Solve 48

[leedogg]

Brackets first :p I can't believe this thread is still going on, especially after the first reply got it right.

Let's see what we have:

48:2*(9+3)

We do brackets first

48:2*(12)

no need for brackets anymore

48:2*12

once each of the operations are of the same level (and multiplication and division are the same level operations), you just do it left to right

48:2*12 = 24*12 = 288

/thread

Everybody agrees that Parentheses must be done first so therefore this part of the expression must be done first

2(9+3)

Since the distributive law of multiplication states that

a(b+c) = (ab+ac) you must factor the 2 INTO the equation within the paretheses, it is a part of it, you can not do it later.

It also states that Division can NOT be distributed, so you must solve the parentheses expression BEFORE dividing it into 48.

http://www.mathsisfun.com/associative-commutative-distributive.html

[+theblazingangel MVC]

I originally got an answer of 288, and so did my casio fx-85es, however I to am now leaning towards 2

48 / 2(9 + 3) makes much more sense as a simplification/shorthand of 48 / (2 * (9 + 3)) than 48 / 2 * (9 + 3)

A simple and perhaps silly example why, which supports the post above:

if in 48 / 2a or 48 / 2(a) (same thing) a is a group of 4 people, 48 is the number of apples we have to divide between them, and we wish to know how many to give each person,

as 48 / 2 * a = 24 * 4 = 96 = wrong

as 48 / (2 * a) = 48 / 8 = 6 = correct

obviously dividing the number of apples first by 2 and then multiplying doesn't make sense!

In the same way, if in 48 / 2(a + b), a is 6 pupils and b is 2 teachers (and based on giving teachers and pupils the same),

as 48 / 2 * (a + b) = 24 * (a + b), and substituting values = 24 * 8 = 144 = wrong

as 48 / (2 * (a + b)) and therefore expanded as 48 / (2a + 2b) or 48 / ((2 * a) + (2 * b)), substituting values = 48 / (12 + 4) = 48 / 16 = 3 = correct

[Rigby]

It's just a very poorly written equation.

[Zain Adeel]

guys im really bad at maths.. but i studied that dont we multiple the numbers in the brackets with the one outside .. both of them. and then add.

like this

48/2(9+3)

48/(2x9+2x3)

48/(18+6)

48/24

2 :s

[XerXis]

Everybody agrees that Parentheses must be done first so therefore this part of the expression must be done first

2(9+3)

Since the distributive law of multiplication states that

a(b+c) = (ab+ac) you must factor the 2 INTO the equation within the paretheses, it is a part of it, you can not do it later.

It also states that Division can NOT be distributed, so you must solve the parentheses expression BEFORE dividing it into 48.

http://www.mathsisfun.com/associative-commutative-distributive.html

yes, but as there are no parentheses around the 2(9+3) you must use the left to right rule:

(48/2 * 9 + 48/2*3) or if you do the parentheses first 48/2 * 12

To avoid confusion like this parentheses must be used.

[leedogg]

yes, but as there are no parentheses around the 2(9+3) you must use the left to right rule:

(48/2 * 9 + 48/2*3) or if you do the parentheses first 48/2 * 12

To avoid confusion like this parentheses must be used.

The equation is poorly written and relies on our implied interpretation of the expression. The fundamental implication in question is whether 2(9+3) implies (2(9+3)) or not. I believe that by juxtaposition it does:

Mathematical Reviews Database - Guide for Reviewers

http://www.ams.org/authors/guide-reviewers.html

that "multiplication indicated by juxtaposition is carried out before

division." Thus, in general, for any variables a, b and c, we would

have a/bc = a/(bc) (assuming, of course, that b and c are nonzero).

Indeed, this convention is consistent with what I have seen in many

mathematical books at various levels; for example, on p. 84 of

Allendoerfer and Oakley, _Principles of Mathematics_, 1969 (my

pre-college math book), we find:

(a / b) x (c / d) = a c / b d

which is generally true only if the right side is interpreted as:

(a c) / (b d)

http://mathforum.org/library/drmath/view/57021.html

[nub]

If you follow the proper order of operations the answer is 288. /thread

[cooky560 Veteran]

Dim intt

intt = 48 / 2 * (9 + 3)

MsgBox intt

returns 288

[abecedarian paradoxious]

x?2(y+z) = x?(2y+2z)

thus, where x=41; y=9; z=2:

48?2(9+3) = 48?(2(9)+2(3)) = 48?(18+6) = 48?24 = 2

[cooky560 Veteran]

Well I just tapped the above code into vb6 and it came out with 288 :s

[JonathanVP]

It is? I don't recall having a detailed discussion on the presidence of distributive multiplication versus standard multiplication in my 5th grade class. Also those who take the grade school PEMDAS a bit too literally can find themselves in trouble.

If I ever saw an equation written in the format of this one on an exam, I would ask the professor for clarification as to whether (9+3) were in the numerator or the denominator. Unless it was an intentional tricky question on a somewhat obscure presidence rule that seems pretty reasonable to me.

I also would not be surprised to see marks taken off of my work if I were to answer with an equation in this format, rather than in a much clearer fraction form.

It is because this is what my son is studing right now in 5th grade math. He laughed at this and did this and the answer is: 288 and not 2.

[Hardcore Til I Die]

The equation is poorly written and relies on our implied interpretation of the expression. The fundamental implication in question is whether 2(9+3) implies (2(9+3)) or not. I believe that by juxtaposition it does:

http://mathforum.org/library/drmath/view/57021.html

If you go with basic math (the BODMAS rule) then the equation would be treated like this:

48 / 2 * (9 + 3)

I think everyone is overthinking it.

2(9 + 3) should not be treated as (2(9 + 3)) because the second set of () were not specified.

[Prince Charming]

288.

Why is this a discussion, there's only one possible answer. Anything else is just wrong.

[Detection]

What does a sum with (xxx) another sum after it mean ?

[Hardcore Til I Die]

For everyone's info, Google Calc gets '2' when a second set of parenthesis is used to control the order of evaluation:

48 / (2(9 + 3))

= 2

48 / 2(9 + 3)

= 288

Both of which are correct answers :)

[nub]

This thread makes me sad.

[deactivated_]

This thread makes me sad.

+1

[hondaa]

I originally got an answer of 288, and so did my casio fx-85es, however I to am now leaning towards 2

You think you are smarter, better and can compute faster than your Casio FX-85es?

:laugh:

Someone please close the thread.

[cooky560 Veteran]

My computer says 288, my Casio FX-83 says 2

[webeagle12]

This thread makes me sad.

:laugh: :laugh: :laugh:

[micro]

288

[Poom]

http://en.wikipedia.org/wiki/Order_of_operations

As mentioned before, 4-7+3 should be viewed as 4+(-7)+3=0. This is because subtraction is just adding the additive inverse.

Likewise, 48?2(9+3) should be viewed as 48*(1/2)*(9+3)=288, because division is multiplying by multiplicative inverse. When in doubt, turn "?y" to "*(1/y)" just like "-y" to "+(-y)". Then, it becomes unambiguous because multiplication is associative and commutative. This is why some math teachers say "division before multiplication" in BEDMAS etc. That really isn't accurate though. Division takes the same precedence as multiplication, but you just need the perspective that division means multiplying by multiplicative inverse. I'm pretty sure all TI calculators will agree on this.

[webeagle12]

...

[WickedScribbler]

Due to the way the problem is stated, my Pickett 1010-t slide rule, my TI-36x (solar power) calculator, and my Mk-1 brain (not to mention the years of explosive calcs asked by the U.S. Army COE),e all get the answer of 288. I can see where the answer of 2 might come up, but according to what I was taught in Algebra (way back when), the answer is 288. (and Mrs. Foster would have been ready to whack ANYONE who said 2).

[Hardcore Til I Die]

...

:laugh: :laugh: :laugh: