiplication and division actually have equal priority. Your child doesn’t need to divide before they multiply or vice versa. Instead, they need to evaluate these operations as they appear from the left side to the right side.
• Last come the addition (+) and subtraction (-), again from left to right as they share the same rink. Throughout solving the expression, your child needs to leave the addition and subtraction (except when in brackets) to the final step. 

This is standardized order of operations, one which mathematicians, students, teachers, each calculator, and anyone doing any calculation use to solve problems with precision and stay in sync with each other. We will look at some examples in detail later in the article.

What is the most common BODMAS mistake?

The most common BODMAS mistake, or one of the most common mistakes, is when students assume that division has more power than multiplication, or that addition has more power than subtraction. These two pairs are equal, and which one is more powerful in each expression depends on the left-to-right order. 

How to explain BODMAS to kids?

If you are just introducing your child to order of operations, explaining to them what does BODMAS stand for can feel like a big task. The good news is, it doesn’t have to be! The key is to make the concept relatable and less intimidating. 

I usually like to start with a small analogy comparing the BODMAS meaning as the traffic rules of math. On the roads, without traffic rules, everyone would go in different directions and cause a crash. It’s also true in math, but in this case, it would be a clash of different answers. To avoid this, your child needs to understand why the sequence of actions matters in the final result, and you need to demonstrate that to them as simply as possible, and use this simple language throughout the entire learning process.

Start explaining the BODMAS rule from the brackets. Clarify that the numbers inside the brackets are a special group, so they need to be treated as one entity. Next up, move to orders, using simple examples like 2^2. Then move to divisions and multiplications, leaving the addition and subtraction at the end. Make sure they understand the left-to-right process. Make sure that they know which step follows which, and are comfortable with solving exercises. Throughout the learning process, you can use these free order of operations worksheets for some well-structured exercises that will strengthen their grasp of order of operations. 

For young learners, visual aids are a powerful tool that you can use. You could, for example, draw a BODMAS Ladder, where brackets are at the top, followed by orders, and so on until addition and subtraction at the bottom. Show them that the process of solving a math expression by following BODMAS math rules is similar to climbing down that ladder, and they need to complete each step without skipping. You can also do mini-challenges using the problems in the worksheets, starting with simpler expressions with 1-2 operations, and gradually increasing complexity.

If, after some explanations and practice, your child is still struggling with the logic of the BODMAS rules, or simply wants additional practice or professional help, the Brighterly math and reading platform is a great solution. The platform works with highly vetted math tutors and offers one-on-one classes to children, during which the friendly and experienced teacher will make learning BODMAS engaging, fun, and, most importantly, make it make sense. Instead of repetitive drills, your child will get to have interactive lessons with visuals and games that will make order of operations intuitive. 

And if you are looking for some assisting resources to supplement your explanations, on Brighterly, you can find many free order of operations PEMDAS practice worksheets and other valuable resources. The worksheets come for various skill levels, and can be a great supplementary material as your child is grasping the “why” and “how” of BODMAS. 

BODMAS examples

Now, let’s look at some BODMAS rule examples to see how BODMAS works in action. We’ll walk together through some simple and more complex examples to see how you can apply the rule in different scenarios.

Example 1: Let’s solve the expression 10 + 5×2 to find the value.

Solution: As you can see, we don’t have brackets and orders in the expression. Next up in BODMAS come Division and Multiplication. We do have multiplication, so let’s do it:

5 x 2 = 10

Our expression now looks like 10 + 10, so we simply need to add the two tens together, like so:

10 + 10 = 20

The final answer is 20.

Example 2: What is the final answer of the 24 ÷ 4 – 2 expression?

Solution: This expression is straightforward in the sense that the steps left to right coincide with the rules of BODMAS. Since we don’t have brackets and orders, next comes the division, which is also the first operation in our problem. 

24 ÷ 4 = 6

Now, we simply subtract 2, and get the answer:

6 – 2 = 4

The answer is 4. 

Example 3: Let’s now solve the more complex 3 + (6×2^2) ÷ 4 expression.

Solution: Here, we have brackets, so we look into them first. In the brackets, there is a multiplication and an order. Since, according to BODMAS order of operations, orders come before multiplication, the solution of this bit will look like this:

(6×2^2) = (6 x 4) = 24

The next step is the division of 24 by 4, as division comes before addition:

24 ÷ 4 = 6

Lastly, we add 3 and 6:

 3 + 6 = 9

The answer is 9.

Example 4: What is the answer of 15 – [2 x (3 + 1)]?

Solution: In this example, we have nested brackets. Don’t worry, they are simple! You simply need to work outwards, starting with the innermost brackets. In this case, it’s the:

(3 + 1) = 4

Next, you solve the expression in the square brackets:

[2 x 4] = 8

Lastly, you subtract:

15 – 8 = 7

The final answer is 7. 

It’s not hard, is it? With enough practice, which you can also find in free PEMDAS            Worksheets, your child will get the grasp of how to approach these exercises quite quickly.

BODMAS vs PEMDAS: What’s the difference?

What’s the difference between PEMDAS and BODMAS? This is one of the most common BODMAS questions. As mentioned earlier, the difference is mainly that of terminology. While BODMAS is used in the UK and Australia, PEMDAS is most common in the United States. The letters differ because of the regional names for specific operations. For example, Americans use Parentheses instead of Brackets and “Exponents” instead of “Orders”. Same for Exponents vs. Orders. However, they both follow the same logic and the same steps, and lead to the same answer.

Despite this, it’s important that your child remembers that there is no difference in mathematical logic in PEMDAS rule vs BODMAS, otherwise they might get confused. Whether they follow BODMAS or PEMDAS, the rule is that first come brackets, then orders, then multiplication and division (performed from left to right), and lastly addition and subtraction (again, left to right).

Where do we use BODMAS in real life?

Wherever you need to solve multi-step arithmetic problems in your life, you will use BODMAS. An example you’ve probably come across is calculating the cost of groceries when dealing with discounts. The examples are too many to count, from complex finance to basic daily calculations.

What’s a trick to remember BODMAS?

To help your child remember BODMAS better, you can introduce a creative twist into it, which will help the name stick. Here are a couple of mnemonic devices you can use:

• Bears Often Drink Milk At Sunrise
• Big Orange Dogs Make Awesome Sandwiches

You can, of course, come up with your own versions, and even let your kid invent them.

Conclusion

The importance of learning and remembering BODMAS (the same as PEMDAS) in arithmetic is hard to overestimate. It’s a fundamental skill that lies in the foundation of math, and guides the logical processes your child will go through as they solve each expression. With BODMAS, they will have the right tool to find the correct answer every time. 

If you are looking for experienced tutors to help your kid understand BODMAS, you can book free lesson on Brighterly for your child and see how the classes take place.