The Murky World of BODMAS!

August 3, 2014 § Leave a comment

Recently a parent asked me about a question they had come across in one of their 11 Plus practice papers. Their child had put E as the answer and his Mum was sure this was correct, but the answer book said it should have been A.

The answer came down to BODMAS (or BIDMAS). It’s one of those awkward little things that no one ever remembers! But, it’s something that rears its head in 11 Plus, SATs and GCSE exams.
BODMAS is basically the order in which we complete a complex sum. It stands for:

Brackets
Orders (or Indices)
Division
Multiplication
Addition
Subtraction

It reminds us that when dealing with a sum, we have to do whatever is in the brackets first, then deal with any indices (e.g. square numbers or cube numbers), then we can do divisions and multiplications, then finally additions and subtractions.

We must be careful, though, because all is not as it seems when it comes to BODMAS!

Although Addition comes before Subtraction, this does not mean that all the additions have to be done before the subtractions. For instance, 6 – 3 + 1 is done from left to right, so the answer is 4. If you were to do the adding first, you would get an answer of 2, but this is not correct. So, really, BODMAS should be read as:

Brackets first
Orders or Indices next
Then any Divisions and Multiplications in order from left to right
Then any Additions and Subtractions in order from left to right

Basically, BODMAS sounds better than BOMDSA! It’s just a reminder to do your multiplications and divisions before moving on to your additions and subtractions.

So, that brings us to the question the parent raised. The question was:

Which of the following gives the same answer as 6 x 2 + 12?
A. 48 – 8 x 3     B. 3 + 11 x 2     C. 3 x 7     D. 24 ÷ 2 – 1     E. 2 + 4 x 4

Using the rules of BODMAS, 6 x 2 + 12 = 12 + 12 = 24
A. 48 – 8 x 3 = 48 – 24 = 24
B. 3 + 11 x 2 = 3 + 22 = 25
C. 3 x 7 = 21
D. 24 ÷ 2 – 1 = 12 – 1 = 11
E. 2 + 4 x 4 = 2 + 16 = 18

And that is why the answer is A, not E!

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