Confusion over the order of operators

[springer5]

Hi

I'm new to the forum and this is my first post, so greetings to everyone here

I'm relearning some basic arithmetic long forgotten since my (far too) distant school days and I've run into a bit of confusion about when to apply the different operators when evaluating an expression.

My book tells me to apply the BODMAS rule when doing this, but when I got to the test at the end of the chapter I was confronted with this....

Evaluate 3 + (5 – (6 * (7 - 4)) + 8)

Here's what I came up with...
3 + (5 –(6*(7-4))+8)
= 3+(5-(6*3)+8)
= 3+(5-18+8)
=3+(5-26)
=3+(-21)
=-24


but my book tells me the answer should have been -2 and reasoned it this way...

3 + (5 –(6*(7-4))+8) ... same
= 3+(5-(6*3)+8) .... same
= 3+(5-18+8) ... same
= 3+(-5) .... different !!
= -2


The difference, as far as I can see, is that on line 3 of the process (5-18+8) the book is subracting 18 from 5 first and then adding the 8 to give -5 whereas I am adding the 18 and 8 together first to get 26, then subracting the 26 from 5 to get -21, hence the difference in the end result.

Who is correct, me or the book? and if it's the book, what happened to the BODMAS rule here and why is the book doing the subtraction before the addition given that BODMAS states...

Brackets
Of
Division
Multiplication
Addition
Subtraction

not Subtraction then Addition as my book appears to have done.

I'd very much appreciate anyone's thoughts on this please as I'm concerned that I may have completely misunderstood how BODMAS should work and it's such a fundamental principle that I need to get it clear for myself.

Thanks for any help.

 

[pka]

My book tells me to apply the BODMAS rule when doing this, but when I got to the test at the end of the chapter I was confronted with this....

Evaluate 3 + (5 – (6 * (7 - 4)) + 8)
Here's what I came up with...
3 + (5 –(6*(7-4))+8)
= 3+(5-(6*3)+8)
= 3+(5-18+8)
=3+(5-26)
=3+(-21)
=-24

I have indicated your error.

\(\displaystyle (5-18+8)=(-13+8)=-5\)

 

[stapel]

Evaluate 3 + (5 – (6 * (7 - 4)) + 8)

Here's what I came up with...
3 + (5 –(6*(7-4))+8)
= 3+(5-(6*3)+8)
= 3+(5-18+8)
=3+(5-26)

How did you get that -18 + 8 equalled -26?

 

[springer5]

I have indicated your error.

\(\displaystyle (5-18+8)=(-13+8)=-5\)

Your answer agress with what the book has done, so 2 people agreeing suggests your both correct and I'm wrong, but (back to my initial question)......

why is the minus operator on the indicated line (i.e. 5-18) being executed before the plus operator which follows it (i.e. 18+8 = 26 THEN 5 minus 26

bodmas states ADDITION BEFORE SUBTRACTON. At least in this book I've got anyway. Hence my confusion. If that's wrong and subtraction should be carried out before addition (as you and the book have indicated then the correct anagram is BODMSA not BODMAS

Which is it?

Thanks

 

[springer5]

Why 5-18+8=-26? Please, pay attention.

Hi

Don't want to start anything here but with great respect I think it is you who haven't paid attention.

What I wrote was....

5-18+8 = 5 -26 as in not the whole expression becomes -26 but the 18+8 part of it does which is later subtracted from the 5.

I'll resist saying the obvious thing to say hear as , like I said,. I really don't want to start anything.

Just needed to clarify your confusion.

thanks

 

[ksdhart]

I may be wrong here, but I believe I understand why you're confused on this issue. For order of operations you have the BODMAS rule. You've, quite naturally, applied these steps in exact order. However, some of the steps have the same priority. Your book should have done a better job explaining this. The actual order is like this:

Brackets
Orders
Multiplication / Division
Addition / Subtraction

And when two steps have the same priority, you work from left to right. So, to use your example problem, you and the book agree up until this step here:

Evaluate 3 + (5 – (6 * (7 - 4)) + 8)
...
=3+(5-18+8)
=3+(5-26)

You reasoned that you should apply addition first, and 18+8 is 26. But as I stated earlier, when faced with multiple steps of the same priority, you simply start at the left and work right. So the correct answer, as the book shows, is:

3+(5-18+8) = 3+(-13+8) = 3+(-5) = -2

Hopefully my explanation makes sense. Sometimes I try to explain concepts but I actually end up confusing people more. If you're still confused, just ask for clarification, and I or another member will help you out.

 

[springer5]

How did you get that -18 + 8 equalled -26?

because it's not minus 18 it's plus 18.

5-18+8. Surely that should be read as Positive 5 minus positive 18 plus positive 8 (there isn't a separate minus between the 18 and the subtraction operator preceding it!).

Strange though that several people have made the same mistake when reading it. Yet looking back at it on my OP now it is exactly as I've said it.

 

[springer5]

That would be correct IF you had 3+(5-(18+8))
Then: 3+(5-26)

Thanks Denis. Yes I realised afterwards that was what the book had done as well and is obviously the correct way. My confusion was why that directly contradicts BODMAS.

In BODMAS the A (addition) precedes the S (subtraction) and yet everyone is giving the subtraction priority over the addition. So I reasoned that either the book (and now everyone here) is wrong, or BODMAS is rubbish.

Given that everyone seems to agree with the book so far it must be that the BODMAS rule is not to be trusted. The subtraction (using my example) is being carried out before the addition so that correct anagram is not BODMAS but BODMSA.

Edit: I have now identified the problem with help from folks here. Which is that my book didn't explain that the multiplication/division operators are equal 'rank' to each other in 'priority', as are the addition/subtraction operators. Now I realise that when a subtraction operator precedes an addition one it is correct to do them in the order written - i.e. subtraction first (not do the addition first regardless, as the lettering of BODMAS woudl suggest if taken literally).

My book had not clarified this and that's where the confusion lay.

Put simply, it was the book's fault for not explaining BODMAS properly.

Thanks for your help.

 

[stapel]

bodmas states ADDITION BEFORE SUBTRACTON.

No, it doesn't, but even if it had, you're still only subtracting the 18, not the 8 which follows the 18:

. . . . .5 - 18 + 8 = 5 + 8 - 18 = 12 - 18 = -6

As for BODMAS (or PEMDAS), just as multiplication and division are at the same "level" and are done from left to right, so also addition and subtraction are at the same "level" and are done from left to right. The priorities are:

. . . . .Brackets (or Parentheses)
. . . . .Orders (or Exponents)
. . . . .Division and Multiplication (or Multiplication and Division)
. . . . .Addition and Subtraction

For further information and examples, try here and here.

 

[stapel]

because it's not minus 18 it's plus 18.

5-18+8. Surely that should be read as Positive 5 minus positive 18 plus positive 8

Okay. Now work just with that expression:

. . . . .-(+18) + (+5) = -18 + 5 = -13

To learn better how to work with subtraction and negatives, try here.

 

[springer5]

I may be wrong here, but I believe I understand why you're confused on this issue. For order of operations you have the BODMAS rule. You've, quite naturally, applied these steps in exact order. However, some of the steps have the same priority. Your book should have done a better job explaining this. The actual order is like this:

Brackets
Orders
Multiplication / Division
Addition / Subtraction

And when two steps have the same priority, you work from left to right. So, to use your example problem, you and the book agree up until this step here:

Evaluate 3 + (5 – (6 * (7 - 4)) + 8)
...
=3+(5-18+8)
=3+(5-26)

You reasoned that you should apply addition first, and 18+8 is 26. But as I stated earlier, when faced with multiple steps of the same priority, you simply start at the left and work right. So the correct answer, as the book shows, is:

3+(5-18+8) = 3+(-13+8) = 3+(-5) = -2

Hopefully my explanation makes sense. Sometimes I try to explain concepts but I actually end up confusing people more. If you're still confused, just ask for clarification, and I or another member will help you out.

This is a very helpful post sir/madam. Thank you . You understood my confusion correctly. That is exactly how I interpreted the rule (as absolute - no 'equals' in the priorities). And you're right again it is something the book hasn't explained at all, which is poor.

All my book says is apply the operators in the BODMAS order (implying literally). Now you've explained about the equality of M/D and A/S parts of the rule, and working from left to right with those operators when they're adjacent, it all makes perfect sense.

Many thanks for helping me!! A lot of head scratching and frustration is finally over

 

[springer5]

No, it doesn't, but even if it had, you're still only subtracting the 18, not the 8 which follows the 18:

. . . . .5 - 18 + 8 = 5 + 8 - 18 = 12 - 18 = -6

As for BODMAS (or PEMDAS), just as multiplication and division are at the same "level" and are done from left to right, so also addition and subtraction are at the same "level" and are done from left to right. The priorities are:

. . . . .Brackets (or Parentheses)
. . . . .Orders (or Exponents)
. . . . .Division and Multiplication (or Multiplication and Division)
. . . . .Addition and Subtraction

For further information and examples, try here and here.

Yes, this is where my book had failed me stapel. It had failed to give me the complete explanation of the BODMAS rule. So I was trying to do the 18 + 8 first (=26), then do the subtraction 5 - 26 (=-21) second. That's why I was getting the wrong answer.

I now realise the book had told me to use BODMAS but it hadn't told me that for addition and subtraction it doesn't mean always do subtracxtion fist, as I did. It means do them in the order written. That's the bit it hadn't told me.

Anyway, thanks for explaining it better than my book has!! Much appreciated