48÷2(9+3) = ?

Dodgy · Post by **Dodgy** » Mon Apr 18, 2011 2:16 pm

2....

kellz5460 · Post by **kellz5460** » Mon Apr 18, 2011 2:44 pm

my calculator says 288

sbtamu · Post by **sbtamu** » Mon Apr 18, 2011 3:36 pm

kellz5460 wrote:my calculator says 288

You need to follow the rules.

48/2(9+3)=

48/2(12)=

48/24=

2

Best 19 · Post by **Best 19** » Mon May 02, 2011 8:26 am

Mine also says 288.

v_aviles · Post by **v_aviles** » Mon May 02, 2011 5:49 pm

It's 288:

48/2 (9+3) = (48/2) * (9+3) = 24 * 12 = 288

Belgarath · Post by **Belgarath** » Mon May 02, 2011 6:06 pm

Depends.

Written as is, this is extremely poor notation because it doesn't differentiate very well between

(48÷2)*(9+3)

versus

48÷(2*(9+3))

Most people who do math mentally rather than with a calculator would see it the second way. That is, they rewrite it in their minds to be more notationally correct:

__48__
2(9+3)

That is how I automatically reinterpret the equation as well, and I majored in math. This results in the answer of 48/(2*12) = 48/24 = 2. Note that this reinterpretation of the equation places the emphasis on the multiplication, where multiplying comes before division.

However, the official PEMDAS rules in the US (I believe it's called BEDMAS in Canada) states that division and multiplication are of equal weight - that is, first come, first served. Therefore, you do not multiply before you divide unless that's the actual order the equation gives. So by following the official PEMDAS rules, the first way is the correct way, and the equation becomes:

48 * (9+3)
2

= 24*(12) = 288

Personally, I would throw this equation back at whoever wrote it and say that it is poorly written and therefore undeserving of an answer until it is corrected. After all, you wouldn't accept a grammatically incorrect sentence riddled with spelling errors from an English teacher, so why accept a poorly written equation from a math instructor? Unless, of course, you're taking a PEMDAS-based test that's doing this on purpose.

sbtamu · Post by **sbtamu** » Mon May 02, 2011 6:47 pm

The equation is a fraction. I do not have a divide key on my keyboard so I'll type it out. The equation is written as a fraction. 48 over 2*(9+3) = 2.

If it were written 48 divided by 2*(9+3) it would be 288.

edit, I could of swore the title read 48/2(9+3) and that would be 2.

But, looking at the title now it reads 48 divided by 2(9+3) so the answer is 288.

Belgarath · Post by **Belgarath** » Mon May 02, 2011 8:04 pm

Right, all division involves fractions, as can be seen in the different ways that division notation can be written:

÷

is synonymous with

/

and with

*(1/x) [where x = the number succeeding the notation in the original equation]

and with

y
x

[where y = the number preceding the notation in the original equation, and x the succeeding]

So

48÷2(9+3)

=

48/2(9+3)

=

48*(1/2)(9+3) = 48*.5*12 = 288

=

48 * (9+3) = 288
2

This is, again, following the PEMDAS rule. If you follow the PEMDAS rule, you can't say that

48÷2(9+3) = 48÷(2(9+3)) = 2

because that's not how it's written. Written as is, PEMDAS rule states

48÷2(9+3) = (48÷2)(9+3) = 288

So it comes down to whether you follow the PEMDAS rules or not. From what I'm told, the Texas Instruments line of calculators, which I believe is still the leading scientific/graphing calculator in the US, used to be non-PEMDAS compliant (so the older models would've given an answer of 2 in this case), but in more recent models have started to use PEMDAS-compliant orders of operating, resulting in an answer of 288 in this example. I don't have the actual TI calculators to verify this for myself, though.

If you're using a non-scientific calculator, don't even bother. Non-scientific calculators don't follow any orders of operation at all and will likely give you the wrong answer in equations with both multiplication/division and addition/subtraction.

hayasidist · Post by **hayasidist** » Tue May 03, 2011 3:12 pm

y'know that "missing" multiply sign in the problem as stated makes a difference for me...

48/2(9+3) ... substitute y for 48 and x for (9+3) you get y/2x

if it had been written 48/2*(9+3) that would be a diferent problem... y/2*x.

y/2x is not the same problem as y/2*x ...

implied parentheses and all that ...

dm · Post by dm » Wed May 04, 2011 8:20 am

Matlab gives me 288 typed in as written. My calculator (hp50g) gives 288 when entered as written.

Why do you want to know?

neilmonee · Post by **neilmonee** » Wed May 04, 2011 3:37 pm

You get an answer of 2 following the order of operations to the T. PEMDAS: Parenthesis Exponents Multiplication Division Addition Subtraction. But once you solve the parenthesis, then you go back to doing the math left to right which would mean dividing 48 by 2 before multiplying you get the correct answer of 288.

hayasidist · Post by **hayasidist** » Wed May 04, 2011 6:46 pm

hi again!

Tom Lehrer's song "New Math" springs to mind here. An aside he made in the live recording I have goes something like "if you're over 30 and went to a public school you [do it this way] if not ..." [that's Public School as in US not UK BTW!]

Anyhoo .. I looked on the web!!

seems to about 50:50 on whether it's 2 or 288...

Here's a "2" URL...

http://answers.yahoo.com/question/index ... 505AA0F9In

Distributive property of multiplication over addition. Early Algebra problem.

The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire statement and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it. You do NOT compute this expression from left to right until you use Algebra to simplify the statement 2(9+3).

So this can be rewritten as:
48 / (2*9 + 2*3)

Which leaves us with

48 / 24 = 2

Answer = 2.

Lastly for those using Google or any other online calculator. These do not understand many theorems or properties so you must explicitly explain what you mean. There is a difference between 48 / 2 * (9+3) and 48 / 2(9+3). The first notation reads 48 / 2 * 1(9+3) while the second reads 48 / (2*9+2*3). ...

BUT... I personally like this one:

http://www.physicsforums.com/showthread.php?t=494675

An issue of mathematical grammar circulating the internet lately has been how to read a mathematical expression like 48/2(9+3) that involves a combination of division and implied multiplication.

The standard way to read arithmetic expression (i.e. order of operations) involves dealing with parentheses first, then you do all division and multiplication operations from left to right, then all addition and subtraction operations from left to right.

So, this expression is computed as
48 / 2(12)
= 24(12)
= 288

...

One thing to keep in mind is that not everybody follows the standard. Some people prefer to do implied multiplication before other multiplication and division operations. Some people prefer to do all multiplications before division with /. Some people even prefer to do addition before division with /.

So, when you are reading math from an unfamiliar source, make sure you know what convention they are adopting. And no matter what convention you prefer, you really ought to write things in an unambiguous fashion -- e.g. you should avoid

48/2(9+3)

and instead use the crystal clear

(48/2)(9+3) [Ed: or 48/(2(9+3)) or ... whatever it was you actually wanted to say]

although personally I still can't imagine anyone really wanting to do y/2x as anything other than y/(2x)... (over 30, public school ??!!

)

but hey - maths doesn't have a monopoly on ambiguous "punctuation"... try these:
"General flies back to front." "Allies push bottles up enemy." "What is this thing called, love?"

for more fun have a read of "Eats, shoots and leaves"