Just did a search on this. Apparently the jury is not in on whether implied multiplication comes first or not. It looks as though those who do more computer math say no, but those that do more written math say yes.

Oh well. I guess I'm from a time when all my university mathematics was done by hand. It does indeed seem times have changed.

You'll have to forgive me if I regress when I write a mathematical expression. I will try to use parenthesis, but cannot guarantee I'll always remember.

 

Gee, I've never seen so much trouble over such a simple matter.

Guys, 48/2(9+3) = 288

There is no such thing as PDMAS or whatever you call it, this is the simplest of operations, ALL calculators --and ALL brains-- will solve 288.

I would be really wary of any calculator giving any other result.

The matter is not "what goes first", "what goes next", or what the order of operation is, there isn't even ambiguity in this problem.

About #Post 12

In the picture, it should say "YOUR CALCULATOR IS RIGHT!", because all calculators solve 288.

AND YES: THE ANSWER IS 9 > ALWAYS! ALWAYS!

 

You were taught your way, we were taught ours. Ours is older, I learned math long before there were electronic calculators, so I will agree to disagree.

 

I am beginning to come around on this. In fact I have...


\(48/2(9+3)\)

just looked too much like

\(48+2(9+3)\)

so I had a brain fart and thought about it the wrong way. It happens to old people...

I realized that if I did want to distribute anything on the left though the parenthesis I have to do it like this:

\(48/2(9+3) \ = \ \frac{48}{2} \times 9 \ + \ \frac{48}{2} \times 3 \ = \ 24 \times 9 \ + \ 24 \times 3 \ = \ 216 + 72 \ = \ 288\)

So, the answer, by the long and troubled route, is 288.

I apologize for my previous argument

 

About #Post 12

In the picture, it should say "YOUR CALCULATOR IS RIGHT!", because all calculators solve 288.

Actually, not all. See the picture at the top of the thread, and there are stories on the web of other calculators basically making the same mistake as me.

I still follow that implied multiplication comes first, but just not in this case.

 

WOW, sure was easy to stir this up...

I think theres no set rules, other than you just avoid questionable situations, and that way you don't have to actually bother with getting around to making the rules, because people are lazy.

 

Do you not do functions of variables anymore?

Back in ancient times things like this could be written:

y = 3/2x + c

Wherein everyone in the class would see that 1st term as ‘3 over 2x’

When I took calculus, we would read that as (3/2) x, so 1.5 times x (+c)

 

Gee, I've never seen so much trouble over such a simple matter.

Guys, 48/2(9+3) = 288

There is no such thing as PDMAS or whatever you call it, this is the simplest of operations, ALL calculators --and ALL brains-- will solve 288.

I would be really wary of any calculator giving any other result.

The matter is not "what goes first", "what goes next", or what the order of operation is, there isn't even ambiguity in this problem.

Yes, the answer is 288.
There IS a such thing as PEMDAS. It came long before calculators, and it is the rule that they follow to do this sort of problem.

 

This is a cool thread, and it's amusing the calculator gets it wrong!

My (limited) math skills come from the computer programmer side of the fence, as one of the poor fools that has to make the computer come up with the right answer at the end of the process.

Multiply and divide must be equally weighted, it's very silly to try to handle them in different precedence unless there is a specific gain or loss (like in integer rounding).

So to me; a * b / c must always give the same result as b / c *a and there is no precedence.

And to prove a point *0.5 and /2 are exactly the same process to be carried out so neither * or / can have a precedence.

I think the only valid rules should be;
1. Mult/Div are equal and done before Add/Sub (which are also equal)
2. Precedence should be forced by parentheses! Hopefully always.

So the original problem can only be handled as;
48 / 2 * 12 = 288

Note that in a computer there can never be a "2X". There is either;
1. a single variable X which is first multiplied by 2, it must therefore be; (2*X) in a process.
2. a temporary variable used in calcs, it must therefore be; A = 2 * X and then A is used in future processes.

So that whole confusion of 2X, (2X), 2*X etc that might apply in pen math doesn't exist.

Also I feel that the * symbol should be used. There is no need for two ways to write the same process; AB or A*B, it's redundant and old fashioned. * and / are the correct symbols and I use them, but then I'm very heavy handed with parentheses too.

 

One thing I'd like to point out, and it's not in my defense as I have changed my position, but this, this....thing, is horribly written.

48/2(9+3) is a complete botch-up and no one in their right mind would ever write it that way or enter it into a calculator that way either. Ever!

Entering it into a calculator (9+3)*48/2 (order is not important, but you must have the explicit operators) is the correct way to do it. Then every calculator will get it right.

Writing it:

\(\frac{48}{2} (9 + 3)\)

Would be preferred.


Edit: Noticed this looked like I was angry, but I'm not. I'm actually having fun with this. Forgot to dd the happy faces so...

 

Is this mix up due to "new math"?

 

BODMAS...BODMAS...BODMAS...BODMAS...BODMAS...BODMAS...BODMAS...BODMAS...BODMAS...BODMAS...BODMAS...

There is....I was taught this pattern when I was in 8th grade.

Calculator gives me a 2, let see how my math is.

 

Ha !! I got 2

BODMAS ...Rules !!!

 

OK..This is funny...

I can get 2, 144 and 288...from all of the above methods...
What Gives????

 

Ok. I'm gonna stir this up.

I'm gonna give my reasoning, and explain why "PDMAS" or whatever method you talk about does not matter and comes not into play here.

In Algebra, there are only two operations:

Multiplication & Addition

1. DIVISION is multiplication by the reciprocal.

What you see here: 48/2(9+3) are 3 factors.

2. and the Commutative Rule says: "The order of factors does not matter"

Therefore:

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

Pay attention that /2 = 2^-1 (because it's the reciprocal)

There is NO method called PDMAS that applies here, not at all.

How can you multiply 3 factors (abc) and get two different answers? IMPOSSIBLE.

 

Umm!..WRONG...

 

Yes, the definition of algebra through the axioms of the * and + operators will serve us more in this level.

I feel that BODMAS or whatever acronym has value only to elementary school students. Unfortunately, this is the age that memories stay imprinted for life.

I too would like to rewrite the expression as:
\(48 \cdot 2^{-1} \cdot (9 + 3)\)

This leaves no ambiguity.

 

Umm!..WRONG...

Some have said "Before there were calculators..."

Nope, before there were calculators there was "MULTIPLICATION" and "ADDITION" alone too.

This comes from WAAY back.

 

So who is correct ?

 

What you see here: 48/2(9+3) are 3 factors.

What you seem to be completely ignoring is that what you see here is an implied multiplication between the 2 and the (9+3) term. They are adjacent and should not be. This is what is confusing everyone.

This is badly, horribly, incorrectly, 'you get a zero for doing such mind bogglingly dumb thing'ly written. It should never, ever, ever, ever, ever, be written like this. EVER!

The multiplication is supposed to be with the numerator, not the denominator, so just show it that way and have done with it.

(9+3)*48/2 is correct 48/2(9+3) is outright, stupidly and absolutely ignorantly bogus. Plain and (p)ucking simple!