But it's still that first bracket that I stuffed up ... I used the BODMAS rule within that bracket and got 10 but to get the right answer you DON'T use the rule .. you just work left to right.

I wrote it different to the paper and put the words to half and a quarter to get away from putting the / sign which I had used before to mean divide.

In the book it is

(23-4+9)x(1/2 - 1/4) of 24 =

TO my way of thinking if he got the problem

23-4+9=

the answer would be 10 using BODMAS

but as it's within that bracket the answer is 28.

I don't understand how you got 10 from 23-4+9?

How does 23-4+9 not equal 28?

I read it as 23-4= 19, 19+9=28, or if you like 23+9=32, 32-4=28, or even -4+9=5, 23+5=28.

Can you please explain how you got 10?

And with PEMDAS/BODMAS, as a general rule everything in the parentheses is done first. So you would compute both 23-4+9 and 1/2-1/4, before multiplying the two results together. Then once you're in the parentheses, you do all of the exponents first, then multiplication/division, then addition/subtraction. Then you'd do the second or third (or however many parenthetical phrases there are) before you do the operations between the parenthetical phrases. Make sense?

So for example:

(2^2 * 4 - 2) * (2 - 2^3) = ?

Starting with the first ( ), you do E first, so 2^2 = 4. Then M/D, 4 * 4 = 16. Then A/S, 16 - 2 = 14.

Then with the second ( )...starting with E, 2^3 = 8. Then 2 - 8 = -6.

Then you do the ( ) * ( ), so 14 * -6 = -84.

So the overall order used in this case is P1, E1, M1, S1, P2, E2, S2, M(overall), where 1 and 2 refer to the 1st and second set of ( ).

In the special case where you'd have a term that is ( )^x, you would do everything inside the parentheses first as seen above, since P comes before E, and then you would apply the ^x to your final result from inside the ( ).