48÷2(9+3) = ???

sponsoredwalk

We're equally valid in interpreting 48÷2(9+3) as any one of:

48÷[2(9+3)] = ...
[48÷2]•(9+3) = ...
4•[8÷[2(9+3)]] = ...
4•[8÷2]•(9+3) = ...
[4•8]÷[2•(9+3)] = ...
[[4•8]÷2]•(9+3) = ...

Yakuza

sponsoredwalk wrote: »

We're equally valid in interpreting 48÷2(9+3) as any one of:

48÷[2(9+3)] = ...
[48÷2]•(9+3) = ...
4•[8÷[2(9+3)]] = ...
4•[8÷2]•(9+3) = ...
[4•8]÷[2•(9+3)] = ...
[[4•8]÷2]•(9+3) = ...

In chaosland, perhaps. According to convention, it is 48 / 2 x (9 + 3).
If everyone chose to interpret such things according to some whim, chaos would ensue.

bnt

Kavrocks wrote: »

Also if I type in exactly what you have in the thread title in to my calculator I get 2.

48/2(9+3) = 2 and 48/2*(9+3) = 288

Can we have make and model, please, so we know what not to buy? We already have three reports in this thread of calculators giving 288: my HP 35 and Casio FX-991ES, and PaulieBoy's TI-89.

I just tried my old Sharp EL-531VH, and that gives 2 if I enter it as written. Never liked that one, anyway, I only bought it in an emergency for an exam ... if anyone wants it, I'll stick it in the post for a Thanks.

seamus

Miss Lockhart wrote: »

Maybe you were taught incorrectly but I wasn't.

It's explained very clearly and correctly in school maths textbooks. Perhaps it was taught poorly to a lot of people but I find it hard to believe it was taught incorrectly by that many teachers.

It came up here before, and it would appear that a large number of people were taught that BOMDAS is an actual description of precedence. It was only last year that I found out it wasn't; 11 years after I got a B1 in higher-level maths.

It's a little like the rounding issue I discovered before. Straw polls I've done suggest that about 50% of people were taught the incorrect way to round decimals.

This thread also confirms that a lot of people were taught that BOMDAS cites actual order.

Maybe it is right in the textbook, but my experience of maths in school was that textbooks were for problems, not for reference. The teacher explained and demonstrated the concepts, you didn't read them from the book.

What surprises me most is that neither of these incorrect methods were ever discovered either by myself or subsequent teachers; presumably they never resulted in any incorrect answers due to the way tests were written.

I know in State exams in particular, they go to great pains to clearly write out equations to avoid any possible ambiguity about what should be multiplied or divided by something else.

MathsManiac

The crux of the debate is whether it is reasonable to say that the following two expressions should be considered identical:

• 48÷2(9+3)
• 48÷2*(9+3)

If these are considered equivalent, and if the most common conventions for order of precedence of operations are followed, then the OP is correct.

However, it is genuinely debatable whether multiplication implied by juxtaposition should be considered to be of higher precedence than multiplication denoted by an explicit symbol. There is significantly less consistency on this point between different sources.

For example, even though most people would agree that 2x is the same as 2*x, it is interesting to note that Wolphramalpha does not consider the following two expressions to be equivalent:

• 2x/2x
• 2*x/2*x

It evaluates the first as 1 and the second as x^2.

So, even though it agrees with the OP on the original question, it recognises that there are circumstances in which multiplication implied by juxtaposition is considered stronger than multiplication denoted by an explicit symbol.

The Casio fx83-GTPLUS, which is probably the most popular school calculator on the market today, would give 2. The manual explicitly states that it considers multiplication where the multiplication sign is omitted to have higher precedence than regular multiplication/division.
Manual here: http://support.casio.com/pdf/004/fx-83_85GT_PLUS_E.pdf

OP, you may disagree with this convention, but it is reasonably widespread. The evidence clearly indicates that this point of disagreement is one that has knowledgeable people on both sides. It is not simply a disagreement with knowledgeable people on one side and ignorant people on the other.

Shakakan

It's an ambiguous / (badly posed) question

like

Have you stopped beating your wife?

It did make me think though:)

citrus burst

I honestly can't see what the confusion is.

If the expression was written as

48/2(a+3)

We'd all have no problem saying its the same as

48/(2a + 6) (I use brackets to show that the 2a and 6 are together)

The convention is anything to the left of the divisor operator is on the numerator (top) and to the right is denominator (bottom).

Computer programs don't understand things like this and give funny answers like 288 instead of 2. This is a limitation of the code that was written by the developers giving certain operators priority over other.

An implied operator has as much priority as an explicit operator

8a == 8 x a == 8(a)

computers however don't really know how to deal with this, it will treat treat each case above differently, giving varying answers depending on how the data is imputed into it.

On a side note, BOMDAS, PEMDAS etc aren't "rules" per se, more like guidelines to follow. For example whats the answer to this simple sum?

10 - 3 + 2

9