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Mr Barton’s Maths Notes
Number
3. BODMAS / BIDMAS
www.mrbartonmaths.com
3. Bodmas
A question…
What is: 3 + 2 x 4 ?
Now, if you said 20, then I am afraid you are wrong.
If you try the sum on your calculator – and so long as it is not one of those you get free
in a cereal packet – then the answer that should appear on the screen is 11
But why?...
Well, it’s all to do with BODMAS, or BIDMAS depending on which one you prefer.
This is a set of rule which tells you which order you must do operations (like add, divide
etc) in order to get questions like the one above correct.
So, what does it stand for?...
B
Brackets
If there are any brackets in your sum, work out what is
inside them first. And remember: you must use the rules
of Bodmas inside your brackets!
O or I
Order or
Indices
Next up you must look for powers, such as 23 and work
them out
Now it’s time to sort out your divisions. And remember:
D
Divide
M
Multiply
Next comes the multiplications
A
Add
Then add the additions
S
Subtract
And last but not least, the subtractions
divisions can look like this:
÷ or this:
9
4


And so long as you follow these rules carefully, you shouldn’t go wrong!
But let’s go through three examples together…

Example 1 – Quite Nice
20  (3  2)  3
1. The first thing we need
to do is to sort those
brackets out. 3 + 2 = 5, so
we are left with this new
sum:
2. We have no powers and
no divisions, so next up is our
multiplication. 5 x3 = 15,
leaving us with this:
3. And now life is easy!
20  5  3
20 15
5
So, as I hope you can see, all we need to do is break down long, complicated
sums into smaller, more manageable ones. And so long as we take our time, and
write down each step, we should be okay.
But they do get harder…
Example 2 – A Bit Trickier
3  (2  32  3)  5
1. Again, the first thing we need to do is to sort those
brackets out. Let’s concentrate on them and worry
about the rest of the sum later:
2. We must make sure we use the same rules of
Bodmas inside the brackets. So first we must deal with
our power. Remember: 32 is 9, not 6!
3. No divisions, so next up is the multiplication:
4. Which leaves as a nice subtraction, and tells us the
value of our brackets:
5. Now we can return to our original problem, and
thankfully it looks a lot nicer:
6. Keep your brain switched on at this point and
remember to do the division first.
7. And even though you might have to go onto two
hands to count your fingers, you should get the answer
to this one correct
Right, are you ready for this one…
(2  32  3)
(2  9  3)
(18  3)
15
3 15  5
33
6
Example 3 – A Nightmare
10  2  3
10  23
1. Now, you might not think there are any brackets on
this sum… but there are! Whenever the division line
goes right across, it is like there are brackets on the
top and the bottom, because the whole of the top must
be divided by the whole of the bottom:
2. Right, let sort the top bracket out first:
(10  2  3)
(10  23 )
(10  2  3)
(10  6)
3. Usual deal, multiplication first:
4. Which means the top of the division is easy enough
to work out:
16
(10  2 3 )
5. Now we have the bottom to deal with:
6. We have to do the power first, and remember, 23 is
8, it is definitely not 6!
(10  8)
7. Which tells us that the bottom of the division is:
8. Which leaves us with a very nice division to do:
9. Which finally gives us our answer:
16
2
Phew! And if you followed that, you deserve a break!
2
8
Good luck with
your revision!