48÷2(9+3) = ?

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Reply 200

Awesomesauce

BODMAS
brackets: (9+3)=12
Division: 48/2=24
Multiplication last: 24 x 12 = 288

Reply 201

muffingg

According to wolfram alpha it is 288 and since they are also never wrong, the answer has to be 288:

http://www.wolframalpha.com/input/?i=48%C3%B72%289%2B3%29

It is like writing it this way:

24 (9+3)
24 (12)
288

(edited 13 years ago)

Reply 202

arabcnesbit

It depends.

11 pages on this. Jesus.

Guys it's sunny outside.

Get up and get down and get outside.

The misc is strong

Ok let me just make this very clear.

Multiplication and Division have EQUAL precedence
BIDMAS is an oversimplification of operator precedence taught to childeren. In reality, Multiplication and Division are equal, as are Addition and Subtraction.
What this means is that when you encounter a sum with them both, you do it left to right.

In our case:
48/2(9+3)
Brackets first
48/2(12) = 48/2*12
Now we do NOT do multiplication before division here - we do it LEFT TO RIGHT. To make that easier with brackets -
(48/2)*12
Now it's simple
24*12 = 288

There is NO ambiguity. It is blatently clear and there is no debate to be had. If you think the answer is anything other than 288, you are wrong. This is not a matter of opinion.

Reply 205

Good bloke

Original post by ily_em

288! 288! 288!

Cue for the opposition fans to come in with:

Come on you twooos! Come on you twooos!

Reply 206

summer_l

The brackets definitely need to be solved first. That's the rule with order of operations (BEMDAS or BEDMAS - since D and M are interchangeable; source: http://en.wikipedia.org/wiki/Order_of_operations#Mnemonics)

So, this means we can re-write the given equation as 48 ÷ 2 x 12
From here, doing either the division first or the multiplication first are both acceptable, depending on which format of the order of operations you follow. In some formats, multiplication comes before division, in others, multiplication comes after division.

So you could either have: 48 ÷ 24 = 2
or
24 x 12 = 288

Both 2 and 288 are correct, but the "right" answer ultimately depends on which format of the order of operations is used (both are equally acceptable).

Reply 207

neilpatel

wolfram says 288, but I still think it is two, BIDMAS and all that jazz

http://www.wolframalpha.com/input/?i=48%C3%B72%289%2B3%29

Reply 208

HistoryRepeating

Original post by Awesomesauce

BODMAS
brackets: (9+3)=12
Division: 48/2=24
Multiplication last: 24 x 12 = 288

Right answer, wrong reason.

BODMAS is misleading unless you remember it properly.

The rule actually goes
Brackets
then powers Of (or Other)
then Division AND Multiplication (same precedence)
then Addition AND Subtraction (same precedence)

However there is an additional rule, that you parse operators of the same precedence from left to right, so you do do the division first in this case

Reply 209

HistoryRepeating

Original post by Jallenbah

this this oh god this.

Reply 210

HistoryRepeating

Original post by summer_l

The same wikipedia page you linked to tells you you are wrong (look at the last paragraph before Mnemonics section.

With operators of the same precedence (ie / and *), you work left to right, always

Thus the answer is 288. No "depends"

Reply 211

Good bloke

Original post by summer_l

From here, doing either the division first or the multiplication first are both acceptable, depending on which format of the order of operations you follow.

That way ambiguity lies. Mathematics doesn't do ambiguity.

Reply 212

Aeschylus

Original post by arabcnesbit

It depends.

11 pages on this. Jesus.

Guys it's sunny outside.

Get up and get down and get outside.

Speak for yourself it's chucking it down here :frown:

Reply 213

DanielleT192

Original post by HistoryRepeating

Its been explained to you several times what the rules are and how they apply.

Which part do you disagree with - the rule that multiplication and division are of equal precedence, the rule that you deal with equal precedence operators left to right, or that these rules apply to give 288?

Please explain your thinking.

PS: I have a feeling its a wooly "doing the multiplication first just FEELS more normal"

Well I do agree with what you are saying but I'd personally take the unclearly written 48÷2(9+3) to be 48/2(9+3). If it were 288 it would've been (48÷2)(9+3) in separate brackets to show that the both of those are multiplying together but by putting the 2 right in front of the (9+3) shows to me that you work that out first and then do the calculation from left to right as 48÷24 to give you 2.

Again, it's the way the questioner has presented it with.

Your whole argument on the BODMAS palava is still being applied to the way me and others have done it.

(edited 13 years ago)

Reply 214

smiffhead

Original post by Ree69

Yes but 48÷2(9+3) and 48/2 x (9+3) are the same thing. BIDMAS clearly explains that division is before multiplication. Hence 288.

I'm quite worried about the number of people who thought this was 2...

It is two...what you guys are missing out is the fact that multiplications without a multiplication sign (such as ab, or 3y, 2x) should be done first - this is not included in any variant of bodmas.

Reply 215

py0alb

It's worth noting that its largely irrelevant because no-one past GCSE level uses the divide sign. This is the reason we use either:

48
_______

2(9+3)

or

48/2 . (9+3)

depending on which we mean.

Reply 216

HistoryRepeating

Original post by DanielleT192

You are right when you take 48÷2(9+3) to be 48/2(9+3)
These are identical in meaning.

You are wrong on the bold bit. You dont multiply out brackets before applying the left-to-right rule - why would you?

Again you are just basing this on your gut instinct (which is sadly wrong) rather than the actual notation standards.

By the way do you interpret 1/2x as half x or 1/(2x) ?

Reply 217

HistoryRepeating

Original post by smiffhead

It is two...what you guys are missing out is the fact that multiplications without a multiplication sign (such as ab, or 3y, 2x) should be done first - this is not included in any variant of bodmas.

That isn't true. Please cite any source.

Multiplications using a heavy dot, or a dash, get done first. Multiplicands are dealt with normally.

Reply 218

$Avatar for Get me off the £\?%!^@ computer$

Get me off the £\?%!^@ computer

Original post by HistoryRepeating

What on EARTH does the order that various calculators parse symbols have to do with which way is correct.

In any case, if we are playing the calculator game:
The equation gives 2 on a TI-82, but 288 on a TI-83.

Oh look....

The correct order of precedence is left to right for equal priority operators. This is not just "technically" correct but how it is done, correctly, in practice.

as I've said however, normally you would not use the divide symbol, instead using fractional notation, and the vertical position of the elements of the equation would make things clear (vertical position effectively acts like parentheses, similarly to the way the top bar of a route symbol does)

You're funny. :smile:

I'm guessing you didn't read my post properly.

I'm not arguing about rules of precedence. I hope we both understand them very well. I'm talking about conventions adopted by manufacturers of calculators.

Am I allowed to do that?

Reply 219

HistoryRepeating

Original post by py0alb

It's worth noting that its largely irrelevant because no-one past GCSE level uses the divide sign. This is the reason we use either:

48
_______

2(9+3)

or

48/2 . (9+3)

depending on which we mean.