What is BODMAS? – BODMAS, BIDMAS and The Order of Operations Made Easy
If you are a parent of a child in KS2, you may have come across this somewhat-complicated acronym. Most likely, it is your child who has come across it first in class, not understood it, and then come to you for more advice.
This article will help clarify what BODMAS is, how to use it, and where your children may encounter this in their maths learning.
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What is BODMAS?
BODMAS is an acronym used to refer to the order of operation, in which a complex maths sentence (e.g. an equation or an expression) can be correctly solved.
What does BODMAS stand for?
BODMAS stands for Brackets (all calculations within brackets – like these!), Orders (commonly referred to as “indices” or “square roots” – e.g. 42, where ‘2’ is the power), Division, Multiplication, Addition, Subtraction.
What is BIDMAS?
BIDMAS is exactly the same – the only change is the ‘I’ which means the same thing, which in this case means Indices.
The only reason why BODMAS is more appropriate is because the term ‘index’ – or ‘indices’ – doesn’t not contain “square roots” for example.
Another reason why children may hear of BIDMAS, before BODMAS, is because indices are introduced much earlier than squares – for example, 22 for ‘2 squared’, 23 for ‘2 cubed’, or 24 for ‘2 to the power of 4’.
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How you can help your child to remember BODMAS:
The most common way to remember BODMAS is to learn BODMAS as a standalone word, meaning the correct order of operations in a maths sentence.
Once learnt and then spelt out, each of the letters stand for the each of the operations.
Reviewing the order of operations
Brackets come first – anything inside a bracket is calculated separately to the rest of the problem, regardless of the operation.
Orders then follow, so anything with a power of or a square root is solved next.
Division and multiplication follow, so any numbers separated by a or a must be calculated next.
Finally, any addition or subtraction sums must be completed.
This is something that is usually reviewed by Year 6 – along with BODMAS.
A fun fact about BODMAS:
Did you know that while BODMAS dictates the order of operation in a maths sentence, the order can be written like this: (B)(O)(D/M)(A/S)?
This means that as long as you follow the order, it does not matter whether you do multiplication before division, or subtraction before addition.
Just as long as you remember that any division and multiplication come before any addition or subtraction, you will be absolutely fine.
Let’s look at an example:
Consider the equation below. If we follow BODMAS, understanding we can swap multiplication and division, we can go from left to right very smoothly. Where there are no brackets, the next step is to solve orders (which we know are powers), so is 4.
Then we can do the 4 x 4, which equals 16, and then divide by 2 to make 8.
However, in that last example we did multiplication before division. Let us see if we are right if we follow BODMAS – to the letter.
Like before, we start with our which equals 4. Then instead of going from left to right, we check our acronym, and see that D is next, so we focus on which we know is 2.
Now we’re left with 4 x 2 which still equals 8. This shows that swapping the order of division and multiplication, then addition and subtraction will still give you the same answer.
Common mistakes with BODMAS questions and answers
Let us look at some common examples, where mistakes can be easily made but BODMAS can help calculate correctly.
BODMAS Question 1: 5 + 3 x 5 = ?
The right answer would be 20.
Using BODMAS, we know that multiplications must be done first, before adding, so would work out to (3 x 5 = 15) and then adding the remaining 5 to make 20 (5 + 15 = 20).
This is commonly mistaken for 5 + 3 = 15, then 15 x 5 = 75. This is incorrect as it does not follow BODMAS.
BODMAS Question 2: 2 x (5 – 3) + 3² = ?
The right answer is 13.
It will be important to use BODMAS here, as we have quite a few different components.
First, we must use B, which tells us (5-3) = 2.
Next, we must look at O, which tells us 32 is equal to 9.
So far, our equation should look like this: 2 x 2 + 9 = ?
Following on, we must look at D & M. We have a multiplication of 2 x 2, which equals 4.
Finally, we look at A & S. We have a remaining addition, which is 4 + 9 = 13.
The most common mistake for this is working directly left to right: 2 x 5 = 10, then 10 – 3 = 7, then 7 + 32 = 7 + 9 = 16. This would be incorrect.
BODMAS Question 3: 9 – 3 + 9 ÷ 3 = ?
Initially this looks confusing, but the answer works out to be 9, when using BODMAS.
We have no brackets or orders, so we must focus on the division first, which is 9 3 = 3.
Then we have left 9 – 3 + 3. Addition and subtraction can be done in any order, as long as it comes after everything else.
If we do addition first, providing we understand negative numbers at this point, we have – 3 + 3 which cancels out to 0, and leaves us with 9 + 0 = 9.
If we do subtraction first, we have 9 – 3 = 6, which leaves us with 6 + 3 = 9. Both the same!
The common miscalculation for this is 5, when everything is worked out left to right, without the BODMAS rule.
When and how should we prepare for BODMAS questions?
BODMAS comes up towards the end of KS2, along with order of operations and indices. Therefore, getting a good grasp before or within Year 5/6 will keep you in good stead.
When it comes to supporting your child with BODMAS, to help calculations you may use calculators to ensure you have the right answer. However, it is important to remember you dictate how you input numbers into a regular 8-digit calculator, and it will not recognise the BODMAS rule for you. It is best to find one that help you complete the task – or better yet, if it is for home use, you can find online versions.
You may also like to read:
30 Fun Maths Games to Help Kids Learn Maths for Free
The KS2 Long Multiplication Method – The Step by Step Guide for Parents and Kids
