Do you think it’s possible to be too logical for math? Follow this thread below, and see my question and my professors response… It legitimately looks to me like you can’t figure out the order of operations in a word problem unless you know what you’re answer is supposed to look like… does that mean the rules of the order of operation doesn’t necessarily apply without some other external logical application?

 

I think this is why math frustrates me – I probably just over think everything. =(

 

My Original Question:

Content Author: Jed Logiodice

When determining BAC (page 34), the following word problem is given:

BAC = number of oz X % alcohol X 0.075 / body weight in lb – hr of drinking X 0.015.

To simplify the question let w = number of ounces, let x = % of alcohol, let y = body weight and let z = hours of drinking.

When the book gives the BAC equation of being:

w * x * .075 / y – z * .015

This can create an order of operation like this (w * x * .075 / y) – (z * .015) [which results in the answer the book is looking for], however, why could one not equally contrive the following equation out of the above word problem:

(w * x * .075)
___________
y – (z * .015)

The way the word problem is written, it appears equally valid to assume either order of operation – however, unless one assumes the first, the answer will not match what the book states it should.

Is there some rule of order of operations that I’m missing for word problems that says “Never use fractional notation, unless the question is asking for a fraction”?

Thanks!

 

My Professors Response:

(w * x * .075 divided by y) – (z * .015)
Note: I have added parentheses to show that we do ALL multiplication and division from left to right before any addition or subtraction.

w = 4 * 12 = 48 oz

(w * x * .075 divided by y) – (z * .015)
(48 * 3.2 * .075 divided by 190) – (2 * .015)
= (153.6 * .075 divided by 190) – (2 * .015)
= (11.52 divided by 190) – (2 * .015)
= (.060631578) – (2 * .015)

Remember, we do ALL multiplication and division from left to right before any addition or subtraction so our next step is to multiply 2 * .015

= (.060631578) – (2 * .015)
= (.060631578) – (.03)

= .030631578

Rounded to the nearest thousand (3 digits to the left of zero), we have .031 as our answer

 

My Follow up Question:

Author: Jed Logiodice

But when I read the statement I saw this:

(w * x * .075)
____________
y – (z * .015)

instead of this (w * x * 0.75 / y) – (z * 0.15).

i.e. how was one to know that it was intended to be a linear equation (where the rules of operations went across from left to right, instead of above and below the division line separately).

I really thought that (w * x * .075) was the dividend and (y – (z * .015)) was the divisor…

Does that make sense?

I know it might seem like a foolish question; but I literally spent like 20 minutes doing that question over and over and over and never getting the right answer (but always getting the same answer); until I accidentally figured out that it was just a single linear equation, and then I started to ask myself “How was I supposed to know that, other than just assuming, was there some clue I missed”?

My single biggest problem with math is that I way over-think things!

 

My Professors Follow up Response:

One should always assume that we should follow the order of operations unless brackets or parentheses or a fraction bar is in the formula. OK?

 

My Follow up Request:

 

Even in word problems?

Take for example this problem: If you take 6 eggs and divide them among 2 women and 1 man, how many eggs does each person have?

If we always keep the order of operations (without brackets in the sentence) then the answer is (6 / 2) + 1 = 4; 4 Eggs a piece is obviously the wrong answer in this case – although it meets the rule of the order of operations we’re describing.

However, it would seem more logical (and in this case correct) to do 6 / (2 + 1) = 2. This gives the right answer (which we can verify because we know what the value should be), but doesn’t follow our prescribed operational rule.

Taking this discussion back to the case of the BAC – the same logical argument could be applied to the word problem, causing one to interpret the problem with a numerator and a denominator as a fractional statement, rather than just a linear equation – but one wouldn’t necessarily know that the answer was wrong (and what real order of operation was intended), unless one knew what the answer was supposed to be…

So I’m still left wondering – how we can tell in a word problem like the BAC what the real order of operation is supposed to be – without knowing what the answer is supposed to be?

I apologize if this appears as sophistry… I’m legitimately trying to figure out why I had the wrong answer; when from my viewpoint the way I executed the problem was equally as accurate as the way the book did.

Perhaps I’m too logical for math? 🙁