Here's another one...

[Vinny]

It appears there is more than one correct answer to this one.



I'll post something about it a little later.

[wawoodman]

Well, as I learned it, do the parentheses first, so that's 10, times 2, that's 20. 20 divided by 20=1.

Of course, I had the same math teacher in junior high that my father had 25 years earlier, so who knows...

[f350ca]

I'll have to go with Mike 1

[awemawson]

Yes BODMAS says 1 :)

[Vinny]

Here's from Quora:

Is the order of operations unclear for expressions like 20/2(5+5)?
I've witnessed confusion among some people with math or math education degrees over expressions like this.

Does the expression evaluate like 10(5 + 5) = 10*10 = 100 (multiplication and division have equal precedence, and are carried out left to right) or 20/2(10) = 20/20 = 1 (remove parenthesis first, as dictated by "p.e.m.d.a.s.")?

Alon Amit, PhD in Mathematics; Mathcircler.
Written Sep 20, 2015 · Upvoted by Ricky Kwok, Ph.D. in Applied Math from UC Davis and Allan Steinhardt, PhD EE, published in various math journals, inventor, hyperbolic Householder
If you have to ask, then the answer is Yes, there's confusion.

It is true that there are various standard systems for interpreting the order of precedence of operators in such expressions, but the mere fact that the question comes up (over, and over, and over, and over, and over again) should strongly suggest to anyone that there's no clear, obvious, universal agreement on this.

This would have been a problem if we were ever forced to write expressions like 20/2(5+5)
, but we're not. There's just no reason to wrestle with the question: Just. Don't. The simple rule is to never, ever, ever mix multiplication and division by juxtaposing them without parentheses. Unsure whether people will be confused? Deconfuse them. Use parentheses, or simplify your expressions so that there's a single division operator at the very end.

ab/c is fine.

a/(bc) is fine.

a/(b/c) is ok, but it simplifies to ac/b so why not use that?

(a/b)/c is ok, but it simplifies to a/(bc).

(a/b)c is kind of ok, but potentially disorienting. Leave the division to the end: use c(a/b) instead.

a/bc is... not to be used, ever. Just... don't. Why on earth would you? Why would anyone? Just to confuse? Just to show off your mastery of precedence rules? Just to spare the parentheses puppies from extinction? Why?

Writing math is communicating. Do your best to communicate clearly and unambiguously.

And from another person:

In my opinion, this expression is very unclear and should never be written this way in the first place.

Written how it is, 20/2(5+5) = 20/2(10). Since multiplication and division really don't have any priority, we evaluate left to right, and the "proper" answer would be 20/2(10) = 10(10) = 100.

But wait. Let's substitute 5+5 with variable x.

Now we have 20/2x. Seeing this form on paper, a majority of people would conclude that the answer would be 10/x = 10/(5+5) = 1. Not even a debate.

Two equivalent ways of writing it; two contrasting answers.

I believe that any teacher who puts this on homework or an exam is just setting up the student to fail. Don't do it.

[schor]

Brackets first then multiplication and division in the order they appear from left to right so to me the answer is 100.

20/2(5+5)
(20/2)*10
10*10
100

[awemawson]

NO! You always evaluate the term inside the bracket first - (That's the B of BODMAS) - then any attached terms to the bracket which imply Multiplication (which is the M of BODMAS)

So 5+5 = 10

2(10) is 2 x 10 so = 20

Then 20 divided by 20 gives you the answer = 1`

[schor]

(04-16-2017, 12:22 PM)awemawson Wrote: NO! You always evaluate the term inside the bracket first - (That's the B of BODMAS) - then any attached terms to the bracket which imply Multiplication (which is the M of BODMAS)

So 5+5 = 10

2(10) is 2 x 10 so = 20

Then 20 divided by 20 gives you the answer = 1`

I am doing brackets first and then multiplication/division in the order they appear. 2(5+5) implies multiplication and the division comes before this multiplication.

[awemawson]

No the rule is applied to each term, so the 2(5+5) has to be evaluated, as does the preceding '20' term before one is divided by the other.

A useful link here:

https://www.skillsyouneed.com/num/bodmas.html

[hermetic]

Vinny makes the point very eloquently, I know the aswer is 1, because I borrowed my maths degree wifes scientific calculator! It is the confusion engendered by the fact that calling Bodmas a "rule" is useless unless you fully understand that you need to be so carefull with the interpretation of it to get the correct answer, even Andrews link tells you that
"Multiplication and division rank equally, so you go from left to right in the sum, doing each operation in the order in which it appears" Going by this rule, you divide next, then multiply, and so end up with 100 which is wrong. Unles it is properly explained that the brackets remain to be dealt with and the 2X is considered to be part of the brackets, and not part of the division, then as vinny says, set up to fail. BODMAS is about as much use as I before E except after C, which applies in every case, except of course where it doesn't! Use a calculator!